Quantum computing

Abstract

The quantum computing system includes a plurality of photon cavities; a plurality of coupling locations for quantum emitter positioning, each coupling location associated with a different photon cavity of the plurality of photon cavities, the quantum emitter associated with each coupling location configured to mediate interactions between successive incoming optical quantum bits to generate a graph state; a photon generator configured to provide photons to the plurality of photon cavities, the photon cavities configured to couple the optical quantum bits to the quantum emitters; and a plurality of photon output channels downstream of the plurality of cavities that output the graph state.

Description

[Technical Field]

[0001] Related applications This application claims priority based on U.S. Provisional Application No. 63 / 320,454 filed on 16 March 2022 and Israeli Patent Application No. 282705 filed on 27 April 2021, both of which are incorporated herein by reference in their entirety.

[0002] This disclosure generally relates to quantum computing using cavity quantum electrodynamics (cavity QED), as well as related apparatus, systems, computer-readable media, and methods. Some embodiments involve the generation of photon graph states. [Background technology]

[0003] Building a commercially useful quantum computer (QC) can be difficult for many reasons, such as scalability issues arising from increased complexity, noise, and crosstalk as more qubits are added. Furthermore, quantum computing algorithms can leverage entangled states, and some quantum computing architectures can use a source of entangled states (also referred to as a resource state generator) to obtain such entangled states. This disclosure relates to a mechanism for such a source of entangled states or a mechanism used in connection with such a source. Currently, quantum computing remains limited to proof-of-concept stages using a relatively small number of qubits sufficient to demonstrate that quantum computing is feasible in principle. To make quantum computing practical for handling real-world problems, current devices include 10 qubits, including qubits for error correction. 6 It needs to be scaled up to handle a large number of qubits exceeding a certain limit.

[0004] Quantum bits for quantum computing are often composed of one of three physical platforms (or domains): a superconductor (superconducting state), an atom (ionic state), and a photon (photon state).

[0005] Optical platforms offer numerous highly practical advantages over other platforms. Photons are relatively easy to generate, do not require cryogenic or ultra-high vacuum environments, and the construction of miniaturized, reliable optical devices and their communication infrastructure can be achieved using readily available manufacturing techniques. Therefore, optical platforms are currently the leading candidates to achieve the high levels of scaling required for practical quantum computing devices.

[0006] However, the full potential of optical platforms is not currently realized, primarily because generating entangled photon states for use as entanglement resources in optical quantum computing is currently highly inefficient. Conventional mechanisms rely on the nonlinear effects of crystals to generate single photons. Linear optical elements are used to probabilistically entangle these photons to generate photon graph states. For this purpose, the generated photons must be indistinguishable and produced in accordance with identically shaped pulses at perfect timing. Unfortunately, this requirement comes at the expense of generation efficiency. Furthermore, to obtain a photon graph state of a specific number of qubits, the probabilistic entanglement process requires a much larger number of initial single photons, and therefore a much larger number of elements. These points regarding inefficiency accumulate and significantly limit efforts to scale optical platforms to a meaningful number of qubits.

[0007] Therefore, it is highly desirable to have apparatus and methods for generating photon graph states that reduce or eliminate probabilistic processes and the inefficiencies inherent in such probabilistic processes, and instead deterministically generate photon graph states with maximum or improved efficiency for use as qubits. This objective is satisfied or facilitated by embodiments of the present disclosure. [Overview of the project]

[0008] The source of entangled states used in a quantum computing architecture can use a matter-based mechanism or an optical-based mechanism. Matter-based quantum computing mechanisms, such as those using trapped ions, superconducting qubits, or quantum dots, may be considered to achieve entangled states more efficiently than optical-based ones. Optical-based quantum computing mechanisms, such as silicon photonics, are considered to be more scalable and modular. Therefore, the optical-based mechanism may be useful for addressing the scalability issue described above.

[0009] Using embodiments consistent with the present disclosure, the source of entangled states used in quantum computing using a large number of qubits can be possible, for example, with respect to optical quantum computing. The architecture can also provide a scalable architecture that can be fabricated in a standard silicon manufacturing laboratory. The cavity quantum electrodynamics (cavity QED)-based mechanism used in embodiments consistent with the present disclosure can utilize both the properties of light and the properties of matter, and thus can function as a source of entangled states in the architecture, leading to the ability to fabricate a scalable architecture even in a standard silicon manufacturing laboratory, possibly at a reasonable cost.

[0010] For example, some embodiments consistent with the present disclosure include a novel entangled photon cluster state generation device. More specifically, the present disclosure includes an explanation of a chip implementation aspect of a cavity QED system. Entangled photons can be used as a basic building block for a quantum computer.

[0011] Photon-based quantum computing is one of several approaches to quantum computing. In an optical quantum computer, quantum data can be stored in the quantum state of photons. The building blocks of an optical quantum computer can include entangled photons. Therefore, it is necessary to efficiently generate entangled photons.

[0012] Embodiments of this disclosure can provide, or enable, deterministic apparatuses and methods for generating single-photon, multi-photon, and photon graph states usable in quantum computing, as well as entanglement thereof. By avoiding probabilistic processes, this disclosure can achieve high efficiency and enable the use of highly generated photons in qubits.

[0013] According to aspects of this disclosure, systems, methods, devices, integrated circuit devices, circuits, layouts of integrated circuit devices, computer-readable storage media, non-temporary computer-readable storage media, and signals are provided herein. Other features of embodiments of this disclosure will become apparent from the following descriptions of dependent claims, sections, accompanying drawings, and preferred embodiments with reference to the accompanying drawings.

[0014] Some embodiments of the present disclosure involve coupling quantum emitters at each of a plurality of coupling positions, such that each of the plurality of quantum emitters is associated with a different coupling position, each coupling position is associated with a different photon cavity among a plurality of photon cavities, and the quantum emitters associated with each coupling position are configured to mediate interactions between consecutive incident optical qubits to generate a graph state; supplying photons to the plurality of photon cavities, each photon cavity is configured to couple optical qubits to quantum emitters; and outputting the graph state through a plurality of photon output channels located downstream of the plurality of cavities.

[0015] Some embodiments of the present disclosure involve positioning a plurality of quantum emitters at a plurality of coupling locations associated with a plurality of cavities; initializing the state of a quantum emitter qubit associated with each of the plurality of quantum emitters; transmitting an optical qubit to the plurality of quantum emitters in at least one first instance transmission to generate an entanglement gate between the optical qubit and the quantum emitter qubit so as to entangle the quantum emitter qubit and the optical qubit; and, after at least one of the first instance transmissions, transmitting an optical qubit to the plurality of quantum emitters in at least one second instance transmission to generate a SWAP gate between the optical qubit and the quantum emitter qubit, thereby mapping the quantum emitter qubit to the optical qubit.

[0016] Some embodiments of the present disclosure involve coupling a quantum emitter to a cavity; generating a first dirty photon having a first time profile; using the first dirty photon to form a first optical qubit; generating a second dirty photon having a second time profile; using the second dirty photon to form a second optical qubit; using a quantum emitter coupled to the cavity to entangle the first optical qubit with the second optical qubit to form a pair of entangled optical qubits; and using the pair of entangled optical qubits to perform quantum computation.

[0017] According to aspects of the present disclosure, a quantum computing system, method, and computer-readable medium (or non-temporary computer-readable medium) are provided, comprising: initializing the state of a resonator-coupled quantum emitter; receiving at least two photon graph states, each of which contains at least two photons; selecting at least one photon from each graph state; supplying the selected photon through an entanglement gate via the resonator-coupled quantum emitter; and unentangling the resonator-coupled quantum emitter from the selected photon, wherein unentangling includes at least one of detecting the state of the resonator-coupled quantum emitter or mapping the state of the resonator-coupled quantum emitter to the state of an additional photon.

[0018] Aspects of the present disclosure provide a quantum computing system, method, and computer-readable medium (or non-temporary computer-readable medium) for initializing the state of a resonator-coupled quantum emitter having at least four levels arranged in an N configuration, wherein the N configuration has a first ground state, a second ground state, a first excited state, and a second excited state; adjusting the frequency of a first transition between the first ground state and the first excited state; adjusting the frequency of a second transition between the second ground state and the second excited state; adjusting the frequency of a third transition between the second ground state and the first excited state; supplying a plurality of photons at frequencies corresponding to the frequency of the second transition, thereby entangling the plurality of photons in the resonator-coupled quantum emitter; and supplying photons at frequencies corresponding to the frequency of at least one of the first or third transition, thereby mapping the state of the resonator-coupled quantum emitter to the photons.

[0019] Some embodiments of the present disclosure include a plurality of optical processing stages, each optical processing stage comprising at least two of the following: optical switches, beam splitters, waveguides, or photon generators; a plurality of non-messenger connections, each connection located between adjacent optical processing stages; and inputs from the previous stage in determining the stage setting or flow between adjacent stages. Without relying on It is accompanied by a circuit configured to regulate the flow of photons between adjacent stages.

[0020] According to aspects of the subject matter of this disclosure, deterministic photon graph state generators and methods relating thereto are provided. Deterministic single-photon generation is combined with deterministic cavity-enhanced photon-atomic entanglement to generate time-continuous entangled photons, and in relevant embodiments, the generation and entanglement units are incorporated within an integrated array that emits multidimensional cluster states of entangled photons having one time dimension and one or two additional dimensions such as one or two spatial dimensions.

[0021] Single-photon generation, atom-photon entanglement, and photon-photon entanglement can be achieved by a four-state atomic system in an optical cavity, and its transitions depend on the energy of the incident photon and polarization These can be handled independently according to the following. Types of operations include single-photon securing, atom-photon entanglement, multiple-photon entanglement, and atomic qubit preparation and measurement.

[0022] According to one embodiment, a method is provided for securing the graph state of quantum entangled photons, (the photon source unit may also be called a photon generator) and the method is The present invention provides a photon source unit for securing a single photon, wherein the photon source unit comprises source unit atoms positioned within the internal cavity field of the source light cavity, The objective is to provide a photon entanglement unit for quantum entanglement of photon states, wherein the photon entanglement unit atom is located within the internal cavity field of the entangled photocavity, A photon pulse is transmitted to a photon entanglement unit, causing the entanglement unit's atoms to enter an atomic quantum superposition state.

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[0023] Performing measurements on entangled unit atoms may include performing measurements in the xy-plane of a Bloch sphere.

[0024] In another embodiment, a device is provided that secures the graph state of quantum entangled photons, and the device is Multiple single-photon source units, A linear optical element in the first stage, The first multiple entangled units, Equipped with, Multiple single-photon source units, a first-stage linear optical element, and a first set of multiple entanglement units are respectively offset along a predetermined spatial axis. Each single-photon source unit of the multiple photon source units outputs a single photon to the first-stage linear optical element, from which it outputs into each of the first multiple entanglement units. The first set of entanglement units outputs a one-dimensional spatial array of entangled photons in a time dimension.

[0025] Each single-photon source unit and / or entanglement unit may comprise an atom in a first ground state, a first excited state, a second ground state, a second excited state, or a superposition thereof, and the atom is The first transition between the first ground state and the first excited state, A second transition between the first excited state and the second ground state, and It is further configured to selectively undergo a third transition between the second ground state and the second excited state, The device comprises an optical cavity with an internal cavity field for arranging atoms, an optical waveguide coupled to the optical cavity, a magnet configured to generate a magnetic field in the atoms, and a laser source configured to generate pulses of photons in an interference state, wherein each transition is configured to be within the resonance range of the optical cavity.

[0026] The first and second transitions can be selected such that they are orthogonally polarized with respect to each other.

[0027] The first and second excited states can be at the same energy level.

[0028] The first and second ground states can be at different energy levels.

[0029] The laser source is, A pulse for initializing a photon configured to initialize an atom by causing the atom to undergo first and second transitions from a first ground state to a second ground state via a first excited state, and It can be configured to selectively generate pulses that secure a single photon from an atom, configured to secure a single photon from the atom by causing the atom to undergo second and first transitions from a second ground state to a first ground state via a first excited state.

[0030] The laser source may be configured to selectively generate a preparatory photon configured to set the state of an atom to a quantum superposition state, the preparatory photon being a superposition state of first and second preparatory modes, and as a result of the interaction of the preparatory photon with the atom, its first and second ground states are superposition states corresponding to the superposition state of first and second preparatory modes, that is, as a result of the interaction, the first and second ground states of the atom are a superposition having probability amplitudes equal to the probability amplitudes of the first and second preparatory modes of the incident preparatory photon.

[0031] The atom could be a rubidium atom.

[0032] A magnet can be a solenoid.

[0033] The first stage of the linear optical element may include phase control.

[0034] The device is The second stage linear optical element, A second set of multiple entangled units, It can also be equipped with, The second-stage linear optical element and the second plurality of entanglement units are accordingly offset along a predetermined spatial axis with respect to the plurality of single-photon source units, the first-stage linear optical element, and the first plurality of entanglement units. The single photons in the entangled state output from each of the first set of entangled units are input to a linear optical element in the second stage, and from there are input to each of the second set of entangled units.

[0035] A second set of entanglement units may be configured to output a two-dimensional spatial array of entangled photons in a time dimension.

[0036] The device can be configured to generate entangled qubits for use in quantum computers.

[0037] The device may be configured to perform any of the methods of the subject matter of this disclosure.

[0038] The above summary provides specific examples of embodiments of the Disclosure to illustrate the features of the Disclosure and is not intended to summarize all aspects relating to embodiments of the Disclosure. Additional features and advantages relating to embodiments of the Disclosure are partially described in the following description, partially evident from such description, or may be understood by convention of embodiments of the Disclosure. Features and advantages relating to embodiments of the Disclosure are realized and achieved by elements and combinations specifically provided in the appended claims.

[0039] It should be understood that both the above-mentioned general description and the following detailed description are merely examples and illustrative and do not limit the embodiments of the claimed disclosure. The accompanying drawings constitute part of this specification. The drawings illustrate several embodiments of the disclosure and, together with the description, help illustrate the principles of the embodiments of the disclosure as described in the accompanying claims. [Brief explanation of the drawing]

[0040] The subject matter to be disclosed can best be understood by referring to the detailed description below and reading it together with the attached drawings. [Figure 1] Figure 1 schematically shows a device used in quantum computing according to the embodiment of this disclosure. [Figure 2A] Figure 2A is a state diagram of the process for the device shown in Figure 1. [Figure 2B] Figure 2B is a state diagram for a different process of the device shown in Figure 1. [Figure 2C] Figure 2C is a state diagram showing the device shown in Figure 1 in an interaction-free state. [Figure 2D] Figure 2D is a state diagram showing another non-interaction state of the device shown in Figure 1. [Figure 2E] Figure 2E schematically shows the implementation of atomic measurements of the device shown in Figure 1 according to an embodiment of this disclosure. [Figure 3] Figure 3 schematically illustrates atomic entanglement with photons using the device shown in Figure 1. [Figure 4A] Figure 4A schematically shows a single-photon source unit according to an embodiment of this disclosure. [Figure 4B] Figure 4B schematically illustrates the generation of a series of single photons from the photon source unit shown in Figure 4A. [Figure 5A] Figure 5A schematically shows an entanglement unit for quantum entanglement of a photon state with an atomic state, according to an embodiment of this disclosure. [Figure 5B] Figure 5B schematically illustrates the quantum entanglement of a continuous series of photon states with atomic states according to an embodiment of this disclosure. [Figure 6] Figure 6 is a flowchart of a method for securing a photon graph state according to the embodiment of this disclosure. [Figure 7] Figure 7 schematically shows an apparatus for securing a multidimensional cluster state of entangled photons according to an embodiment of this disclosure. [Figure 8] Figure 8 schematically shows atoms bonded to a cavity consistent with some embodiments of this disclosure. [Figure 9A] Figure 9A schematically shows waveguides that can be used for atoms coupled to a cavity according to some embodiments of this disclosure. [Figure 9B] Figure 9B schematically shows photon generation according to some embodiments of this disclosure. [Figure 9C] Figure 9C schematically shows an entanglement gate according to some embodiments of this disclosure. [Figure 10] Figure 10 schematically shows a system including a vacuum chamber usable for atomic and optical chips according to some embodiments of this disclosure. [Figure 11A] Figure 11A schematically shows a quantum computation method according to one embodiment of entanglement of photon graphs. [Figure 11B] Figure 11B schematically shows a quantum computation method according to one embodiment of entanglement of photon graphs. [Figure 11C] Figure 11C schematically shows a quantum computing system according to one embodiment of the entanglement of photon graphs. [Figure 11D] Figure 11D schematically shows a quantum computing system according to some embodiments relating to entangling photon graphs to form clusters, in accordance with some embodiments of the present disclosure. [Figure 12A] Figure 12A schematically shows a preferred implementation of a quantum computing system relating to providing multiple cavities that generate graph states consistent with some embodiments of this disclosure. [Figure 12B] Figure 12B schematically shows a photon generator that provides multiple cavities consistent with some embodiments of the present disclosure. [Figure 12C] Figure 12C is a block diagram of an exemplary process relating to providing a plurality of cavities that generate graph states, according to some embodiments of this disclosure. [Figure 12D] Figure 12D schematically shows a preferred implementation of a quantum computing system relating to providing a plurality of cavities that generate graph states, according to some embodiments of this disclosure. [Figure 13A]Figure 13A schematically shows a preferred implementation of a system according to some embodiments relating to the generation of a photon graph state. [Figure 13B] Figure 13B schematically shows a preferred implementation of a system according to some embodiments relating to the generation of a photon graph state. [Figure 13C] Figure 13C schematically shows a preferred implementation of a system according to some embodiments relating to the generation of a photon graph state. [Figure 13D] Figure 13D is a block diagram of an exemplary process according to one embodiment of generating a photon graph state. [Figure 14A] Figure 14A schematically shows a preferred implementation of a system or device according to some embodiments relating to generating photon graph states for quantum computing. [Figure 14B] Figure 14B is a flowchart illustrating an exemplary process according to one embodiment of generating a photon graph state for quantum computing. [Figure 15A] Figure 15A schematically illustrates a single-photon Raman interaction (SPRINT) mechanism using a quantum emitter coupled to a resonator (or cavity), according to some embodiments of this disclosure. [Figure 15B] Figure 15B schematically illustrates a single-photon Raman interaction (SPRINT) mechanism using a quantum emitter coupled to a resonator (or cavity), according to some embodiments of this disclosure. [Figure 15C] Figure 15C schematically illustrates a single-photon Raman interaction (SPRINT) mechanism using a quantum emitter coupled to a resonator (or cavity), according to some embodiments of this disclosure. [Figure 16A] Figure 16A is a flowchart of a quantum computing method according to one embodiment of an N-configuration resonator-coupled quantum emitter. [Figure 16B] Figure 16B schematically shows a quantum computing system according to one embodiment of an N-configuration resonator-coupled quantum emitter. [Figure 16C]Figure 16C schematically shows a quantum computing system according to one embodiment of an N-configuration resonator-coupled quantum emitter. [Figure 16D] Figure 16D schematically shows a quantum computing system according to one embodiment of an N-configuration resonator-coupled quantum emitter. [Figure 17A] Figure 17A schematically shows a preferred implementation of a system or device according to some embodiments relating to the use of heralding-free connections. [Figure 17B] Figure 17B schematically shows a preferred implementation of the optical processing step according to some embodiments relating to the use of a messenger-free connection. [Figure 17C] Figure 17C schematically shows a preferred implementation of the optical processing step according to some embodiments relating to the use of a messenger-free connection. [Figure 17D] Figure 17D is a flowchart of an exemplary process according to one embodiment of the use of a messenger-free connection.

[0041] For the sake of simplification and clarity of the illustration, the elements shown in the figures are not necessarily drawn to scale, and the dimensions of some elements may be exaggerated relative to others. In addition, reference numbers may be repeated between figures to indicate corresponding or similar elements.

[0042] In the following description, various operational examples are provided for illustrative purposes only. However, it should be understood that this disclosure may be implemented without one or more of these detailed descriptions. Hereinafter, non-limiting examples of this disclosure are given in detail, and these examples are shown in the accompanying drawings. These examples are described below by reference to the drawings, in which similar reference numerals refer to similar elements. Where similar reference numerals are given, the corresponding descriptions are not repeated, and the reader should refer to the previously given drawings for descriptions of similar elements if they are of interest.

[0043] Various embodiments are described herein by reference to systems, methods, devices, or computer-readable media. Disclosure of one is intended to be a disclosure of all. For example, it should be understood that disclosure of computer-readable media described herein also constitutes disclosure of methods implemented by the computer-readable media, as well as disclosure of systems and devices that implement such methods, for example, via at least one processor or circuit. It should be understood that these forms of disclosure are for illustrative purposes only, and one or more aspects of an embodiment described herein may be combined with one or more aspects of other embodiments described herein, to the extent intended by this disclosure. [Modes for carrying out the invention]

[0044] Preferred embodiments are described with reference to the accompanying drawings, which are not necessarily drawn to scale. Examples and features of the principles of the disclosure are described herein, but modifications, alterations, and other implementations are possible without departing from the spirit and scope of the embodiments of the disclosure. The words “comprising,” “having,” “containing,” and “including,” and other similar forms, are intended to be synonymous and are open-ended in that the items or sets of items following any one of these words do not mean an exhaustive enumeration of such items or sets of items, or that the enumerated items or sets of items are the only ones that are included. Note also that the singular forms “a,” “an,” and “the” as used herein and in the accompanying claims include plural references unless specifically defined in context. Furthermore, relational terms herein, such as “first” and “second,” are used solely to distinguish one entity or action from another entity or action and do not require or imply any actual relationship or order between these entities or actions.

[0045] Unless otherwise specifically stated, the term “or” as used herein encompasses all possible combinations, except in cases where it is not feasible. For example, if it is stated that a component may include A or B, then unless otherwise specifically stated or unless it is not feasible, that component may include A, B, or A and B. As a second example, if it is stated that a component may include A, B, or C, then unless otherwise specifically stated or unless it is not feasible, that component may include A, B, C, A and B, A and C, B and C, or A, B, and C.

[0046] Embodiments described herein may refer to a non-temporary computer-readable medium or computer-readable medium containing instructions, which, when executed by at least one processor (or system, circuit, or device), cause at least one processor (or system, circuit, or device) to perform a method according to the embodiments of this disclosure. The non-temporary computer-readable medium (or computer-readable medium) may be any medium capable of storing data in any memory so that it can be read by any computing device (or any system) having a processor to execute any other instructions, either in the manner stored in memory or in the manner stored in memory. The non-temporary computer-readable medium (or computer-readable medium) may be implemented as hardware, firmware, software, or any combination thereof. Furthermore, the software may be implemented as an application program that is physically embodied on a program storage unit or computer-readable medium consisting of elements or specific devices and / or combinations of devices. The application program may be uploaded to and executed by a machine having any suitable architecture (or circuit). Preferably, the machine may be implemented on a computer platform having hardware (or circuitry) such as one or more central processing units ("CPU"), memory, and input / output interfaces. The computer platform may also include an operating system and microinstruction code. Various processes and functions described herein may be part of the microinstruction code, part of an application program, or any combination thereof, and may be executed by the CPU, whether or not such computer or processor is explicitly indicated. In addition, various other peripheral units may be connected to the computer platform and vacuum chamber, such as additional data storage units. Furthermore, non-temporary computer-readable media may be any computer-readable media other than temporary propagated signals.

[0047] Memory may include random access memory (RAM), read-only memory (ROM), hard disks, optical disks, magnetic media, solid-state storage devices, flash memory, other persistent memory, fixed memory, volatile memory, or non-volatile memory, or any other mechanism capable of storing instructions. Memory may include one or more separate storage devices located side-by-side or distributed, capable of storing data structures, instructions, or any other data. Memory may further include a memory section containing instructions that the processor executes. Memory may also be used as an operational scratchpad for the processor or as temporary storage.

[0048] Some embodiments include at least one processor. “At least one processor” may include any physical device or group of devices having electrical circuits that perform logical operations on inputs or a plurality of inputs. For example, at least one processor may include one or more integrated circuits (ICs), including application-specific integrated circuits (ASICs), microchips, microcontrollers, microprocessors, all or part of a central processing unit (CPU), an image processing unit (GPU), a digital signal processor (DSP), a field-programmable gate array (FPGA), a server, a virtual server, or other circuits suitable for executing instructions or performing logical operations. Instructions executed by at least one processor may be preloaded into memory integrated into or incorporated into the controller, for example, or stored in separate memory. Memory may include random access memory (RAM), read-only memory (ROM), hard disks, optical disks, magnetic media, solid-state storage devices, flash memory, other persistent memory, fixed memory, or volatile memory, or any other mechanism capable of storing instructions. In some embodiments, at least one processor may include multiple processors. Each processor may have a similar structure, or processors may have different structures that are electrically connected or separated from one another. For example, processors may be separate circuits or may be integrated into a single circuit. When multiple processors are used, they may be configured to operate independently or cooperatively, and may be located side by side or apart from one another. Processors may be connected electrically, magnetically, optically, acoustically, mechanically, or by other means that enable the processors to interact with each other.

[0049] Alternatively or additionally, some embodiments involve a circuit (or integrated circuit or integrated circuit device layout). The circuit (or integrated circuit or integrated circuit device layout) may include one or more functional units (or one or more layout portions), each functional unit (or each layout portion) configured to perform one or more process steps. The one or more functional units (or one or more layout portions) may be arranged (for example, they may be positioned and connected to each other or to other functional units or other layout portions) so that the circuit (or integrated circuit or integrated circuit device layout) can perform some or all of the steps of the method or process. For example, the circuit (or integrated circuit or integrated circuit device layout) may perform some or all of the steps of the method or process according to some embodiments of this disclosure.

[0050] In the examples or embodiments described herein, at least some of the features of a system, device, apparatus, integrated circuit device, or circuit, such as an optical chip or optical integrated circuit (PIC), are formed using a manufacturing method such as lithography, which uses a lithographic process on a silicon-based substrate to form the features on the silicon-based substrate. It is also understood that other types of substrates may be used with a lithographic process to form the features thereon. Other techniques that are alternative to or in addition to lithography (e.g., etching, doping, diffusion, sputtering, or deposition, or other semiconductor device manufacturing techniques such as self-assembly techniques) may be used to form the features on the substrate, and it is also understood that such other techniques may enable the manufacture of features having a structure capable of supplying the functionality of the features described herein.

[0051] The following paragraphs provide definitions of terms used in this disclosure and examples associated with those terms. Where a feature is functionally described using such terms, it should be understood that the feature may be interchangeable with another feature that shares equivalent functionality. Embodiments and examples described herein may refer to the following:

[0052] Some embodiments involve graph states. A graph refers to a graph state. A graph state represents a relationship between groups of qubits, which are the fundamental units of quantum information. Groups of qubits can be, for example, entangled. The relationship between groups of qubits can be an entangled relationship. For example, qubits can be stored in (or belong to) a two-state quantum mechanical system such as a photon, atom, and quantum emitter. For example, a graph state can include a representation of a composite quantum system. A composite quantum system can include multiple quantum subsystems. Each such subsystem can be represented by a node or vertex of a graph, and entanglement or interaction between pairs of subsystems can be represented by edges connecting corresponding pairs of vertices. Examples of graph states include a photon graph state, a cluster state where the graph is a d-dimensional lattice of connected subsets, or a Greenberger-Horn-Zeilinga state (GHZ state) where the graph is a number of vertices exclusively connected to a central vertex.

[0053] As a non-limiting example, Figures 6 and 7 show a method and apparatus for securing a photon graph state (for example, n photons are shown in step 609).

[0054] Some embodiments involve photon states. A photon state refers to a state or configuration of one or more photons. For example, a photon state may include quantum states associated with the degrees of freedom of one or more photons. An example of a photon state is a single-photon state, which corresponds to the presence of exactly one photon in a given mode. As a non-limiting example, Figures 4B and 5B show a time-sequential series (4¹²) of single-photon states.

[0055] Some embodiments involve photon graph states. A photon graph state refers to a graph state as described above that applies to photons. For example, a photon graph state includes photon states where the vertices represent photon states. An example of a photon graph state is one where each vertex corresponds to a single-photon qubit, and the qubits are the paths of single photons, and the deviations of single photons. light, a graph state describing the time bin of a single photon, or the frequency of a single photon, or each vertex being a continuous variable light Corresponding to qubits, the graph states include pairs of orthogonal superposition states where the qubit represents a photon number state.

[0056] The graph states in Figures 6 and 7, as described above, are non-restrictive examples of photon graph states.

[0057] Some embodiments involve optical qubits. An optical qubit refers to a fundamental unit of quantum information stored (or belonging to) one or more photons or electromagnetic fields. For example, an optical qubit includes a qubit encoded with degrees of freedom associated with the propagation or stationary mode of an electromagnetic field. Examples of optical qubits include: light This includes qubits encoded by the number of photons, phase, time bin, frequency, or position in the electromagnetic field. The electromagnetic field can be a propagation mode in an optical waveguide in a vacuum, or a mode confined in an electromagnetic resonator.

[0058] Some embodiments involve quantum emitters. A quantum emitter refers to a component configured to couple to an electromagnetic mode. For example, a quantum emitter includes a stationary quantum system having an anharmonic spectrum configured to couple to an electromagnetic mode. In other words, a quantum emitter can be a stationary qubit capable of interacting with photons. A stationary qubit can refer to a material quantum system usable for storing and processing quantum information. For example, a stationary qubit can refer to a qubit that (i) reliably stores quantum information on a timescale of nanoseconds or longer, (ii) reliably performs computations and / or operations that can transfer or convert the information to flying qubits (e.g., non-stationary qubits or photons), (iii) is reliably measured or read out, and / or (iv) is capable of operating in a highly entangled manner (or satisfies these conditions). Examples of stationary qubits may include qubits stored in or belonging to a quantum emitter. For example, qubits stored in or belonging to rubidium or cesium atoms can function as sources of stationary qubits. For example, Rydberg atoms can also function as a source of stationary qubits. The use of Rydberg atoms can yield properties favorable to quantum computing applications, such as (i) a strong response to electromagnetic fields, (ii) a long decay period, and (iii) a large electric dipole moment. A Rydberg atom may refer to an excited atom with one or more electrons having a large principal quantum number n. Examples of quantum emitters include quantum systems having one or more of the following: an electron or nuclear configuration of an ion or neutral atom, an electron or nuclear configuration of a defect or quantum dot in a material substrate, or a superconducting circuit configuration including one or more Josephson junctions. Quantum emitters may be superconducting qubits, quantum dots, atoms, neutral atoms, ions, rubidium atoms, cesium atoms, strontium, erbium, ytterbium, calcium, barium, beryllium, or magnesium atoms. Atoms or ions may be obtained from Rydberg atoms. A superconducting qubit may refer to a solid-state qubit obtained from a superconducting material such as aluminum or a niobium-titanium alloy. A superconducting qubit may include or be coupled to at least one Josephson junction.Examples of superconducting qubits may include charge qubits, flux qubits, phase qubits, and / or hybrids thereof (e.g., transmons). A quantum dot may refer to a quantum emitter having a substrate (e.g., a solid-state substrate such as semiconductor particles) that exhibits optical and / or electronic properties that demonstrate quantum mechanical principles as described above. For example, a quantum dot may be a nanoparticle having optical and electronic properties different from its bulk component. In the presence of high-energy photons (e.g., UV light), electrons in a quantum dot may be excited to a high-energy state and emit one or more photons when transitioning to the ground state. For example, a quantum dot may be fabricated from one or more binary compounds such as lead sulfide, lead selenide, cadmium selenide, cadmium sulfide, cadmium telluride, indium arsenide, or indium phosphide. For example, a quantum dot may be self-assembled from indium arsenide in a gallium arsenide substrate. For example, a quantum dot may refer to an atomic defect in a solid-state substrate, such as a nitrogen vacancy center in diamond. Atom 102 shown in Figures 1 and 3, atom 402 in Figures 4A and 4B, atom 502 in Figures 5A and 5B, and rubidium in Figures 8 to 9C. 87 Rb) Atom 820, and one or more atoms 1020 in Figure 10, are non-restrictive examples of quantum emitters.

[0059] Some embodiments involve a fluctuating quantum emitter. A fluctuating emitter refers to a quantum emitter whose physical state or properties vary over time (at least temporarily). For example, a quantum emitter may fluctuate because its resonant frequency changes over time due to a stray magnetic field or electric field. For example, a fluctuating emitter includes a quantum emitter whose transition frequency may vary over time (temporarily) due to ambient noise. Examples of fluctuating quantum emitters include atoms whose transition frequency varies due to a time-varying magnetic field, electric field, or optical trap field, or quantum dots whose transition frequency varies due to stochastic charges or spins in the surrounding solid-state lattice.

[0060] Some embodiments involve quantum emitter qubit states. A quantum emitter qubit state refers to a state or configuration of the quantum emitter. For example, a quantum emitter state includes a configuration of the quantum emitter corresponding to a superposition of eigenstates of the Hamiltonian describing the quantum emitter. An example of a quantum emitter qubit state is the ground state of the quantum emitter corresponding to the lowest energy eigenstate.

[0061] Some embodiments involve a cavity or resonator. A cavity may function as a resonator, and a resonator refers to a component that establishes or supports vibrations and / or normal modes. Vibrations may be, for example, resonant vibrations of normal modes of a discrete set at the resonant frequencies of an associated discrete set. For example, a resonator may be capable of confining an electromagnetic field in electromagnetic modes having a particular vibration frequency. For example, a cavity or resonator includes an electromagnetic resonator configured to confine an electromagnetic field in space and time. A cavity or resonator may support a discrete set of electromagnetic modes, each associated with a particular resonant frequency and lifetime in the confined field. Examples of cavities or resonators include photon cavities, optical cavities, whispering gallery mode cavities, Fabry-Perot cavities, or ring cavities. Typical cavities may be optical cavities or microwave cavities. The optical cavity 103 in Figures 1 and 3, and the cavity 818 in Figures 8 through 9C, are non-limiting examples of resonators.

[0062] Some embodiments involve a quantum emitter coupled to a resonator (or resonator-coupled quantum emitter). A quantum emitter coupled to a resonator (or resonator-coupled quantum emitter) refers to a quantum emitter capable of interacting with a resonator. For example, a quantum emitter coupled to a resonator (or resonator-coupled quantum emitter) may include a quantum emitter positioned to interact with an electromagnetic field confined by the resonator, which may be a component or group of components configured to confine the electromagnetic field in space and time. The component or group of components may support a discrete set of electromagnetic modes, each associated with a specific resonant frequency and lifetime in the confined field. The quantum emitter coupled to a resonator (or resonator-coupled quantum emitter) may also Depending on the components that function as a resonator, It can also be called a quantum emitter coupled to a cavity, a quantum emitter coupled to a photon cavity, or a quantum emitter coupled to an optical cavity. stomach. Therefore, quantum emitters coupled to a resonator (or resonator-coupled quantum emitters) may include quantum emitters whose dipole fields overlap with the electromagnetic modes of the resonator (e.g., cavity, photon cavity, or optical cavity).

[0063] For example, inside a cavity (or photon cavity, resonator, or optical cavity) Cavity The quantum emitters (or atoms) placed within the field are quantum emitters coupled to a cavity (or quantum emitters coupled to a photon cavity, quantum emitters coupled to a resonator, or quantum emitters coupled to an optical cavity). The atom 102 confined within the optical cavity 103 in Figure 1, the rubidium (87Rb) atom 820 coupled to cavity 818 in configuration 810 in Figure 8, and the rubidium (87Rb) atom 820 coupled to cavity 818 in Figures 9A to 9C are non-restrictive examples of quantum emitters coupled to a resonator (or resonator-coupled quantum emitters).

[0064] Some embodiments involve a coupling location or coupling site. The coupling location or coupling site includes an area (e.g., volume or region) configured to enable coupling between a quantum emitter and a resonator (or cavity, photon cavity, or optical cavity). For example, the coupling location or coupling site may include an area that positions the quantum emitter within the internal cavity field of the resonator (or cavity, photon cavity, or optical cavity), or an area that allows the dipole field of the quantum emitter to overlap with the electromagnetic modes of the resonator (or cavity, photon cavity, or optical cavity).

[0065] Some embodiments involve quantum emitter positioning. Quantum emitter positioning refers to arranging or positioning a quantum emitter so as to enable interaction between the quantum emitter and a resonator (or cavity, photon cavity, or optical cavity). Examples of quantum emitter positioning include one or more of the following: positioning a quantum emitter so that it is located at a coupling position or location (for example, positioning or installing a quantum emitter at a coupling position or location); coupling a quantum emitter to a resonator (or cavity, photon cavity, or optical cavity); positioning a quantum emitter within the internal cavity field of a resonator (or cavity, photon cavity, or optical cavity); trapping a quantum emitter in the vicinity of a resonator (or cavity, photon cavity, or optical cavity); lithographically installing a quantum dot in the vicinity of a resonator (or cavity, photon cavity, or optical cavity); or lithographically installing a resonator (or cavity, photon cavity, or optical cavity) in the vicinity of a self-assembled quantum dot.

[0066] Some embodiments involve trapping a quantum emitter (e.g., an atom or alkali atom). Trapping a quantum emitter refers to generating a trap that keeps the quantum emitter within a coupling location. For example, trapping a quantum emitter may involve restricting the spatial degrees of freedom of the quantum emitter (or atom or alkali atom) using an electromagnetic field configuration. Examples of trapping a quantum emitter (or atom or alkali atom) include trapping ions using electric and radio frequency (or microwave) fields, trapping atoms using a magneto-optical trap (MOT) configuration, or trapping atoms using a non-resonant laser beam (atomic tweezers). As a non-limiting example, Figure 9A shows a utility waveguide 910 carrying a pulse or field that generates a trap, and Figure 10 shows a magneto-optical trap (MOT) that traps one or more atoms 1020. The pulse or field in Figure 9A is configured to trap an Rb atom 820 next to a coupling location, for example, a cavity 818 (or a resonator or ring shape in the figure). The pulse or field may be configured to generate and / or include an evanescent field around the waveguide 910, and as a result, the evanescent field trap may be used to maintain Rb atoms 820 at or within the coupling position. The magneto-optical trap in Figure 10 is configured to trap one or more atoms 1020 at or within the coupling position.

[0067] Some embodiments involve being in the vicinity of a photon cavity (or a cavity, resonator, or optical cavity). Being in the vicinity of a photon cavity (or a cavity, resonator, or optical cavity) means being within the electromagnetic modes of the photon cavity (or a cavity, resonator, or optical cavity). Examples of being in the vicinity of a photon cavity (or cavity, resonator, or optical cavity) include being between the two reflective surfaces of a Fabry-Perot cavity, being within or located within the aforementioned coupling location or coupling site, being within the internal cavity field of the aforementioned resonator (or cavity, photon cavity, or optical cavity), being within or located within the coupling location or coupling site that allows the quantum emitter's dipole field to overlap with the electromagnetic modes of the aforementioned resonator (or cavity, photon cavity, or optical cavity), and / or being within the evanescent field of the aforementioned whispering gallery cavity.

[0068] Some embodiments involve coupling an optical qubit to a quantum emitter, or a qubit to an atomic qubit. Coupling an (optical) qubit to a quantum emitter (atomic qubit) means enabling interaction between a qubit (a qubit of one or more photons) and the qubit of the quantum emitter (an atomic qubit, i.e., the qubit of the atom when the atom is acting as a quantum emitter). For example, coupling an (optical) qubit to a quantum emitter (atomic qubit) may include enabling interaction between a qubit (or optical qubit) and a quantum emitter (or atomic qubit) by generating an overlap between the dipole field of the quantum emitter (or atom) and the electromagnetic field of the qubit (or optical qubit), as described above.

[0069] Some embodiments involve superconducting qubits. A superconducting qubit refers to a qubit stored in or belonging to a superconducting electronic circuit (e.g., a network of electrical elements using superconductors). For example, a superconducting qubit may include an electrical circuit from a superconducting material that includes one or more Josephson junctions or is coupled to one or more Josephson junctions. Examples of superconducting qubits include superconducting transmon qubits, superconducting fraxonium qubits, or superconducting bosonic qubits.

[0070] Some embodiments involve quantum emitters containing quantum dots. A quantum emitter containing quantum dots may refer to a quantum emitter having a substrate (e.g., a solid-state substrate such as semiconductor particles) having optical and / or electronic properties that exhibit quantum mechanical principles. For example, quantum dots may be formed from nanoscale semiconductor materials arranged to tightly confine electrons or electron holes. For example, a quantum emitter containing quantum dots may include a stationary quantum system having an anharmonic spectrum configured to be coupled in electromagnetic degrees of freedom, the quantum system including a spatially defined region within a solid-state substrate to confine charge carriers within the substrate in all three dimensions. Examples of quantum emitters containing quantum dots include gate-defined quantum dots where the spatial region is defined by an electric field controlled by electrodes, or self-assembled quantum dots composed of a material where the spatial region has a smaller band gap than the surrounding region. For example, quantum dots may be self-assembled from indium arsenide in a gallium arsenide substrate. A quantum dot may refer to an atomic defect in a solid-state substrate, such as a nitrogen vacancy center in diamond.

[0071] Some embodiments involve photon-quantum emitter entanglement. Photon-quantum emitter entanglement occurs when the state of one or more photons is intertwined with the state of one or more quantum emitters. knotThis refers to an attached state. For example, the state of one or more photons may be related to the state of one or more quantum emitters, and those states cannot be described independently of each other. Such entanglement can, for example, correlate measurements of the state of one or more photons with measurements of the state of one or more quantum emitters to generate a correlation between the measurements of those states, thereby allowing mutual information to be stored or processed using that correlation. For example, photon-quantum emitter entanglement may include an inseparable (not separable) state of a composite quantum system consisting of at least one photon and at least one quantum emitter, where at least one quantum emitter is also entangled with a photon state (e.g., the photon state of at least one photon). As a non-limiting example, Figure 3 shows the entanglement between atom 102 and photon 302 indicated by double line 310.

[0072] Some embodiments involve entanglement gates. As used herein, the term “entanglement gate” refers to any component, group of components, control sequence, or operation (reversible or irreversible) that results in any degree of entanglement between quantum elements (e.g., any quantum particle, group of quantum particles, or qubit). For example, an entanglement gate may include a quantum circuit configured to entangle qubits. For example, a quantum emitter coupled to the aforementioned resonator (or cavity, photon cavity, or optical cavity) may be capable of functioning as an entanglement gate. An entanglement gate or operation may involve sending a single photon through a beam splitter to two resonator-coupled quantum emitters. Furthermore, the mapping of two quantum emitter qubits to an optical qubit may generate a three-photon entangled state (i.e., a Greenberger-Horn-Zeilinga state). Examples of entangled gates include controlled Z-entanglement gates (CZ gates), controlled NOT-entanglement gates (CNOT gates), the square root of a SWAP-entanglement gate, or virtual SWAP-entanglement gates (iSWAP gates).

[0073] As a non-limiting example, Figures 8 and 9C show rubidium coupled to cavity 818 in configuration 810 in Figure 8. 87Rb) Atom 820, and rubidium bonded to cavity 818 in Figure 9C ( 87 Rb) shows atom 820, which is implemented as an entanglement (CZ) gate, and Figures 5A to 5B show entanglement unit 501 (including entanglement unit atom 502) implemented as an entanglement gate.

[0074] A controlled Z gate (CZ gate) refers to a quantum gate that can operate on two qubits, and their coupled quantum state obtains a conditional phase shift (e.g., a phase shift of pi). For example, the coupled quantum state of two qubits may obtain a phase shift of pi if both qubits are associated with logic 1, and otherwise no phase shift is obtained. As a non-restrictive example, Figure 3 shows a controlled Z gate implementation, and Figures 8 and 9C show a rubidium gate coupled to a cavity 818 in configuration 810 implemented as an entangled (CZ) gate. 87 Rb) indicates 820 atoms.

[0075] A SWAP gate refers to a quantum gate that can operate on two qubits, where the quantum state of the first qubit is transferred to the second qubit, and the quantum state of the second qubit is transferred to the first qubit. For example, if two qubits are represented by quantum systems A and B, the quantum state of A is transferred to B, and the quantum state of B is transferred to A. As a non-restrictive example, Figure 2E shows a SWAP gate 201 that performs qubit "read" and "write" operations on atom 102.

[0076] Some embodiments involve mapping quantum emitter qubits to optical qubits. Mapping quantum emitter qubits to optical qubits refers to transferring quantum emitter qubits to optical qubits. For example, such mapping may include transferring quantum information stored in the quantum emitter qubits to one or more photon qubits. In one example, mapping quantum emitter qubits to optical qubits may be the result of performing a SWAP gate operation on the quantum emitter qubits and optical qubits as described above. For example, the state of a resonator-coupled quantum emitter can be mapped to photons by supplying photons at frequencies corresponding to frequencies related to specific transitions of the resonator-coupled quantum emitter. As a non-restrictive example, Figure 2E shows a mapping using the SWAP gate 201, where the initial superposition state of atom 102 (a non-restrictive example of a quantum emitter) of first and second ground states 111, 113 having probability amplitudes γ and δ is transferred to the emitted photon 204 (shown as its superposition state of modes 1 and 2 having probability amplitudes δ and γ), and the superposition of incident photons 202 of optical modes 1 and 2 having probability amplitudes α and β is transferred to atom 102 (shown as atom 102 remaining in the superposition state of first and second ground states 111, 113 having probability amplitudes β and α).

[0077] Some embodiments involve an optical chip. An optical chip refers to a device that integrates elements or components that operate at visible or infrared wavelengths. For example, such a device may be microfabricated. The microfabrication process may involve lithography as described above. Examples of optical chips include chips that incorporate one or more of the following: an integrated laser; a channel or waveguide for carrying the laser, pulses of photons, and / or one or more single photons; a waveguide; a switch; a phase modulator; a resonator; an interferometer; a beam splitter; an optical amplifier; a nonlinear waveguide; a nonlinear resonator; an amplitude modulator; an integrated magnetic field generator such as a solenoid; a detector; and one or more controllers (or circuits) configured to control or receive outputs from one or more of the elements or components of the chip.

[0078] Some embodiments involve an atomic dispenser. An atomic dispenser refers to a component or group of components arranged to provide one or more atoms. An atomic dispenser is a non-limiting example of a quantum emitter dispenser arranged to distribute (or provide) one or more quantum emitters. For example, an atomic dispenser may include a source of atoms that generates atomic vapor in a chamber. The chamber may typically include a vacuum chamber. Examples of atomic dispensers include a source configured to be resistance-heated to distribute or provide atoms. For example, the atoms to be distributed may be one or more of cesium, potassium, sodium, rubidium, and lithium, in particular.

[0079] Some embodiments involve an atomic jet. An atomic jet refers to a stream or beam of atomic vapor. This stream or beam may be supplied or distributed by the aforementioned atomic dispenser. For example, an atomic jet may include a directional beam containing high-temperature atomic vapor emanating from an atomic dispenser.

[0080] Some embodiments involve cooling of the atomic jet. Cooling of the atomic jet refers to cooling (or reducing) the motion and / or velocity of the atoms in the jet. For example, cooling of the atomic jet may include cooling the degrees of freedom of the atoms in the jet.

[0081] Some embodiments involve cavities (or resonators) formed within a silicon nitride layer. For example, such cavities (or resonators) formed within a silicon nitride layer may include a planar layer incorporating a connecting region containing silicon nitride. The connecting region may be made of a different material having a refractive index lower than that of silicon nitride. Cavities (or resonators) formed within a silicon nitride layer may be formed within a silicon nitride region surrounded by silica, and the silicon nitride region may include straight lines or curves, or the silicon nitride region may include rings. As non-limiting examples, the optical cavity 103 in Figures 1 and 3, and the cavity 818 in Figures 8 to 9C, may be formed within a silicon nitride region.

[0082] Some embodiments involve dirty photons. Dirty photons refer to photons that are distinguishable from other photons when performing quantum computations, for example. Dirty photons may include, for example, propagating photons of mixed states with respect to multiple space-time modes, e.g., multiple time profiles. It becomes possible to use these dirty photons in quantum computations by entangling the photons through cavity-enhanced atom-photon interactions (for example, using a quantum emitter coupled to the aforementioned resonator or a resonator-coupled quantum emitter). This is because entangling the photons through cavity-enhanced atom-photon interactions (for example, using a quantum emitter coupled to the aforementioned resonator or a resonator-coupled quantum emitter) does not require the use of indistinguishable photons (clean photons), which would otherwise be the case of probabilistic entanglement using linear optics. For example, this means that the input photon pulse (e.g., pulse 404 in Figure 4A) does not need to be precisely timed and shaped. Single photons generated according to certain embodiments of this disclosure are perfectly suitable for qubit entanglement using the aforementioned resonator-coupled quantum emitters or resonator-coupled quantum emitters, even when the photons exhibit disorder that makes the photons easily distinguishable.

[0083] Some embodiments involve time profiles. A time profile refers to the time envelope of the propagating photon field. Examples of time profiles include exponentially decreasing or increasing profiles with specific decay times and initial times, constant profiles with specific initial and final times, or Gaussian profiles with specific mean times and time variations.

[0084] Some embodiments involve photon delay lines. A photon delay line refers to a component or group of components arranged to introduce a time delay for one or more photon pulses or light beams. For example, a photon delay line may include an optical configuration that incorporates an optical waveguide that functions to delay the arrival time of incident pulses for pulses that do not enter the optical waveguide. An example of a photon delay line is an optical delay line that can utilize the visible portion of the electromagnetic spectrum. Optical delay lines may have a fixed delay or an adjustable delay. A (photon or optical) delay line may be controlled by an (optical) switch that determines whether an optical pulse passes through the delay line. For example, a (photon or optical) delay line may be implemented in free space, fiber, or on-chip waveguide.

[0085] Some embodiments involve manipulating alkali atoms (or quantum emitters). Manipulating alkali atoms (or quantum emitters) refers to controlling the external or internal state (e.g., state or configuration) of the alkali atoms (or quantum emitters). For example, the internal state may correspond to the electronic configuration, nuclear configuration, or a combination thereof. The external state may correspond to, for example, the motion of alkali atoms at the bonding site.

[0086] Some embodiments involve cooling of alkali atoms (or quantum emitters). Cooling in this context refers to a reduction in the motion and / or velocity of alkali atoms (or quantum emitters). For example, cooling of alkali atoms (or quantum emitters) may affect the degrees of freedom of motion of alkali atoms (or quantum emitters).

[0087] Some embodiments involve messenger-free connections. A messenger-free connection refers to a connection or link that does not use messenger (or feedforward). For example, messenger (or feedforward) may be achieved by using photons or optical delay lines to detect one photon from a pair of single photons generated in a strongly correlated state and "messenger" the other photon from the pair, so that the state of the other photon is known before its detection (feedforward). Thus, a messenger-free connection refers to a connection or link that does not require or involve such messenger (or feedforward).

[0088] The embodiments, sections, claims, or examples described herein relate to the use of one or more cavities (e.g., resonators as described herein) coupled to quantum emitters (e.g., ions, atoms, or quantum dots) used in quantum computing, and related systems, devices, apparatus, methods, (non-temporary) computer-readable media, or computer-readable media. Such uses may be compatible with other embodiments described herein.

[0089] As a non-limiting example, the coupled cavity and quantum emitter (or cavity-coupled quantum emitter) described herein may be used in one of the exemplary configurations of an atomic and optical cavity (or cavity QED) used in a device for a deterministic photon graph state generator described herein, wherein the optical cavity (or resonator) and atom (or quantum emitter) are arranged such that coupling between them occurs in the atomic trap or other particle trap (also referred to as the coupling location or coupling site, or the location (site) where the internal cavity field of the source optical cavity or entangled optical cavity exists) of the exemplary configuration. In the example configuration for a deterministic photon graph state generator of this disclosure, the cavity corresponds to optical cavity 103, and the quantum emitter corresponds to atom 102 shown in Figures 1 and 3, atom 402 in Figures 4A and 4B, and atom 502 in Figures 5A and 5B. In other non-limiting examples, the cavity corresponds to cavity 818 in Figures 8 to 9C, and the quantum emitter is rubidium in Figures 8 to 9C. 87 Rb) corresponds to atom 820, or one or more atoms 1020 in Figure 10.

[0090] For example, the coupled cavity and quantum emitter (or cavity-coupled quantum emitter) described herein may be used in embodiments relating to providing one of the exemplary configurations of a photon cavity-coupled quantum emitter, for example, a plurality of cavities that generate a graph state, or those shown in Figures 12A to 12D (e.g., exemplary optical cavities 1112_1, 1112_n, 1138_1, 1138_n and exemplary quantum emitters 1114_1, 1114_n, 1140_1, 1140_n).

[0091] For example, the coupled cavity and quantum emitter (or cavity-coupled quantum emitter) described herein may be used in embodiments relating to generating one of the exemplary configurations of a cavity-coupled quantum emitter, for example, a photon graph state, or one shown in Figures 13A to 13D (e.g., exemplary cavities 1202_1, 1202_n and exemplary quantum emitters 1206_1, 1206_n shown in Figures 13A, 13B, and 13C).

[0092] For example, the coupled cavity and quantum emitter (or cavity-coupled quantum emitter) described herein may be used in embodiments relating to generating one of the exemplary configurations of a cavity-coupled quantum emitter, for example, a photon graph state for quantum computation, or one of those shown in Figures 14A, 15A-15C (e.g., the exemplary cavity 1404 and exemplary quantum emitter 1402 shown in Figure 14A, or the exemplary resonator 1434 and exemplary quantum emitter 1432 shown in Figures 15A-15C).

[0093] For example, the coupled cavity and quantum emitter (or cavity-coupled quantum emitter) described herein may be used in embodiments relating to entangling one of the exemplary configurations of a resonator-coupled quantum emitter, such as a photon graph, or one shown in Figures 11A to 11D (e.g., the exemplary resonator 1733 and exemplary quantum emitter 1731 shown in Figure 11C or Figure 11D).

[0094] For example, the coupled cavity and quantum emitter (or cavity-coupled quantum emitter) described herein may be used in embodiments relating to one of the exemplary configurations of a resonator-coupled quantum emitter, for example, an N-configuration resonator-coupled quantum emitter, or those shown in Figures 16A to 16D (for example, exemplary resonators 1833, 1863 and exemplary quantum emitter 1831 shown in Figures 16B to 16D).

[0095] For example, the coupled cavity and quantum emitter (or cavity-coupled quantum emitter) described herein may be used in embodiments relating to the use of one of the exemplary configurations of a resonator-coupled quantum emitter, such as a messenger-less connection or those shown in Figures 17A to 17D (e.g., exemplary resonators 1904, 1944 and exemplary quantum emitters 1902, 1942 shown in Figures 17B and 17C).

[0096] The use of micron-scale optical cavities in at least some of these non-limiting examples allows for the coupling of a single photon (or alternatively, two or more photons) to a single atom, thereby allowing that optical cavity-coupled atom to be used as a photon generator, as shown in Figures 8–9B, or as an atom from which input photons can establish entangled states, as shown in Figures 8, 9A, and 9C.

[0097] For example, rubidium bonded to cavity 810 shown in Figure 8 ( 87 The Rb) atom may be used in conjunction with a waveguide (e.g., formed using a fiber 816, nanofiber, or on-chip waveguide) to generate photons ("single-photon source" 812 or "photon generator") or to entangle photons passing through ("entanglement gate" 814, e.g., a controlled Z gate (CZ gate)).

[0098] As illustrated by the example shown in Figure 9A, the waveguide may include a utility waveguide 910 that carries pulses that generate a trap to trap Rb atoms 820 at the coupling site, for example, next to the cavity 818 (or a resonator or ring shape in the figure). The pulses may be configured to generate an evanescent field around waveguide 910, and as a result, the evanescent field trap can be used to trap Rb atoms 820 at the coupling site. The parameters of the pulse that generates the evanescent field may be determined based on the Rb atoms 820 (or any other quantum emitter used at that location), the cavity 818, the coupling site, and / or the specific mechanisms of waveguides 816, 910, 930. The pulses may be configured so that the pulses can trap cold atoms (Rb atoms 820 or quantum emitters) in the vicinity of the optical nanofiber (waveguide 816). As a non-limiting example, in an optical nanofiber with a diameter of approximately 400 nm, the majority of the fiber guide light propagates in an evanescent field in the surrounding vacuum. An optical dipole trap can then be generated in this evanescent field when pulses having two wavelengths are injected in the nanofiber as guide mode. The first pulse may be red-detuned and configured to pull atoms toward the nanofiber, with a stronger evanescent field. The second pulse may be blue-detuned and configured to provide a repulsive potential that prevents (or hinders) atoms from colliding with the surface of the nanofiber. The combination of the two contributions may result in the smallest potential at a coupling site located, for example, about 200 nm away from the surface of the nanofiber. In one embodiment, the red-detuned pulse may have a wavelength of 850 nm (or, for example, 980 nm), and the blue-detuned pulse may have a wavelength of 690 nm (or, for example, 720 nm). The detector 951 may be located at the end of the utility waveguide 910 that carries the pulses that generate the trap, and as a result the pulses may be detected at the detector 951, and appropriate control of the pulses may be performed based on measurements from the detector 951.

[0099] As illustrated by the example in Figure 9A, the waveguide may also include a quantum waveguide 930 that outputs a photon. This output photon may be a photon produced by an Rb atom 820 (when the cavity QED is used as a photon source 812) or an entangled photon that is in an entangled state with an Rb atom 820 (when the cavity QED is used as an entanglement (CZ) gate 814 and the photon is input through the quantum waveguide 930 and carried by the quantum waveguide 930). This facilitates single-photon generation, CZ gates, or atomic state readout. The switch / router 970 may be positioned on the output channel side of the quantum waveguide 930, so that, if measurement (or detection) of the output photon is required, the output photon is directed to a detector 952 located at a branch of the quantum waveguide 930 that branches off from the quantum waveguide 930.

[0100] When the configuration is used for photon generation 812, as shown by the atom 820 coupled to the cavity 818 configuration example in Figure 9B, the utility waveguide 910 can be connected to the pump laser input and carry blue and red lasers that trap the atom 820 at the coupling position between waveguide 910 and cavity 818 (resonator). Another waveguide (e.g., quantum waveguide 930) may be provided within the interaction distance of cavity 818 (resonator) so that generated photons can be carried by the other waveguide.

[0101] When the configuration is used for an entangled (CZ) gate 814, as shown by the atom 820 coupled to the cavity 818 configuration example in Figure 9C, the utility waveguide 910 can carry blue and red lasers that trap the atom 820 at the coupling position between waveguide 910 and cavity 818 (resonator). Another waveguide (e.g., quantum waveguide 930) may be provided within the interaction distance of cavity 818 (resonator) to facilitate interaction between the carried photon and the trapped atom 820, thereby causing the carried photon to become entangled with the atom 820 and output as an entangled photon.

[0102] According to embodiments of the present disclosure, the perforated vacuum chamber 1013 may be used in an exemplary mechanism 1011 shown in Figure 10, which includes a combination of one or more optical chips 1015 with a cold atomic source 1017-based resource state generator (RSG), the combination forming part of a hybrid system 1011, in which one or more lasers 1033 and a controller (or control system 1031) provide input to an optical chip 1015 that controls its operation, or to a magneto-optical trap (MOT) that traps one or more atoms 1020 from the cold atomic source 1017, and a photon detector 1035 connected to the optical chip 1015 detects photons in or from the optical chip 1015, and as a result the optical chip 1015 can be controlled to output a cluster state 1041 of photon states. For example, either or both of the controller (or control system 1031) and / or the optical chip 1015 may include circuitry and / or at least one processor and at least one memory, the circuitry and / or at least one processor being configured to perform some or all of the steps of the quantum computing method described herein according to some embodiments of this disclosure.

[0103] Some embodiments involve multiple photon cavities, each associated with a coupling site and a quantum emitter. A cavity refers to a structure, housing, or container that can function as a resonator, which is a component that establishes or supports vibrations, as described above. Thus, a photon cavity may refer to a resonator (or component) that establishes or supports electromagnetic modes associated with photons. For example, a photon cavity may correspond to a cavity in a cavity-QED configuration, an optical cavity, a whispering gallery-mode cavity, or a Fabry-Perot cavity. A coupling site includes an area (e.g., volume or region) configured to enable coupling between a quantum emitter and a photon cavity. For example, a coupling site may include an area that positions the quantum emitter within the internal cavity field of the photon cavity, as described above, or an area that allows the dipole field of the quantum emitter to overlap with the electromagnetic modes of the photon cavity. For example, when a quantum emitter is in a coupled position, it can couple with a photon cavity, thereby allowing the quantum emitter to interact with the electromagnetic modes of the established or supported photon cavity. A quantum emitter refers to a component configured to couple with electromagnetic modes, as described above. For example, a quantum emitter includes a stationary quantum system having an anharmonic spectrum configured to couple with electromagnetic modes. In other words, a quantum emitter can be a stationary qubit capable of interacting with photons.

[0104] When a quantum emitter is coupled to a photon cavity (also called a photon cavity-coupled quantum emitter) at its associated coupling position, the quantum emitter is coupled to the electromagnetic modes of the photon cavity. Thus, the quantum emitter has a quantum emitter dipole field that overlaps with the electromagnetic modes of the photon cavity, and a photon cavity-coupled quantum emitter can be configured to release or emit photons when excited (e.g., function as a photon generator) or to interact with photons passing through the photon cavity (e.g., function as an entanglement gate that entangles photons). Thus, by providing or having multiple photon cavities associated with the coupling position and the quantum emitter, it is possible to release or emit multiple photons, interact with multiple photons, or interact with photons multiple times.

[0105] For example, multiple photon cavity coupled quantum emitters can be used as multiple photon generators. These photon generators can provide multiple single photons simultaneously (e.g., in parallel). Multiple photon cavity coupled quantum emitters can be used as multiple entanglement gates. These entanglement gates can operate to entangle multiple photons simultaneously (e.g., in parallel). Alternatively, multiple photon cavity coupled quantum emitters can be used as a combination of photon generators and entanglement gates (e.g., as a group of components comprising at least one photon generator and at least one entanglement gate) to generate and interact with photons. As previously stated, a photon generator refers to a source of individual photons, and an entanglement gate refers to a component, group of components, or control sequence configured to entangle qubits, in this case photons or optical qubits. For example, an entanglement gate may include a quantum circuit configured to entangle optical qubits.

[0106] As a non-limiting example, Figures 4A and 4B show source unit 401 implemented as a photon generator (including source unit atom 402 as a quantum emitter), Figures 8-9B show rubidium (87Rb) atom 820 as a quantum emitter coupled to cavity 818 to function as a photon generator, Figures 5A and 5B show entanglement unit 501 implemented as an entanglement gate (including entanglement unit atom 502 as a quantum emitter), and Figures 8 and 9C show rubidium (87Rb) atom 820 as a quantum emitter coupled to cavity 818 to function as an entanglement gate.

[0107] When used in entanglement gates, each quantum emitter (associated, for example, with a coupling position and one of the photon cavities) may mediate interactions between consecutive incident optical qubits to produce, for example, a graph state (or a plurality of graph states) as an output. As previously stated, a graph state represents a relationship between a group of qubits, and a qubit is the fundamental unit of quantum information. Thus, the graph state (or a plurality of graph states) generated from consecutive incident optical qubits represents a relationship between qubits that is stored (or belongs to) the output photon. The photon generator may be provided, for example, to enable interactions between consecutive incident optical qubits via quantum emitters, to supply photons to each of a plurality of photon cavities. In some embodiments of this disclosure, the photon generator may include one or more photon cavity coupled quantum emitters configured to supply photons. Each of the plurality of photon cavities may facilitate interactions between optical qubits and their associated quantum emitters. Multiple output channels can also be positioned downstream of multiple photon cavities to output graph states after the interaction between the optical qubit and the associated quantum emitter. For example, each photon cavity may have an associated output channel that outputs a graph state. Alternatively, some or all of the multiple photon cavities may share an output channel that outputs a graph state.

[0108] As a non-limiting example, Figure 12A shows a preferred implementation of a quantum computing system 1100 relating to providing multiple cavities that generate graph states. The quantum computing system 1100 in Figure 12A is merely intended to facilitate the conceptualization of one preferred implementation of a quantum computing system and does not limit this disclosure to any particular implementation. Output graph states or multiple graph A state can be, for example, one or more time-sequentially entangled photons, which can be used as qubits for quantum computing purposes. System 1100 may include a plurality of entanglement gates 1102_1 to 1102_n, each containing a configuration suitable for entangling optical qubits as described above, where n is any integer greater than 1. Each of the entanglement gates 1102_1 to 1102_n can receive a series of input photons 1106_1 to 1106_n from the photon generator 1104. Each of the entanglement gates 1102_1 to 1102_n can output a series of time-sequentially entangled photons 1108_1 to 1108_n to form a photon graph state 1110_1 to 1110_n or 1122. Figure 12A depicts the input photons 1106_1~1106_n as separate photons without connectors between them, showing the state of the input photons 1106_1~1106_n before they are input to the entanglement gate 1102_1~1102_n. Before the input photons 1106_1~1106_n are input to the entanglement gate 1102_1~1102_n, the states of the input photons 1106_1~1106_n are independent; in other words, the input photons 1106_1~1106_n are not entangled (they are untangled), and there is no correlation between the input photons 1106_1~1106_n. Symmetrically, a temporally continuous series of output photons 1108_1~1108_n are connected via a double line 1108a to show their entanglement. Photon entanglement occurs when the states of two or more photons are intertwined with each other's states. knotThis refers to the attached state. For example, the states of two or more photons may be related to each other and cannot be described independently of each other. This entanglement can, for example, generate a correlation between the measured values ​​of those states, thereby allowing mutual information to be stored or processed using this correlation.

[0109] In Figure 12A, the entangled gate 1102_1 includes a first waveguide 1118_1, a photon cavity 1112_1, a quantum emitter 1114_1, a second waveguide 1120_1, and a coupling position 1116_1 located between the photon cavity 1112_1 and the second waveguide 1120_1. Similarly, in Figure 12A, the entangled gate 1102_n includes a first waveguide 1118_n, a photon cavity 1112_n, a quantum emitter 1114_n, a second waveguide 1120_n, and a coupling position 1116_n located between the photon cavity 1112_n and the second waveguide 1120_n. In the following description, the details provided for entanglement gate 1102_1 may also apply to entanglement gate 1102_n.

[0110] Some embodiments involve quantum computation. Quantum computation may refer to computation performed through the use or application of one or more quantum state properties, such as superposition, entanglement, and interference. Some embodiments involve a quantum computing system, which may include components or groups of components configured to facilitate the performance of computations or operations via quantum computation. For example, a quantum computing system may generate a graph state which may include multiple temporally consecutive sequences of entangled photons to be used as qubits in quantum computation.

[0111] As a non-limiting example, Figure 12A shows a preferred implementation of a quantum computing system 1100 consistent with some embodiments of the present disclosure. The quantum computing system 1100 in Figure 12A includes a plurality of entanglement gates 1102_1 to 1102_n. Each of the entanglement gates 1102_1 to 1102_n may receive a series of consecutive input photons 1106_1 to 1106_n from a photon generator 1104. The entanglement gates 1102_1 to 1102_n may collectively generate one of the graph states 1110_1 to 1110_n and / or 1122 from the input photons 1106_1 to 1106_n, which are associated with a time-sequential series of entangled photons 1108_1 to 1108_n.

[0112] Some embodiments involve multiple photon cavities. A cavity, as described above, refers to a structure, housing, or container that can function as a resonator, which is a component that establishes or supports resonant oscillations at a discrete set of resonant frequencies. Thus, a photon cavity may refer to a resonator (or component) that establishes or supports electromagnetic modes associated with photons.

[0113] As a non-limiting example, Figures 12A and 12B show preferred implementations of a plurality of photon cavities 1112_1~1112_n and 1138_1~1138_n according to some embodiment relating to providing a plurality of cavities that generate graph states. The photon cavities 1112_1~1112_n may each be contained within an entanglement gate 1102_1~1102_n, and can facilitate the generation of either graph states 1110_1~1110_n or 1122 associated with a time-sequential series of entangled photons 1108_1~1108_n. The photon cavities 1138_1~1138_n may each be contained within a photon generation unit 1132_1~1132_n, and can facilitate the generation of one or more photons.

[0114] Some embodiments involve multiple coupling positions for quantum emitter positioning. A coupling position includes an area configured to enable coupling between the quantum emitter and the photon cavity, as described above. For example, by positioning the quantum emitter at a coupling position, the quantum emitter can couple with the photon cavity, thereby allowing the quantum emitter to interact with the electromagnetic modes of the established or supported photon cavity. A quantum emitter refers to a component configured to couple with electromagnetic modes, as described above. Quantum emitter positioning refers to arranging or positioning the quantum emitter to enable interaction between the quantum emitter and the photon cavity, as described above. Therefore, a quantum computing system may position multiple quantum emitters. death, This forms multiple coupling pairs between the quantum emitter and the photon cavity. Includes multiple bonding positions for This allows for, for example, multiple simultaneous (e.g., parallel) interactions between multiple quantum emitters and multiple photon cavities.

[0115] As a non-limiting example, Figures 12A and 12B show preferred implementations of a plurality of coupling positions for quantum emitter positioning according to some embodiments of the present disclosure. The entanglement gates (1102_1~1102_n) and photon generation units (1132_1~1132_n) each include coupling positions (1116_1~1116_n and 1142_1~1142_n), respectively. The coupling positions (1116_1~1116_n and 1142_1~1142_n) are located between the photon cavities (1112_1~1112_n and 1138_1~1138_n) and their respective corresponding waveguides (1120_1~1120_n and 1134_1~1134_n). Positioning (e.g., confinement or trapping) the quantum emitters (1114_1~1114_n and 1140_1~1140_n) between their respective coupling positions (1116_1~1116_n and 1142_1~1142_n), for example, between the corresponding waveguides (1120_1~1120_n and 1134_1~1134_n) and the corresponding photon cavities (1112_1~1112_n and 1138_1~1138_n), enables interaction between the quantum emitters (1114_1~1114_n and 1140_1~1140_n) and the corresponding photon cavities (1112_1~1112_n and 1138_1~1138_n).

[0116] In some embodiments, each coupling position is associated with a different photon cavity among a plurality of photon cavities. This association refers to relating or corresponding to. Thus, each coupling position may be associated with or correspond to a different photon cavity so that each photon cavity can couple with one or more quantum emitters that are positioned at its associated or corresponding coupling position (e.g., only its corresponding coupling position).

[0117] As a non-limiting example, Figure 12A shows preferred implementations of each coupling position associated with different photon cavities among a plurality of photon cavities. Coupling position 1116_1 is associated with photon cavity 1112_1, coupling position 1116_n is associated with photon cavity 1112_n, and each of photon cavities 1112_1 and 1112_n is a different, for example, separate photon cavity. Figure 12B also shows preferred implementations of each coupling position associated with different photon cavities among a plurality of photon cavities, coupling position 1142_1 is associated with photon cavity 1138_1, coupling position 1142_n is associated with photon cavity 1138_n, and each of photon cavities 1138_1 and 1138_n is a different, for example, separate photon cavity.

[0118] In some embodiments of this disclosure, the quantum emitter associated with each coupling position is configured to mediate interactions between consecutive incident optical qubits to generate a graph state. Mediation means facilitating, enabling, or otherwise promoting the interaction. The interaction can transfer, transmit, associate, and / or establish correlations between incident optical qubits. For example, the quantum emitter may facilitate entanglement (e.g., interaction) between incident photons, and the quantum emitter is a means to achieve such interaction between incident photons. Consecutive means following or being continuous, for example, coming successively in time. Optical qubit refers to a fundamental unit of quantum information stored (or belonging to) one or more photons or electromagnetic fields, as described above. For example, optical qubit includes a qubit encoded with degrees of freedom associated with the propagation or stationary mode of an electromagnetic field. Optical qubits may exhibit properties specific to quantum mechanical systems, such as superposition and / or entanglement (e.g., between multiple optical qubits or with a quantum emitter qubit) with respect to degrees of freedom (e.g., one or both of the vertical and horizontal polarization states). Thus, each coupling position may have a corresponding (e.g., associated) quantum emitter positioned thereto to facilitate interaction (e.g., entanglement) between consecutive incident optical qubits by the corresponding (e.g., associated) quantum emitter, thereby generating a graph state. For example, each quantum emitter may facilitate entanglement of multiple optical qubits.

[0119] As a non-limiting example, Figure 12A shows a preferred implementation of a quantum emitter associated with each coupling position and configured to mediate interactions between consecutive incident optical qubits to generate a graph state, consistent with some embodiments of the present disclosure. The entanglement gate 1102_1 includes a quantum emitter 1114_1 associated with coupling position 1116_1. The photon generator 1104 provides a plurality of single photons to the entanglement gate 1102_1 via waveguide 1118_1, for example, as consecutive individual input photons 1106_1. The input photons 1106_1 are not entangled with each other (or are in an unentangled state), as indicated by the absence of connecting double lines between them. The entanglement gate 1102_1 is configured such that each photon of the input photon 1106_1 interacts with the quantum emitter 1114_1 via the photon cavity 1112_1, thereby causing the optical qubits of the input photon 1106_1 to become entangled with the qubits of the quantum emitter 1114_1. When multiple photons from the input photon 1106_1 undergo this interaction with the quantum emitter 1114_1, these multiple photons become entangled with each other. As a result, the consecutive incident optical qubits become entangled and are output as entangled output photons 1108_1. In other words, the quantum emitter 1114_1 mediates the interaction between consecutive incident optical qubits. As a result of this interaction, the output photons 1108_1 become entangled with each other, as indicated by the interconnected double lines 1108a. Similarly, the entanglement gate 1102_n includes a quantum emitter 1114_n associated with the coupling position 1116_n. The entanglement gate 1102_n can also receive an input photon 1106_n and mediate the interaction between them to produce an entangled output photon 1108_n, as indicated by the interconnected line 1108a.

[0120] According to certain embodiments of this disclosure, a quantum emitter may be a stationary qubit capable of interacting with photons. If both are present, the stationary qubit may be capable of interacting with protons. In a non-limiting example, a quantum emitter may be a stationary quantum system having an anharmonic spectrum configured to couple to electromagnetic modes. For example, a quantum emitter may include a quantum system having one or more of the following: an electronic or nuclear configuration of an ion or neutral atom, an electronic or nuclear configuration of a defect or quantum dot in a material substrate, or a configuration of a superconducting circuit including one or more Josephson junctions. Figure 12A shows a non-limiting example of such a quantum emitter according to a certain embodiment relating to providing a plurality of cavities that generate graph states. The quantum emitter 1114_1 may float (e.g., be trapped) between the photon cavity 1112_1 and the waveguide 1120_1, allowing the quantum emitter 1114_1 in the coupling position 1116_1 to interact with photons (e.g., incident optical qubits) carried by the waveguide 1118_1 via the photon cavity 1112_1.

[0121] For example, a quantum emitter may include a superconducting qubit. A superconducting qubit, as mentioned above, refers to a qubit that is stored in or belongs to a superconducting electronic circuit (e.g., a network of electrical elements using superconductors). Referring to Figure 12A or Figure 12B, one or more of the quantum emitters 1114_1~1114_n or 1140_1~1140_n may include a superconducting electronic circuit or a superconducting qubit.

[0122] A quantum emitter may include, for example, a quantum dot. A quantum emitter including a quantum dot may refer to a quantum emitter having a solid-state substrate (e.g., semiconductor particles) that exhibits optical and / or electronic properties that demonstrate quantum mechanical principles, as described above. Referring to Figure 12A or Figure 12B, one or more of the quantum emitters 1114_1 to 1114_n or 1140_1 to 1140_n may include a quantum dot.

[0123] A quantum emitter may include, for example, an atom. Referring to Figure 12A or Figure 12B, one or more of the quantum emitters 1114_1 to 1114_n or 1140_1 to 1140_n may include an atom such as atom 102 in Figure 1. According to some embodiments of the present disclosure, an atom is neutral. Neutral refers to an atom that has no charge overall, such as when the number of protons in the atom is equal to the number of electrons. According to some embodiments of the present disclosure, an atom is an ion. An ion refers to a particle or atom that has a charge overall, such as an atom with an unequal number of protons and electrons. According to some embodiments of the present disclosure, a quantum emitter includes a rubidium atom as described above. A rubidium atom can be neutral or an ion. According to some embodiments of the present disclosure, a quantum emitter includes a cesium atom as described above. According to some embodiments of the present disclosure, a quantum emitter includes at least one of strontium, erbium, ytterbium, calcium, barium, beryllium, or magnesium atoms as described above.

[0124] According to some embodiments, a photon generator is configured to supply photons to a plurality of photon cavities, and these supplied photons may function as incident photons to which incident optical qubits belong or are associated. A photon generator refers to a component or group of components configured to provide one or more photons.

[0125] For example, a photon generator may refer to a source of individual photons as described above with respect to Figures 8 to 9B. As another example, a photon generator may correspond to the photon source unit 401 in Figure 4A. Thus, a photon generator may supply one or more photons, for example, supplying a plurality of consecutive individual photons to each of a plurality of photon cavities. As a non-limiting example, Figures 12A, 12B, and 12D show a preferred implementation of a photon generator configured to supply or generate photons according to a certain embodiment relating to providing a plurality of cavities that generate a graph state. These photons can then be supplied to the plurality of photon cavities to supply incident optical qubits consistent with certain embodiments of the present disclosure. Photon generators 1104 and 1130 may supply an input photon 1106_1 (or photon 1146_1 in Figure 12D) to a photon cavity 1112_1 via a waveguide 1118_1. Photon generators 1104 and 1130 may also supply input photons 1106_n (or photon 1146_1 in Figure 12D) to photon cavity 1112_n via waveguide 1118_n. It is understood that multiple photon generators may exist, each capable of supplying input photons to one or more photon cavities.

[0126] In some embodiments of this disclosure, a photon cavity is configured to couple an optical qubit to a quantum emitter. Coupled an optical qubit to a quantum emitter means facilitating interaction between the optical qubit and the quantum emitter. For example, such interaction can be facilitated when there is no physical contact between the optical qubit and the quantum emitter. The photon cavity can function, for example, as a means to enable such interaction between the optical qubit and the quantum emitter. Such interaction can result in, for example, a statistical correlation or correspondence between the physical behavior of the optical qubit and the physical behavior of the quantum emitter. Therefore, by coupling an optical qubit to a quantum emitter, the photon cavity can result in a statistical correlation between the physical behavior of the optical qubit and the physical behavior of the quantum emitter. For example, a change in the state of an optical qubit may occur simultaneously with a corresponding change in the state of the quantum emitter qubit coupled to it. The photon cavity may function, for example, as a means to enable an optical qubit to become entangled with a quantum emitter qubit, which can be achieved by such coupling between the optical qubit and the quantum emitter. For example, the coupled optical qubit may correspond to or be associated with an input photon (or incident photon) received from a photon generator.

[0127] As a non-limiting example, Figures 12A and 12D show a preferred implementation of a photon cavity configured to couple an optical qubit to a quantum emitter, according to a certain embodiment relating to providing a plurality of cavities that generate graph states. Each of the photon cavities 1112_1 to 1112_n can enable an optical qubit (associated, for example, with input photons 1106_1 to 1106_n in Figure 12A or photon 1146_1 in Figure 12D) to be coupled with a quantum emitter 1114_1 to 1114_n. This coupling then enables, for example, entanglement between the input photons 1106_1 to 1106_n in Figure 12A or photon 1146_1 in Figure 12D and the quantum emitter 1114_1 to 1114_n.

[0128] Some embodiments of this disclosure involve a plurality of photon output channels located downstream of a plurality of cavities that output graph states. Downstream means what happens next, what follows, or what comes after. For example, downstream may mean being positioned to follow in the direction of a temporal or spatial flow or progression. Upstream cavities may be the plurality of photon cavities described above. The plurality of photon output channels may be positioned, for example, in the direction of a spatial flow of input photons. For example, the plurality of photon output channels may be located between the plurality of cavities and the output graph states. The photon output channels may carry or transport a temporally continuous series of entangled photons (e.g., entangled using a photon cavity coupled quantum emitter) to the output, thereby outputting graph states formed from such entangled photons.

[0129] As a non-limiting example, Figure 12A shows a preferred implementation of a plurality of photon output channels downstream of a plurality of cavities that output graph states, according to a certain embodiment relating to providing a plurality of cavities that generate graph states. The plurality of photon output channels, each carrying or transporting a sequence of entangled photons 1108_1~1108_n, are located following (e.g., after or downstream) the photon cavities 1112_1~1112_n, respectively. The entangled photons 1108_1~1108_n can form one or more graph states, which are the output of the quantum computing system 1100 in Figure 12A. Examples of such output graph states include graph state 1110_1 corresponding to entangled photon 1108_1, graph state 1110_n corresponding to entangled photon 1108_n, and graph state 1112 (sometimes referred to as a cluster state, whose graph is a connected subset d-dimensional lattice) formed from combinations of entangled photons 1108_1 to 1108_n. Note that graph states 1110_1 to 1110_n and cluster state 1122 are merely intended as preferred conceptual illustrations and do not limit this disclosure to any particular graph state or cluster.

[0130] Some embodiments involve a photon generator that includes at least one additional photon cavity. In embodiments that include an entanglement gate for entangling photons, the additional photon cavity may be provided to supply photons to the entanglement gate. In embodiments that include a photon generator, the additional cavity may be provided to function as an additional photon generator. As previously stated, with respect to the photon cavity, the additional photon cavity may also be coupled to a quantum emitter, which may interact with the establishment or supported electromagnetic mode of the additional photon cavity to enable the additional photon cavity coupled quantum emitter to release or generate one or more photons when excited. Excitation may occur, for example, using a laser carried in a nearby waveguide 910 as shown in Figure 9B. This allows the additional photon cavity and quantum emitter to function as a photon generator. For example, some embodiments relating to providing multiple cavities that generate graph states may involve a photon generator that functions as photon generator 1104 in Figure 12A.

[0131] In some embodiments of the present disclosure, the photon generator also includes at least one additional quantum emitter and at least one additional coupling position for quantum emitter positioning, each additional coupling position being associated with a different photon cavity of at least one additional photon cavity. The additional quantum emitters may be additions to quantum emitters already provided in the entanglement or photon generator. The quantum emitters may have a configuration similar to that described above. If additional photon cavities are employed as described above, additional coupling positions may be provided. The additional coupling positions, which may have a configuration similar to that described above, may enable the additional quantum emitters to couple to the additional photon cavity and thereby function as a photon generator.

[0132] The photon source units that secure single photons described herein are non-limiting examples of such photon generators. For example, Figures 8–9B show that a rubidium (87Rb) atom 820 as a quantum emitter coupled to cavity 818 can function as a photon generator. As another example, Figures 4A and 4B show one preferred implementation of a photon generator (e.g., source unit 401) that includes at least one additional photon cavity. Source unit 401 includes an optical cavity such as optical cavity 103 in Figure 1, and an atom 402 (e.g., a quantum emitter). After an initialization pulse 403 initializes the state of atom 402 to state 111 (Figure 1), a generation pulse 404 brings about transitions 121A and 122A in Figure 2A, as a result of atom 402 emitting a photon 406. By repeating this process, a temporally consecutive series of output photons 412 in Figure 4B are generated. The output photon can then be supplied to one of the entanglement gates 1102_1 to 1102_n, allowing the entanglement gate to generate graph states 1110_1 to 1110_n.

[0133] As a non-limiting example, Figure 12B shows a photon generator 1130 according to one embodiment relating to providing multiple cavities. Photon generator 1130 is intended to facilitate the conceptualization of a preferred photon generator and does not limit the present disclosure to the details of a particular implementation. It can be understood that additional configurations, modifications, and implementations may function as photon generators for use in some embodiments of the present disclosure. Photon generator 1130 in Figure 12B includes at least one additional photon cavity (e.g., photon cavities 1138_1 to 1138_n) in at least one photon generation unit 1132_1 to 1132_n. If photon generator 1130 is used as photon generator 1104 in quantum computing system 1100, the at least one additional photon cavity is an addition to the photon cavities 1112_1 to 1112_n of quantum computing system 1100 in Figure 12A. Although the photon generator 1130 is shown having multiple photon cavities 1138_1 to 1138_n and multiple photon generation units 1132_1 to 1132_n, this is merely illustrative, and the photon generator 1130 may be implemented with a single additional photon cavity and a single photon generation unit.

[0134] The following description refers to multiple photon generation units 1132_1 to 1132_n, but this is merely a preferred implementation, and the photon generator 1130 may be implemented using a single photon generation unit. The photon generation units 1132_1 to 1132_n in Figure 12B are arranged similarly to the entanglement gates 1102_1 to 1102_n in Figure 12A. Each photon generation unit 1132_1 to 1132_n has a first waveguide 1134_1 to 1134_n, a second waveguide 1136_1 to 1136_n, a photon cavity 1138_1 to 1138_n, and a quantum emitter 1140_1 to 1140_n. The quantum emitters 1140_1~1140_n can be positioned at their associated coupling positions 1142_1~1142_n, which are located between their associated photon cavities 1138_1~1138_n and the first waveguide 1134_1~1134_n (for example, they can float or be trapped). For example, with respect to the single-photon source 812 in Figure 9B, as described above, the first waveguides 1134_1~1134_n can carry a laser (e.g., pulses of photons 1144_1~1144_n) that positions or traps the quantum emitters 1140_1~1140_n at their coupling positions 1142_1~1142_n, and furthermore, the first waveguides 1134_1~1134_n can carry a laser (e.g., pulses of photons 1144_1~1144_n) that excites the quantum emitters 1140_1~1140_n and generates output photons 1146_1~1146_n that are output via the second waveguides 1136_1~1136_n.

[0135] For example, the pulse of photons 1144_1 to 1144_n can alternate between an initialization photon (e.g., photon 403) and a generation photon (e.g., photon 404), as described above with respect to Figures 4A and 4B.

[0136] The photon cavities 1138_1~1138_n are coupled to the corresponding quantum emitters 1140_1~1140_n, allowing the (additional) photon cavity-coupled quantum emitters 1140_1~1140_n to release or generate one or more photons 1146_1~1146_n when excited.

[0137] The released or generated photons 1146_1~1146_n may be supplied to the entangled gate 1102_1~1102_n in Figure 12A as input photons 1106_1~1106_n, as shown in Figure 12D. In other words, in some embodiments relating to providing multiple cavities that generate graph states, the consecutive output photons 1146_1~1146_n in Figure 12B may correspond to the input photons 1106_1~1106_n in Figure 12A, and therefore may be supplied to the entangled gate 1102_1~1102_n via waveguides 1118_1~1118_n, as shown in Figure 12D.

[0138] Therefore, as a non-limiting example, Figure 12D shows a plurality of cavities that generate graph states, where a photon generation unit 1132_1 (having a photon cavity 1138_1) is used as photon generators 1130 and 1104 that supply a photon 1146_1 to an entanglement gate 1102_1 (having a photon cavity 1112_1) to generate a graph state 1110_1 associated with an entanglement output photon 1108_1. In some embodiments of the present disclosure relating to providing a plurality of cavities that generate graph states, the quantum computing system comprises a plurality of such combinations of photon generation units 1132_1 and entanglement gates 1102_1, each combination configured to generate a graph state. In some embodiments of the present disclosure relating to providing a plurality of cavities that generate graph states, the plurality of photon generation units may supply photons to a single entanglement gate. In some other embodiments of the present disclosure relating to providing multiple cavities that generate graph states, one photon generation unit may supply photons to multiple entanglement gates. In these embodiments of the present disclosure relating to providing multiple cavities that generate graph states, a controller controls the flow of input and output photons between the photon generation unit and the entanglement gates (for example, Directional between different waveguides also is cut It may be provided to replace it. For example, the controller may include one or more processors. Memory, circuit components, or circuits may also be provided to perform control.

[0139] The second waveguides 1136_1~1136_n can carry fields that couple to specific electromagnetic modes or multiple modes of the photon cavities 1138_1~1138_n to generate output photons 1146_1~1146_n.

[0140] As previously stated, some embodiments of the present disclosure involve a photon generator including at least one additional quantum emitter. The above-described examples of quantum emitters in some embodiments relating to providing a plurality of cavities that generate graph states are also applicable to at least one additional quantum emitter of a photon generator. For example, at least one additional quantum emitter may include a stationary qubit that can interact with photons. Referring to Figures 12A and 12B, each of the quantum emitters 1114_1 to 1114_n may be associated with a stationary qubit that interacts with photons 1106_1 to 1106_n via the corresponding photon cavities 1112_1 to 1112_n, and each of the quantum emitters 1140_1 to 1140_n may be associated with a stationary qubit that can interact with input photons 1144_1 to 1144_n. For example, at least one additional quantum emitter may include a superconducting qubit, and in another example, at least one additional quantum emitter may include a quantum dot. At least one additional quantum emitter may include an atom such as atom 402 in Figure 4A or atom 820 in Figure 9B. In another example, at least one additional quantum emitter may include a rubidium atom as described above. In yet another example, at least one additional quantum emitter may include at least one of strontium, erbium, ytterbium, calcium, barium, beryllium, or magnesium atoms as described above.

[0141] As a non-limiting example, Figure 12C shows an exemplary process 1150 for generating a graph state, according to one embodiment relating to providing a plurality of cavities that generate a graph state. This exemplary process 1150 may be part of a quantum computing method for generating a graph state. The block diagram in Figure 12C may be described below in relation to embodiments of specific implementations presented in other figures, but such implementations are provided for illustrative purposes only and are not intended to function as limitations on the block diagram. Since examples of process steps are described throughout this disclosure, such examples described above will not be repeated or will be briefly summarized in relation to Figure 12C. In some embodiments of this disclosure, the exemplary process 1150 may be performed by at least one processor or circuit, for example, in the control system 1031 and / or optical chip 1015 in Figure 10, to perform the operation or function described herein. In some embodiments of this disclosure, some aspects of the process 1150 may be implemented as software (e.g., program code or instructions) stored in memory provided by at least one processor or in a non-temporary computer-readable medium or in a computer-readable medium. In some embodiments, certain aspects of process 1150 may be implemented as hardware (e.g., dedicated circuitry). In some embodiments, process 1150 may be implemented as hardware or as a combination of software and hardware.

[0142] Figure 12C includes process steps (or method steps) 1152 to 1156. In step 1152, the process or method involves coupling quantum emitters at each of a plurality of coupling positions, so that each of the plurality of quantum emitters is associated with a different coupling position, each coupling position is associated with a different photon cavity among a plurality of photon cavities, and the quantum emitters associated with each coupling position are configured to generate a graph state by mediating the interaction between consecutive incident optical qubits. For example, Figure 12A shows a preferred implementation of a plurality of quantum emitters (e.g., quantum emitters 1114_1 to 1114_n) coupled at a plurality of coupling positions (e.g., coupling positions 1116_1 to 1116_n), such that each quantum emitter is associated with a different coupling position (e.g., quantum emitter 1114_1 is associated with coupling position 1116_1, quantum emitter 1114_n is associated with coupling position 1116_n). Furthermore, each coupling position is associated with a different photon cavity among the photon cavities (for example, coupling position 1116_1 is associated with photon cavity 1112_1, and coupling position 1116_n is associated with photon cavity 1112_n). Each of the quantum emitters 1114_1 to 1114_n associated with the corresponding coupling positions 1116_1 to 1116_n is configured to mediate the interaction between consecutive incident optical qubits (for example, associated with input photons 1106_1 to 1106_n) to generate a graph state (for example, one of the graph states 1110_1 to 1110_n and 1122).

[0143] In step 1154, the process involves supplying photons to a plurality of photon cavities, which are configured to couple optical qubits to quantum emitters. For example, Figure 12A shows a preferred implementation of supplying photons to a plurality of photon cavities configured to couple optical qubits to quantum emitters. The photon generator 1104 is configured to supply input photons 1106_1 to 1106_n to photon cavities 1112_1 to 1112_n via waveguides 1118_1 to 1118_n. Similarly, the photon generator 1130 or photon generation unit 1132_1 in Figure 12B may, as shown in Figure 12D, supply output photons 1146_1~1146_n as input photons 1106_1~1106_n via waveguides 1118_1~1118_n of entanglement gates 1102_1~1102_n toward the photon cavity 1112_1~1112_n. The photon cavity 1112_1~1112_n may then couple optical qubits (e.g., associated with input photons) toward quantum emitters 1114_1~1114_n. In other words, the photon cavities 1112_1~1112_n can facilitate the interaction between the optical qubit (e.g., associated with an input photon) and the quantum emitter 1114_1~1114_n.

[0144] In step 1156, the process, consistent with some embodiments of the present disclosure, involves outputting graph states via multiple photon output channels downstream of multiple cavities. For example, Figure 12A shows a preferred implementation where graph states are output via multiple photon output channels downstream of multiple cavities. Each entanglement gate 1102_1~1102_n outputs graph states 1110_1~1110_n of entangled photons 1108_1~1108_n. In addition, combinations of entanglement gates 1102_1~1102_n can collectively output cluster states 1122.

[0145] Some embodiments of the present disclosure involve a non-temporary computer-readable medium (or computer-readable medium or computer program) containing instructions, which, when executed by at least one processor (or device), cause at least one processor (or device) to execute a method or process according to some embodiments of the present disclosure.

[0146] For example, a non-temporary computer-readable medium (or computer-readable medium or computer program) may include instructions, which, when executed by at least one processor (or device), cause at least one processor (or device) to execute the quantum computing method described herein. According to embodiments relating to providing a plurality of cavities that generate graph states, instructions may cause at least one processor (or device) to execute the quantum computing method or process 1150 shown in Figure 12C.

[0147] The same examples described above for each system feature of an embodiment relating to providing multiple cavities that generate graph states are also applicable to corresponding features of an embodiment of this non-temporary computer-readable medium (or computer-readable medium or computer program).

[0148] According to other embodiments relating to providing multiple cavities that generate graph states, there exists an apparatus, device, system, integrated circuit device, or circuit that includes at least one processor (and memory) configured to perform a quantum computing method or process 1150 shown in Figure 12C. The same examples described above for each system feature of the embodiments relating to providing multiple cavities that generate graph states are also applicable to the corresponding features of these embodiments.

[0149] According to yet another embodiment relating to providing a plurality of cavities that generate graph states, there exists a layout of an integrated circuit device or circuit comprising layout portions, each layout portion defined to pattern each feature from a combination of features of either the quantum computing system 1100 in Figure 12A, the photon generator 1130 in Figure 12B, or the photon generator 1130 and the entanglement gate 1102_1 in Figure 12D. For example, there exists a layout of an integrated circuit device or circuit comprising: a photon cavity layout portion defined to pattern a plurality of cavities; a coupling position layout portion defined to pattern a plurality of coupling positions for quantum emitter positioning, where each coupling position is associated with a different photon cavity among the plurality of photon cavities; a photon generator layout portion defined to pattern a photon generator, or a channel that carries photons supplied to the plurality of photon cavities by the photon generator; and an output channel layout portion defined to pattern a plurality of photon output channels downstream of the plurality of cavities. In some embodiments of the present disclosure, the photon generator layout portion may be configured to pattern at least one additional photon cavity. In those embodiments of the present disclosure, the photon generator layout portion may also be configured to pattern at least one additional coupling position for quantum emitter positioning, each additional coupling position associated with a different photon cavity from the at least one additional photon cavity. In some embodiments of the present disclosure, the layout of the integrated circuit device or circuit controls the flow of input and output photons between the photon generator and the plurality of photon cavities and the plurality of photon output channels (e.g., Directional between different waveguides also is cut The controller further comprises a controller layout section defined to pattern the controller, and the controller may comprise one or more processors that perform control, and memory, circuit components, or circuits.

[0150] When quantum emitters (e.g., quantum dots) that can be installed by lithography are used, it is understood that the coupling position layout portion may be defined so that the quantum emitters are also patterned. The same examples described above for each system feature of the embodiment relating to providing multiple cavities that generate graph states are also applicable to the corresponding features of this embodiment.

[0151] Some embodiments of this disclosure involve generating a photon graph state using one or more interactions of optical qubits with quantum emitters, each quantum emitter being coupled to a cavity. Such embodiments may involve a quantum computation method for generating the photon graph state. In such a quantum computation method for generating the photon graph state, a plurality of quantum emitters may be positioned at a plurality of coupling positions associated with a plurality of different cavities (e.g., cavities that function as resonators, such as photon cavities or optical cavities, whispering gallery mode cavities, Fabry-Perot cavities, or ring-shaped cavities). The state of the quantum emitter qubit associated with each of the plurality of quantum emitters may be initialized so that the quantum emitters perform specific functions when generating the photon graph state. Such initialization refers to setting a baseline state for cavity-coupled quantum emitters (also referred to as cavity-coupled quantum emitters). For example, initialization may include establishing an initial adjustment state system for cavity-coupled quantum emitters. The initial initialization state of the system may, for example, refer to a cavity-coupled quantum emitter being in a specific state or a superposition state. For example, such initialization may involve using a laser or applying a magnetic field to the quantum emitter. The optical qubit may then be transmitted to multiple quantum emitters in at least a first instance to generate an entanglement gate (e.g., a controlled Z quantum gate or CZ gate) between the optical qubit and the quantum emitter qubit. As a non-limiting example, the entanglement gate may be implemented according to the techniques described herein with respect to Figures 3, 5A-5B, and 9C. After at least one of the transmissions in the first instance, the optical qubit may be transmitted to multiple quantum emitters in at least one second instance to generate a SWAP gate between the optical qubit and the quantum emitter qubit, which may help map the quantum emitter qubit to the optical qubit. As a non-limiting example, the SWAP gate may be implemented according to the techniques described herein with respect to Figure 2E.For example, the entanglement gate in Figure 3 may be performed multiple times (for example, n times to entangle n optical qubits with a quantum emitter qubit, as described with reference to Figure 6), followed by the SWAP gate in Figure 2E (for example, to untangle the quantum emitter qubit from the entangled optical qubit) to generate a photon graph state (for example, of the entangled optical qubit) (the quantum emitter qubit is no longer entangled with the entangled optical qubit).

[0152] For example, multiple configurations may be provided, each including at least one quantum emitter coupled to a cavity at the coupling site. Each configuration can be initialized to operate in one of several operating modes, for example, an entanglement mode in which one or more optical qubits can become entangled with a quantum emitter qubit associated with the quantum emitter, and a SWAP mode in which the state of the quantum emitter qubit is exchanged with the state of an optical qubit, thereby unentangling the quantum emitter qubit from the entangled optical qubit. In the example, since the SWAP mode involves the exchange of qubit states, an initialization pulse of one or more photons (having a specific desired state) may be used in a cavity-coupled quantum emitter operating in SWAP mode to initialize the cavity-coupled quantum emitter. By combining these configurations of different operating modes in a specific order, the quantum computing method can generate a photon graph state as an output. For example, a cavity-coupled quantum emitter can be initialized by operating it in SWAP mode and having it interact with an initialization pulse. Multiple photons can then be introduced to interact with the initialized cavity-coupled quantum emitter, which operates in entanglement mode, causing the photons to entangle with the cavity-coupled quantum emitter. The cavity-coupled quantum emitter can then operate again in SWAP mode, and photons from another pulse will exchange their state with the cavity-coupled quantum emitter, thereby unentangling the entangled photons from the cavity-coupled quantum emitter. The result is a photon graph state of the entangled photons. As a non-limiting example, Figure 6 illustrates this process.

[0153] As another non-limiting example, Figures 13A–13C show a preferred implementation of a quantum computing system 1200 that generates photon graph states, consistent with some embodiments of the present disclosure. The quantum computing system 1200 is intended merely to facilitate the conceptualization of one preferred implementation of a quantum computing system that generates photon graph states, and does not limit the present disclosure to any particular implementation. The quantum computing system 1200 may include a plurality of configurations (1214_1 to 1214_n), each configuration including a cavity (e.g., cavities 1202_1 to 1202_n) that functions as a resonator capable of establishing or supporting electromagnetic modes, and a quantum emitter (e.g., quantum emitters 1206_1 to 1206_n) positioned at coupling sites (e.g., coupling sites 1204_1 to 1204_n), where n is any integer greater than 1. Each coupling site 1204_1 to 1204_n can be associated with a different cavity among the cavities (1202_1 to 1202_n) and a different quantum emitter among the quantum emitters (1206_1 to 1206_n). For example, quantum emitter 1206_1 may be positioned at coupling site 1204_1 associated with cavity 1202_1, and quantum emitter 1206_n may be positioned at coupling site 1204_n associated with cavity 1202_n.

[0154] The quantum computing system 1200 may further include a controller 1208, waveguides (1210_1~1210_n and 1212_1~1212_n), and at least one photon generator 1230. Waveguides (1210_1~1210_n) are, for example, , conclusion At the meeting place or in the vicinity of the meeting place Around its surface By establishing an evanescent field, the quantum emitters (1206_1~1206_n) at the coupling sites (1204_1~1204_n) can be configured to facilitate positioning (e.g., trapping).

[0155] The controller 1208 may include circuits or at least one processor for controlling the operation of the configurations (1214_1 to 1214_n). For example, the controller 1208 may include switches for alternating between operating stages or configurations (1214_1 to 1214_n) operating in different modes. For example, at a given time, each configuration (1214_1 to 1214_n) may be an initialization stage (e.g., Figure 13A), an entanglement stage (e.g., Figure 13B), or a swap stage (e.g., Figure 13C), as described in more detail herein below. The controller 1208 may control the operating mode for any of the waveguides (1210_1 to 1210_n and 1212_1 to 1212_n) by controlling, for example, the timing, phase, frequency, intensity, amplitude, polarity, and any other characteristics of the pulses or lasers carried by the waveguide that may affect the operation of the configurations (1214_1 to 1214_n). For example, controller 1208 can control the properties of trap lasers (e.g., blue and red lasers) that trap or position quantum emitters at coupling locations, which can be transported within waveguides 1210_1 to 1210_n, as shown by the non-limiting examples in Figures 9A to 9C. Controller 1208 can control the properties of a magnetic field or laser that can be used while initializing one or more quantum emitters (1206_1 to 1206_n) to bring about a desired state. Controller 1208 can also control the coupling (e.g., confinement) between quantum emitters (1206_1 to 1206_n) and cavities (1202_1 to 1202_n) at coupling locations (1204_1 to 1204_n).

[0156] The controller 1208 can control the operating modes of the photon generator 1230, which are described in more detail herein below. The controller 1208 can control the synchronization and timing modes of the operation of the configurations (1214_1 to 1214_n). For example, the controller 1208 may initialize configuration 1214_1 while simultaneously operating another configuration 1214_n as an entanglement gate or a swap gate. Alternatively, the controller 1208 may carry the output from configuration 1214_n in a channel and have it function as an input to configuration 1214_1. As one non-limiting example, the controller 1208 may include switches for automatically (e.g., repeatedly) controlling one or more cycles through the initialization, entanglement, and swap phases for each of the configurations (1214_1 to 1214_n). As another non-limiting example, controller 1208 may include a clock for synchronizing the operation between different configurations of configuration (1214_1~1214_n), and optionally, the operation with additional components and / or circuits. As another non-limiting example, controller 1208 may include at least one processor for controlling the operation of configuration (1214_1~1214_n), for example, for synchronizing the operation of different configurations of configuration (1214_1~1214_n) or otherwise monitoring or managing them.

[0157] The configuration generator 1230 can be optically coupled to waveguides (1210_1~1210_n and 1212_1~1212_n) to supply photons to the configurations (1214_1~1214_n). The controller 1208 can control the operation of the photon generator 1230 to supply photons according to different operating stages of the configurations (1214_1~1214_n). For example, the controller 1208 can cause the photon generator 1230 to provide photons to initialize the quantum emitters (1206_1~1206_n) during the initialization phase, to provide photons (1226_1~1226_n) to the entanglement gates (1216_1~1216_n) during the entanglement phase, and to provide photons (1228_1~1228_n) to the SWAP gates (1218_1~1218_n) during the SWAP phase.

[0158] As a non-limiting example, at least one photon generator 1230 (controlled, for example, by controller 1208) may operate in a manner similar to that described herein with respect to Figures 4A, 4B, and / or 9B. According to some non-limiting examples, photon generator 1230 may include at least three photon generators (for example, each operating similarly to single-photon source unit 401 or single-photon source 812). The first photon generator provides photons for the initialization phase (for example, initializing quantum emitters 1206_1~1206_n), the second photon generator provides photons (1226_1~1226_n) for the entanglement phase (for example, generating or operating the associated configurations as entanglement gates 1216_1~1216_n), and the third photon generator provides photons (1228_1~1228_n) for the swap phase (for example, generating or operating the associated configurations as swap gates 1218_1~1218_n). Alternatively, controller 1208 may control the operation of photon generator 1230 (e.g., single-photon generator) to emit one or more of the photons 1224_1~1224_n for the initialization phase, photons 1226_1~1226_n for the entanglement phase, and photons 1228_1~1228_n for the swap phase. As described, controller 1230 may control the operation of photon generator 1230 and configuration (1214_1~1214_n) to cycle through different phases and synchronize their operation between them.

[0159] Controller 1208 can facilitate control of any of the operating modes of the quantum computing system 1200. For example, controller 1208 can control components or groups of components of the quantum computing system 1200 to facilitate the positioning of quantum emitters (1206_1~1206_n) at coupling locations (1204_1~1204_n) by controlling, for example, one or more operating characteristics of waveguides (1210_1~1210_n) with respect to the wavelength, phase, amplitude, polarity, and modality of the pulse or laser carried in the waveguide. Controller 1208 can facilitate the initialization of states for quantum emitter qubits, each state and quantum emitter qubit associated with each of the quantum emitters 1206_1~1206_n in Figure 13A. Controller 1208 can further facilitate the transfer of optical qubits associated with photons (1226_1~1226_n) for entanglement gates 1216_1~1216_n in Figure 13B. Controller 1208 can further facilitate the transfer of optical qubits associated with photons (1228_1~1228_n) for swap gates 1218_1~1218_n in Figure 13C, thereby enabling the generation of photon graph states such as photon graph states 1220_1~1220_n and / or cluster state 1222, as described in more detail herein below. Note that entanglement gates 1216_1~1216_n and swap gates 1218_1~1218_n can each be generated from configurations 1214_1~1214_n in Figure 13A after a suitable initialization process. For example, depending on the mode of operation controlled by controller 1208, the configurations (1214_1 to 1214_n) may alternatively operate in entanglement mode for the entanglement phase and in SWAP mode for the SWAP phase.

[0160] Some embodiments involve quantum computation methods for generating photon graph states. A photon graph state refers to a state or configuration of one or more photons, and a photon state may include quantum states associated with the degrees of freedom of one or more photons, as described above. For example, a photon graph state may represent relationships between groups of optical qubits, where each optical qubit may represent a fundamental unit of quantum information. For example, a photon graph state may include states whose vertices may represent photon states, where a photon state refers to a state of one or more photons, and the edges may represent entanglement between photon states. A photon graph state may, for example, refer to a plurality of entangled photons or states thereof.

[0161] As a non-limiting example, Figures 13A to 13C together illustrate a preferred implementation of a quantum computing system 1200 that generates photon graph states (1220_1 to 1220_n and 1222), consistent with some embodiments of the present disclosure. The quantum computing system 1200 includes quantum emitters (1206_1 to 1206_n) positioned at coupling locations (1204_1 to 1204_n) between respective waveguides (1210_1 to 1210_n) and cavities (1202_1 to 1202_n).

[0162] Referring to Figure 13A, the controller 1208 can control the operation of the photon generator 1230 to initialize the quantum emitters (1206_1~1206_n) of configuration (1214_1~1214_n) by supplying consecutive photons (1224_1~1224_n) (e.g., initialization photons) to the waveguide (1212_1~1212_n). Referring to Figure 13B, the controller 1208 can control the operation of the photon generator 1230 to provide multiple photons (1226_1~1226_n) to the waveguide (1212_1~1212_n) respectively as sources for optical qubits for the entanglement gate (1216_1~1216_n), thereby generating an entanglement gate between optical qubits and quantum emitter qubits, as shown by the quantum emitter qubits (1234_1~1234_n) that are entangled with two optical qubits. Referring to Figure 13C, the controller 1208 can control the operation of the photon generator 1230 to provide one or more photons (1228_1~1228_n) for a SWAP gate (1218_1~1218_n) to the waveguide (1212_1~1212_n), thereby generating the SWAP gate (1218_1~1218_n), and the quantum emitter qubit (associated with, for example, quantum emitters 1206_1~1206_n) is mapped to optical qubits associated with reflected output photons 1236_1~1236_n. As a result, entangled photons 1231_1~1232_n remain, which can form photon graph states 1220_1~1220_n and / or cluster 1222, depending on how the inputs and outputs of the entanglement gate are connected.

[0163] In the example, the photon generator 1230 may include multiple photon generators, one of which is configured to generate photons (1224_1 to 1224_n) for configurations (1214_1 to 1214_n), another is configured to generate photons (1226_1 to 1226_n) for entanglement gates (1216_1 to 1216_n), and yet another generates photons (1228_1 to 1228_n) for SWAP gates (1218_1 to 1218_n). The controller 1208 may switch the photon generators as needed to generate graph states (1220_1 to 1220_n and 1222). Alternatively, controller 1208 may control the operation of photon generator 1230 (e.g., as a single-photon generator) to generate photons (1224_1~1224_n), photons (1226_1~1226_n) (e.g., in the case of a first transfer), and photons (1228_1~1228_n) (e.g., in the case of a second transfer) for the initialization, entanglement, and SWAP phases, respectively.

[0164] Some embodiments involve positioning multiple quantum emitters at multiple coupling locations associated with multiple cavities. A quantum emitter refers to a component configured to couple to an electromagnetic mode, as described above. A coupling location includes an area or region configured to enable coupling between a quantum emitter and a cavity (an example of a resonator), as described above. A cavity refers to a structure, housing, or container that functions as a resonator to establish or support an oscillatory or normal mode, as described above. A photon cavity is an example of a cavity that can establish or support an electromagnetic mode associated with a photon.

[0165] Positioning multiple quantum emitters at multiple coupling locations means, as described above, arranging or setting up quantum emitters in such a way that they enable interaction between each quantum emitter and one or more cavities associated with it. Examples of such quantum emitter positioning include arranging quantum emitters to be located at coupling locations (e.g., positioning or setting up quantum emitters at coupling locations), coupling quantum emitters to cavities, placing quantum emitters within the internal cavity field of a cavity, trapping quantum emitters in the vicinity of a cavity, lithographically setting up quantum dots in the vicinity of a cavity, or lithographically setting up a cavity in the vicinity of a self-assembled quantum dot. For example, positioning quantum emitters s at multiple coupling locations. Trapping quantum emitters means, as described above, generating traps that maintain the quantum emitters within the coupling locations. As a non-limiting example, Figure 9A shows a utility waveguide 910 carrying a pulse or field that generates a trap, and Figure 10 shows a magneto-optical trap (MOT) that traps one or more atoms 1020. The pulse or field in Figure 9A is configured to trap Rb atoms 820 (an exemplary quantum emitter) next to a coupling site, e.g., a cavity 818 (or a resonator or ring shape in the figure). The pulse or field may also be configured to generate and / or include an evanescent field around the waveguide 910, so that an evanescent field trap can be used to maintain Rb atoms 820 at or within the coupling site. The magneto-optical trap in Figure 10 is configured to trap one or more atoms 1020 at or within the coupling site.

[0166] Therefore, a quantum computing system may include multiple coupling locations for positioning multiple quantum emitters, thereby forming multiple coupling pairs of quantum emitters and cavities (e.g., photon cavities). This may enable multiple simultaneous (e.g., parallel) interactions between multiple quantum emitters and multiple photons via multiple cavities. Multiple quantum emitters may be coupled to one cavity, or multiple cavities may be coupled to one quantum emitter and function simultaneously (e.g., in parallel) in a similar manner, and it is understood that the interactions provided between each quantum emitter and each cavity can be made possible by such coupling.

[0167] As a non-limiting example, Figures 13A to 13C show a plurality of quantum emitters positioned at a plurality of coupling locations associated with a plurality of cavities, according to a certain embodiment relating to generating a photon graph state. Configurations (1214_1 to 1214_n), entanglement gates (1216_1 to 1216_n), and SWAP gates (1218_1 to 1218_n) each include coupling locations (1204_1 to 1204_n) associated with a cavity (1202_1 to 1202_n). Each coupling location (1204_1 to 1204_n) is located between the cavity (1202_1 to 1202_n) associated with that coupling location and the waveguide (1210_1 to 1210_n) associated with that coupling location. As previously described with reference to Figures 9A to 9C, blue and red lasers that trap the quantum emitters at the coupling site can be carried by waveguides (1210_1 to 1210_n). These blue and red lasers generate evanescent fields around waveguides (1210_1 to 1210_n), which are used, for example, to trap or maintain associated quantum emitters (1206_1 to 1206_n) in or within the coupling site (1204_1 to 1204_n) associated with the quantum emitters. Controller 1208 can control circuits or optical elements for positioning the quantum emitters at the coupling site. For example, controller 1208 can control the lasers used to trap the quantum emitters at the coupling site. Controller 1208 can control the properties of the blue and red lasers used for trapping. For example, positioning (e.g., confinement or trapping) quantum emitters (1206_1~1206_n) at their respective coupling locations (1204_1~1204_n) between corresponding waveguides (1210_1~1210_n) and cavities (1202_1~1202_n) enables interaction between the quantum emitters (1206_1~1206_n) and the cavities (1202_1~1202_n) associated with them, which allows, for example, the dipole field of each quantum emitter to overlap with the electromagnetic modes of the associated cavity, thereby enabling the quantum emitter to couple with the cavity.For example, the photon generator 1230 may include multiple photon generators, one of which is configured to generate photons (1224_1 to 1224_n) for configurations (1214_1 to 1214_n), another is configured to generate photons (1226_1 to 1226_n) for entanglement gates (1216_1 to 1216_n), and yet another generates photons (1228_1 to 1228_n) for SWAP gates (1218_1 to 1218_n). The controller 1208 may switch the photon generators as needed to generate graph states (1220_1 to 1220_n and 1222). Alternatively, controller 1208 may control the operation of photon generator 1230 (e.g., as a single-photon generator) to generate photons (1224_1~1224_n), photons (1226_1~1226_n) (e.g., in the case of a first transfer), and photons (1228_1~1228_n) (e.g., in the case of a second transfer) for the initialization, entanglement, and SWAP phases, respectively.

[0168] Some embodiments involve initializing the state of a quantum emitter qubit associated with each of a plurality of quantum emitters. A quantum emitter qubit refers to the fundamental unit of quantum information stored in or belonging to a quantum emitter, as described above. Initializing the quantum emitter qubit associated with each of a plurality of quantum emitters may involve setting a baseline state for the quantum emitter. For example, initialization may include establishing an initial adjustment state system for the quantum emitter. As a non-limiting example, Figure 1 shows a four-state system 101 of an atom 102 (an exemplary quantum emitter) contained within an optical cavity 103. This may involve preparing the quantum emitter in a superposition of first and second ground states. Initialization may involve causing the quantum emitter to undergo one or more transitions from one state to another, for example, by exposing the quantum emitter to a laser and / or applying a magnetic field to the quantum emitter.

[0169] In some embodiments of this disclosure, initialization may involve associating the state of a quantum emitter qubit with an equal superposition of two ground states of the quantum emitter. The ground state may be the lowest energy rest state, and the energy of the ground state may be lower than that of the excited states, for example, the zero energy. Superposition may refer to being in multiple states simultaneously, for example, until measurement is performed. Superposition may refer to the sum (or superposition) of two or more quantum states, for example, and equal superposition may refer to having two or more quantum states that have equal probabilities. For example, Figure 1 shows a four-state system 101 of an atom 102 (an exemplary quantum emitter) coupled to an optical cavity 103, where the atom 102 may be initialized with a superposition of first and second ground states 111 and 113, respectively. Figures 2E and 3 show examples of the initialized states of a quantum emitter coupled to a cavity, where atom 102 (an exemplary quantum emitter) is the initial superposition state of the first and second ground states 111, 113 after the initialization process. The frequencies for one or more transitions from one state to another can also be tuned by optical shifts using a laser or by Zeeman shifts due to the application of a magnetic field.

[0170] As one non-restrictive example, one or more of the quantum emitter qubits (e.g., associated with a quantum emitter) may be initialized to a desired state, as described with respect to Figures 4A and 5A, using, for example, pulses 403 and 503, respectively. As another non-restrictive example, the quantum emitter may be... As shown in Figure 1 any of the states or It can be initialized to any superposition of states.

[0171] In the example, a controller (e.g., controller 1208) may control components, groups of components (e.g., optical elements), or circuits to initialize quantum emitter qubits associated with each of a plurality of quantum emitters. The controller may control a photon pulse generator and / or a magnetic field generator to, for example, expose a quantum emitter (where quantum emitter qubits are stored or to which quantum emitter qubits belong) to a laser and / or apply a magnetic field to the quantum emitter. The controller may control, for example, the photon pulse generator 151 and / or the magnet 141 in Figure 1. This may cause the quantum emitter to undergo one or more transitions from one state to another until a desired state for the next step is reached. For example, the next step may be an entanglement step, and the desired state of the quantum emitter allows the quantum emitter to function as an entanglement gate (1216_1~1216_n). The next step may be a SWAP step, and the desired state of the quantum emitter allows the quantum emitter to function as a SWAP gate (1218_1~1218_n). As a non-restrictive example, Figure 3 shows an example of a desired state for the entanglement step, and Figure 2E shows an example of a desired state for the SWAP step, which is the initial superposition state of the first and second ground states 111, 113 after the initialization process.

[0172] Some embodiments involve transmitting an optical qubit to multiple quantum emitters in the transmission of at least one first instance in order to generate an entangled gate between an optical qubit and a quantum emitter qubit so as to entangle a quantum emitter qubit and an optical qubit. An optical qubit, as described above, refers to a fundamental unit of quantum information stored (or belonging to) one or more photons or electromagnetic fields. An entangled gate, as described above, refers to any component, group of components, control sequence, or operation (reversible or irreversible) that results in any degree of entanglement between quantum elements (e.g., any quantum particle, group of quantum particles, or qubit). For example, a controlled Z entangled gate (CZ gate) is a type of entangled gate. As a non-limiting example of an entangled gate, Figure 3 shows a controlled Z entangled gate implementation, and Figures 8 and 9C show a rubidium ( 87 Rb) shows atom 820, which is implemented in a controlled Z entanglement gate. As another example, the photon entanglement unit 501 in Figures 5A and 5B is a type of entanglement gate. Transmission refers to transporting or carrying, for example, through a channel or waveguide. Thus, for example, transmitting an optical qubit to multiple quantum emitters in transmission of at least one first instance to generate an entanglement gate between an optical qubit and a quantum emitter qubit means first, for example, transporting a photon (to which the optical qubit belongs) towards the quantum emitter through a channel or waveguide to bring entanglement between the optical qubit and the quantum emitter qubit (as described with reference to captions 602-609 in Figure 6, for example).

[0173] In the example, a controller (e.g., controller 1208) may control components, groups of components (e.g., optical elements), or circuits to transmit an optical qubit to multiple quantum emitters in the first example, thereby generating an entangled gate between the optical qubit and the quantum emitter qubit, causing the quantum emitter qubit and the optical qubit to become entangled. The controller may, for example, control a photon generator or photon source unit to provide the photons to which the optical qubit belongs. The controller may also control one or more switches, beam splitters, and waveguides to direct and transport the supplying photons to quantum emitters initialized to a desired state for the entangled gate in order to bring about entanglement between the optical qubit and the quantum emitter qubit.

[0174] As a non-limiting example, Figure 13B shows a quantum computing system 1200 including a waveguide (1212_1~1212_n) according to a certain embodiment relating to generating a photon graph state, the waveguide transmitting optical qubits toward a plurality of quantum emitters to generate an entanglement gate between the optical qubits and the quantum emitter qubits so as to entangle the quantum emitter qubits and the optical qubits. For example, a controller 1208 may control the operation of a photon generator 1230 to provide photons 1226_1~1226_n to the waveguide (1212_1~1212_n) during the entanglement phase of the entanglement gate (1216_1~1216_n) of the quantum computing system 1200. The controller 1208 may further control how the cavity (1202_1~1202_n) functions or interacts with the quantum emitter (1206_1~1206_n) by controlling the frequency and / or other characteristics of the optical pulse input to the cavity (1202_1~1202_n) so that photons 1226_1~1226_n (transported, for example, through waveguides 1212_1~1212_n) interact with the quantum emitter (1206_1~1206_n) via the cavity 1202_1~1202_n associated with the quantum emitter, wherein the association is such that the quantum emitter and the cavity are coupled to enable interaction between them. This then entangles the optical qubit (for example, associated with photons 1226_1~1226_n) with the quantum emitter qubit (for example, associated with the associated quantum emitter 1206_1~1206_n). Thus, the controller 1208 can control the operation of system 1200 such that the cavity (1202_1~1202_n), the waveguide (1210_1~1210_n and 1212_1~1212_n), and the quantum emitter (1206_1~1206_n) positioned at the coupling site (1204_1~1204_n) as a whole operate as an entanglement gate (1216_1~1216_n) to output an optical qubit entangled with the quantum emitter qubit (1234_1~1234_n).

[0175] Some embodiments involve, after at least one of the first instance transmissions, transmitting the optical qubit to a plurality of quantum emitters in at least one second instance transmission to map the quantum emitter qubit to the optical qubit in order to generate a SWAP gate between the optical qubit and the quantum emitter qubit. The SWAP gate refers to a quantum gate that can operate on two qubits, as described above, where the quantum state of the first qubit is transferred to the second qubit, and the quantum state of the second qubit is transferred to the first qubit. For example, the SWAP gate 201 in Figure 2E may be a preferred implementation of the SWAP gate.

[0176] Therefore, in the example, after the transmission of a first instance of a photon that entangles an optical qubit (e.g., associated with a photon transmitted in the transmission of the first instance) with a quantum emitter qubit (e.g., from a quantum emitter positioned at a cavity and coupling site, acting as an entanglement gate), the controller (e.g., controller 1208) may control components, groups of components (e.g., optical elements), or circuits to bring about the transmission of a second instance (e.g., another consecutive photon). The controller may also control components, groups of components (e.g., optical elements), or circuits to transmit an optical qubit to multiple quantum emitters at a second time (after the first instance), thereby generating a SWAP gate between the optical qubit of the first photon interacting with the quantum emitter and the quantum emitter qubit, and the quantum emitter qubit is mapped to its optical qubit. The controller may, for example, control a photon generator or photon source unit to provide one or more photons to which one or more optical qubits belong. The controller may also control one or more of the switches, beam splitters, and waveguides to direct and transport one or more supply photons to a quantum emitter initialized to a desired state for the SWAP gate, thereby mapping the quantum emitter qubit to one or more optical qubits. By mapping or transferring the state of the quantum emitter qubit from the quantum emitter to the optical qubit of the photon, the quantum emitter remains with the state of the optical qubit before the mapping or transfer. This effectively unentangles the quantum emitter qubit from the entangled optical qubit with which it previously interacted as an entangled gate. This is because the quantum emitter qubit now has the state of the last optical qubit that was not entangled with that optical qubit. Thus, only the previously interacting optical qubit that is entangled with each other remains, which forms a photon graph state or cluster state (as described, for example, with reference to caption 611 in Figure 6).The mapping can also release the quantum emitter so that it is initialized again to a desired state for the entanglement gate, thereby entangling its quantum emitter qubit with the optical qubit of another incident photon.

[0177] The SWAP gate operation is based on the single-photon Raman interaction (SPRINT) mechanism described in "A passive photon-atom qubit swap operation" by Bechler O. et al., Nature Physics 14, 996-1000 (2018), "Extraction of a single photon from an optical pulse" by Rosenblum S. et al., Nature Photonics 10, 19-22 (2016), and "All-optical routing of single photons by a one-atom switch controlled by a single photon" by Shomroni, I. et al., Science 345.6199, 903-906 (2014), the entire content of these works, as well as the content related to single-photon extraction and the SPRINT mechanism, are incorporated herein by reference. For example, a quantum emitter is coupled to a cavity at the coupling site. Two transitions in a multi-level quantum emitter (e.g., a single atom such as an Rb atom having at least two ground states and at least one excited state) are coupled in different directions of the waveguide via a cavity (e.g., a micro-resonator). The quantum emitter, cavity, and waveguide mechanism (for example, as shown in Figure 13C, having quantum emitters 1206_1~1206_n, cavities 1202_1~1202_n, and waveguides 1212_1~1212_n) is such that light or photons carried within the waveguide are evanescently coupled to the cavity adjacent to the waveguide. Here, evanescent coupling means that the waveguide can interact with or be moved by the evanescent field around it.When a pulse containing multiple photons (e.g., photons 1228_1 to 1228_n in Figure 13C) is introduced into a waveguide (e.g., 1212_1 to 1212_n in Figure 13C), the first photon of the pulse in the waveguide originating from a certain direction interacts with a quantum emitter (e.g., quantum emitters 1206_1 to 1206_n) via evanescent coupling of a cavity coupled to the quantum emitter (e.g., cavity 1202_1 to 1202_n). This interaction, through destructive interference in transmission, deterministically reflects the first photon of the pulse originating from that direction, as shown by the reflected photons 1236_1 to 1236_n in Figure 13C. The interaction between the first photon and the quantum emitter is analogous to mapping the quantum emitter qubit to an optical qubit, as previously described with reference to SWAP gate 201 from Figure 2E or SWAP gates 1218_1~1218_n in Figure 13C. The interaction also results in a Raman transfer of the quantum emitter (e.g., quantum emitters 1206_1~1206_n) from one ground state to another, and the quantum emitter becomes transparent to the next photon from that direction (e.g., the next second photon from that pulse, such as photons 1228_1~1228_n in Figure 13C). This means that the next photon is simply transmitted to the other end of the waveguide. Thus, the mapping photon from the SPRINT mechanism is the first photon of the input pulse that first interacts with the cavity-coupled quantum emitter and is therefore reflected so that the mapping photon is output in the direction from which it first came. Figures 15A to 15C illustrate the SPRINT mechanism, which will be described in more detail later.

[0178] As a non-limiting example, Figure 13C shows a system 1200 according to a partial embodiment of the present disclosure relating to generating a photon graph state, which, after a first instance transmission, transmits optical qubits to a plurality of quantum emitters in a second instance to generate a SWAP gate between the optical qubits and the quantum emitter qubits so as to map the quantum emitter qubits to optical qubits. For example, a controller 1208 may control the operation of a photon generator 1230 so as to provide photons (1228_1~1228_n) to waveguides (1212_1~1212_n) respectively in the SWAP phase of system 1200. The controller 1208 may further control optical elements or circuits, such as switches and waveguides, to direct the optical qubits (associated with, for example, photons 1228_1~1228_n) of the second instance transmission to quantum emitters (1206_1~1206_n). The interaction between the optical qubit from the transmission of a second instance (e.g., associated with photons 1228_1~1228_n) via the cavity (1202_1~1202_n) and the quantum emitter (1206_1~1206_n) acts as a SWAP gate (1218_1~1218_n), causing the quantum emitter (1206_1~1206_n), positioned at the cavity (1202_1~1202_n) and the coupling site (1204_1~1204_n), to act as SWAP gates, as described with respect to Figure 2E, for example. As a result, the states of the quantum emitters (1206_1~1206_n) can be transferred (e.g., exchanged) or mapped to the states of the optical qubits (e.g., associated with the photons 1228_1~1228_n of the second instance transfer). Thus, the transfer of the second instance can, for example, break the entanglement between the quantum emitter qubit associated with the quantum emitters (1206_1~1206_n) and the already entangled optical qubits (e.g., generated by the transfer of the first instance during the entanglement stage). SolveEach of the SWAP gates (1218_1~1218_n) may output mutually entangled photons (1232_1~1232_n) or cluster state 1222, which are described as entanglement by connecting double lines, corresponding to the photon graph states 1220_1~1220_n, respectively, depending on the mechanism of the entanglement gate before the SWAP gate was used.

[0179] According to some embodiments, the transmission in the first instance involves transmitting multiple optical qubits in succession to produce multiple photon-quantum emitter entanglements, and the transmission in the second instance follows the first instance to output a photon graph state. The successive order can refer to a specific sequence, an progression arranged as a specific continuum, or a sequence in the sense of coming one after the other. Thus, the multiple optical qubits in the instance of the first transmission (for example, provided multiple photons during the entanglement phase) can be transmitted in a successive manner, for example, optical qubits one after the other, or photons one after the other (as described, for example, with reference to captions 602-609 in Figure 6). This allows the quantum emitter to interact with the photons one after the other, and its quantum emitter qubit becomes successively entangled with each optical qubit, resulting in multiple photon-quantum emitter entanglements. As a result, the multiple optical qubits also become entangled with the quantum emitter qubits. To output a photon graph state that does not have one of the entangled quantum bits, the quantum emitter quantum bit needs to be unentangled from its multiple optical quantum bits. Thus, the transfer in the second case, which results in a mapping of the quantum emitter quantum bit's state from the quantum emitter to the optical quantum bit, and thus unentangles the quantum emitter quantum bit from the other entangled optical quantum bits, follows the first case (as described, for example, with reference to captions 610-612 in Figure 6), leaving only the optical quantum bits that are entangled with each other, and forming the output photon graph state.

[0180] As a non-limiting example, a combination or sequence of SWAP gates in Figure 13C followed by entanglement gates in Figure 13B may be used to successively transmit optical qubits of a first instance to result in multiple photon-quantum emitter entanglements, and then, following the first instance, transmit optical qubits of a second instance to output a photon graph state. For example, one or more photon generators, one or more entanglement gates, and / or one or more SWAP gates may be arranged in an array 708 shown in Figure 7, where a controller controls linear optics and phase control elements 702, 705 connecting different stages, each stage including at least one of a photon generator, entanglement gate, and / or SWAP gate. Further details on how the array may operate to generate a photon graph state or cluster state are provided below with reference to Figure 7.

[0181] For example, as described above with reference to the transmission and entanglement gate of the first example, the controller (e.g., controller 1208) may first control components, groups of components (e.g., optical elements), or circuits to transmit an optical qubit to multiple quantum emitters in the first example, thereby entangling the quantum emitter qubit and the optical qubit. The controller may, for example, control a photon generator or photon source unit to provide the photons to which the optical qubit belongs in the transmission of the first example. The controller may also control one or more switches, beam splitters, and waveguides to direct and transport the providing photons to quantum emitters that have been initialized to a desired state for the entanglement gate (e.g., under the control of the controller as described above with reference to the initialization of the quantum emitter qubit state) in order to bring about entanglement between the optical qubit and the quantum emitter qubit.

[0182] As previously described with reference to the transmission of the second instance and the SWAP gate, the controller (controller 1208) may control components, groups of components (e.g., optical elements), or circuits to bring about the transmission of a second instance (e.g., another sequence of photons). The controller may also control components, groups of components (e.g., optical elements), or circuits to transmit an optical qubit to multiple quantum emitters at a second time (after the first instance), so that the quantum emitter qubits are no longer entangled with the optical qubits associated with the photon from the transmission of the first instance. This effectively unentangles the quantum emitter qubits from the entangled optical qubits, leaving only the previously interacting optical qubits that are entangled with each other, which form an output photon graph state or cluster state (as described with reference to caption 611 in Figure 6, for example). The controller may control a photon generator or photon source unit to provide one or more photons to which one or more optical qubits belong. The controller may also control one or more of the switches, beam splitters, and waveguides to direct and transport one or more supply photons to a quantum emitter that has been initialized to a desired state for the SWAP gate (for example, under the control of the controller as described above with reference to the initialization of the quantum emitter qubit state).

[0183] According to some embodiments, initialization involves the use of a SWAP gate. As previously stated, a SWAP gate refers to a quantum gate that operates on two qubits, where the quantum state of the first qubit is transferred to the second qubit, and the quantum state of the second qubit is transferred to the first qubit. This exchange means that when a SWAP gate is used between an optical qubit and a quantum emitter qubit, the state of the quantum emitter qubit is mapped to the optical qubit, and vice versa. Therefore, by controlling the properties of photons 1228_1~1228_n (which are input to waveguides 1212_1~1212_n and exchange the state of the photons with the quantum emitter qubit) so that they correspond to desired states, it is possible to map a desired state onto the quantum emitter qubit as part of the initialization step by using a SWAP gate between the quantum emitter qubit and the optical qubits 1228_1~1228_n, thereby allowing them to correspond to desired states. The desired state may, for example, relate to an entangled gate. For example, a controller (or controller 1208) may control a group of components, such as optical elements, or a circuit to control or set the properties of photons 1228_1 to 1228_n. For example, an initialization photon may be supplied to or transmitted to a cavity to interact with the quantum emitter to bring about an exchange (e.g., swap) of quantum states between the quantum emitter and the optical qubit associated with the initialization photon.

[0184] As a non-limiting example, Figure 13C, shown together with Figure 2E, illustrates a preferred implementation of initializing quantum emitters (1206_1~1206_n) using a SWAP gate. The controller 1208 can control the operation of the photon generator 1230 so that photons (1228_1~1228_n) are supplied to the configurations (1218_1~1218_n) via waveguides (1212_1~1212_n), respectively. For example, if the desired state for an initialized quantum emitter is a superposition of ground states 111 and 113 having probability amplitudes β and α, and the quantum emitter (1206_1 to 1206_n) is a superposition of states (e.g., the first and second ground states 111 and 113 in Figure 1, each having probability amplitudes γ and δ, respectively), then the controller 1208 can be controlled to provide photons 1228_1 to 1228_n as a superposition of optical modes (e.g., modes 1 and 2 in Figure 1, each having probability amplitudes α and β, respectively). When photons 1228_1~1228_n interact with quantum emitters 1206_1~1206_n, their states are exchanged, as described in more detail with respect to Figure 2E, potentially outputting reflected photons 1236_1~1236_ne in a superposition of modes (e.g., modes 1 and 2 having probability amplitudes δ and γ, respectively), and leaving quantum emitters (1206_1~1206_n) in a superposition of ground states 111 and 113 (having probability amplitudes β and α, respectively).

[0185] According to some embodiments, initialization includes applying microwaves. Microwaves may refer to electromagnetic radiation having wavelengths corresponding to frequencies between approximately 300 MHz and 300 GHz, ranging from about 1 meter to about 1 millimeter.

[0186] According to some embodiments, initialization includes applying a light beam. The light beam may refer to electromagnetic waves that remain focused around an average axis during free propagation, or electromagnetic waves guided by a structure such as a waveguide. Referring to Figure 13A, the controller 1208 may control the operation of the photon generator 1230 so as to apply the light beam to the configuration (1214_1 to 1214_n) via any of the waveguides (1210_1 to 1210_n and 1212_1 to 1212_n), respectively.

[0187] According to some embodiments, the multiple quantum emitters include atoms, and positioning includes trapping the atoms in the vicinity of the cavity. As previously mentioned, this trapping may involve using blue and red lasers to trap the quantum emitters at the coupling sites. Referring to Figures 13A to 13C, one or more of the quantum emitters (1206_1 to 1206_n) may include atoms such as atom 102 in Figure 1. The atoms can be positioned at the coupling sites (1204_1 to 1204_n) by trapping the atoms in the vicinity of the cavity (1202_1 to 1202_n).

[0188] According to some embodiments, the multiple quantum emitters include quantum dots, and positioning includes at least one of lithographically positioning quantum dots near a cavity or lithographically positioning a cavity near a self-assembled quantum dot. A quantum emitter including quantum dots may refer to a quantum emitter having a substrate (e.g., a solid-state substrate or semiconductor particles) having optical and / or electronic properties exhibiting quantum mechanical principles, as described above. A self-assembled quantum dot may refer to a semiconductor heterostructure that confines charge carriers in three directions. Referring to Figures 13A to 13C, one or more of the quantum emitters (1206_1 to 1206_n) may include quantum dots. The quantum dots can be positioned at the bonding sites 1204_1 to 1204_n by using lithography techniques, for example, by lithographically positioning the quantum dots near the cavities (1202_1 to 1202_n), or by lithographically positioning the cavities (1202_1 to 1202_n) near the self-assembled quantum dots.

[0189] According to some embodiments, optical qubits are generated using a quantum emitter coupled to a cavity. For example, a cavity-coupled quantum emitter may be configured to generate or release one or more photons. As a non-limiting example, the source unit 401 in Figures 4A and 4B and the photon generator 812 in Figures 8 and 9B are examples of such use of a cavity-coupled quantum emitter. Such a cavity-coupled quantum emitter may be provided, for example, in the photon generator 1230 in Figures 13A-13C.

[0190] According to certain embodiments of this disclosure, a quantum emitter may be a stationary quantum system having an anharmonic spectrum configured to couple to an electromagnetic mode. In other words, as described above, a quantum emitter may include a stationary qubit capable of interacting with photons. For example, a quantum emitter may include a quantum system having one or more of the following: electrons or nuclear configurations of an ion or neutral atom, or electrons or nuclear configurations of a defect or quantum dot in a material substrate.

[0191] According to some embodiments, the quantum emitter includes a superconducting qubit. A superconducting qubit refers to a qubit that is stored in or belongs to a superconducting electronic circuit (e.g., a network of electrical elements using superconductors) which includes one or more Josephson junctions, as described above.

[0192] According to some embodiments, the quantum emitter includes quantum dots. A quantum emitter including quantum dots may refer to a quantum emitter having a substrate (e.g., a solid-state substrate or semiconductor particles) having optical and / or electronic properties that exhibit quantum mechanical principles, as described above.

[0193] According to some embodiments, the quantum emitter includes an atom. According to some embodiments, the atom is neutral. Neutral refers to an atom that has no overall charge, such as when the number of protons in the atom is equal to the number of electrons. According to some alternative embodiments, the atom is an ion. An ion refers to a particle or atom that has an overall charge, such as an atom with an unequal number of protons and electrons. According to some embodiments, the quantum emitter includes at least one of a rubidium atom or a cesium atom, as described above. The rubidium or cesium atom may be neutral or an ion. According to some embodiments, the quantum emitter includes at least one of a strontium, erbium, ytterbium, calcium, barium, beryllium, or magnesium atom, as described above.

[0194] According to some embodiments, an entangled gate is one of a controlled Z gate (CZ gate), a controlled NOT gate (CNOT gate), the square root of a SWAP gate, or a virtual SWAP gate (iSWAP gate). A controlled Z gate (CZ gate) refers to a quantum gate that can operate on two qubits, and their coupled quantum state obtains a conditional phase shift (e.g., a phase shift of pi as described above). For example, one or more of the entangled gates 1216_1 to 1216_n can function as one of a CZ gate, a CNOT gate, the square root of a SWAP gate, or an iSWAP gate. For example, entangled gate 1216_1 may be a controlled Z gate (CZ) gate.

[0195] As a non-limiting example, Figure 13D shows an exemplary process 1260 (or an exemplary method thereof) for generating a photon graph state, consistent with certain embodiments of the present disclosure. The block diagram in Figure 13D may be described below in relation to embodiments of specific implementations presented in other figures, such implementations are provided for illustrative purposes only and are not intended to function as limitations. Since examples of process steps are described throughout the present disclosure and are also applicable to exemplary process 1260, such implementations are either not repeated or are briefly summarized in relation to Figure 13D. In certain embodiments of the present disclosure, process 1260 may be performed by at least one processor or circuit, e.g., controller 1208, configured to perform the operations or functions described herein. In certain embodiments, certain aspects of process 1260 may be implemented as memory, non-temporary computer-readable medium, or software (e.g., program code or instructions) stored in computer-readable medium, provided to at least one processor. In certain embodiments, certain aspects of process 1260 may be implemented as hardware (e.g., dedicated circuitry). In some embodiments, process 1260 may be implemented as a combination of software and hardware.

[0196] Figure 13D includes process steps 1262 to 1268. In step 1262, the process involves positioning multiple quantum emitters at multiple coupling locations associated with multiple cavities. For example, referring to Figure 13A, quantum emitters (1206_1 to 1206_n) may be positioned at coupling locations (1204_1 to 1204_n) associated with cavities (1202_1 to 1202_n), respectively.

[0197] In step 1264, the process involves initializing the state of the quantum emitter qubit associated with each of the multiple quantum emitters. Initialization may involve, for example, using a SWAP gate and / or applying microwaves. For example, initialization may involve controlling components, groups of components (e.g., optical elements), or circuits to initialize the quantum emitter qubit associated with each of the multiple quantum emitters. Control may include controlling a photon pulse generator and / or a magnetic field generator to expose the quantum emitter (where the quantum emitter qubit is stored or to which the quantum emitter qubit belongs) to a laser and / or apply a magnetic field to the quantum emitter. For example, the photon pulse generator 151 and / or magnet 141 in Figure 1 may be controlled in this way.

[0198] In step 1266, the process involves transmitting an optical qubit to multiple quantum emitters in the transmission of at least one first instance in order to generate an entangled gate between the optical qubit and the quantum emitter qubit so as to entangle the quantum emitter qubit and the optical qubit. For example, the transmission in the transmission of at least one first instance may involve controlling a component, a group of components (e.g., optical elements), or a circuit to transmit an optical qubit to multiple quantum emitters in the first instance. For example, such control may include controlling a photon generator or photon source unit to provide the photons to which the optical qubit belongs, and controlling one or more switches, beam splitters, and waveguides to direct and transport the provided photons to quantum emitters initialized to a desired state for the entangled gate in order to bring about entanglement between the optical qubit and the quantum emitter qubit.

[0199] In step 1268, the process maps the quantum emitter qubit to the optical qubit by transmitting the optical qubit to a plurality of quantum emitters in the transmission of at least one second instance to generate a SWAP gate between the optical qubit and the quantum emitter qubit, after at least one of the transmissions of the first instance. For example, the transmission in at least one second instance may involve controlling a component, a group of components (e.g., optical elements), or a circuit to transmit the optical qubit to a plurality of quantum emitters at a second time (after the first instance). The control may include, for example, controlling a photon generator or photon source unit to provide one or more photons to which one or more optical qubits belong, and controlling one or more switches, beam splitters, and waveguides to direct and carry one or more supplying photons to the quantum emitters.

[0200] For example, the transmission in the first example may include transmitting multiple optical qubits in succession to result in multiple photon-quantum emitter entanglements, and the transmission in the second example may follow the first example to output a photon graph state. In the example, a non-temporary computer-readable medium (or computer-readable medium or computer program) may include instructions, which, when executed by at least one processor (or device), cause at least one processor (or device) to execute a process or quantum computing method described herein. According to some embodiments relating to generating a photon graph state, the instructions may cause at least one processor (or device) to execute a quantum computing method or process 1260 shown in Figure 13D.

[0201] The same examples described above for each process or system feature of embodiments relating to generating photon graph states are also applicable to corresponding features of embodiments of this non-temporary computer-readable medium (or computer-readable medium or computer program).

[0202] According to other embodiments relating to generating photon graph states, an apparatus, device, system, integrated circuit device, or circuit is provided, comprising at least one processor (and memory) configured to perform a quantum computing method or process 1260 shown in Figure 13D. The same examples described above for each process or system feature of the embodiments relating to generating photon graph states are also applicable to the corresponding features of these embodiments.

[0203] According to yet another embodiment relating to generating photon graph states, a layout of an integrated circuit device or circuit is provided, comprising layout portions, each layout portion being configured to pattern each feature from a combination of features of system 1200 in Figures 13A-13C, entangled gates 1216_01-1216_n in Figure 13B, or SWAP gates 1218_1-1218_n in Figure 13C, according to some embodiments relating to generating photon graph states. As an example, the layout of an integrated circuit device or circuit includes a cavity layout portion configured to pattern a plurality of cavities, a coupling location layout portion configured to pattern a plurality of coupling locations for positioning a plurality of quantum emitters, and a controller layout portion configured to pattern a circuit or at least one processor.

[0204] In some embodiments of the present disclosure, the layout of an integrated circuit device or circuit further includes a photon generator layout portion defined to pattern a photon generator or a channel for carrying photons supplied by the photon generator toward a cavity or quantum emitter. In some embodiments of the present disclosure, the photon generator layout portion may be defined to pattern another cavity and another coupling location for positioning another quantum emitter toward the other cavity. In some embodiments of the present disclosure, the circuit layout portion includes a waveguide for carrying one or more photons or lasers and one or more photons Direction It may be determined to pattern one or more of the following: one or more linear optical elements that perform various functions related to or transporting, controlling the flow of one or more photons, manipulating the state of one or more photons, and / or performing quantum computation.

[0205] In some embodiments of this disclosure, the controller layout portion controls the flow of input and output photons between the photon generator and the entanglement gate or SWAP gate (for example, Directional between different waveguides also is cutThe controller is designed to be patterned, and the controller may comprise one or more processors that perform control, and memory, circuit components, or circuits.

[0206] When quantum emitters (e.g., quantum dots) that can be installed by lithography are used, it is understood that the coupling position layout portion may be defined so that the quantum emitters are also patterned. The same examples described above for each process or system feature of embodiments relating to generating photon graph states are also applicable to the corresponding features of this embodiment.

[0207] Some embodiments involve generating photon graph states for quantum computation. Quantum computation can refer to computation performed through the use or application of one or more quantum state properties, such as superposition, entanglement, and interference. As previously mentioned, a graph state represents a relationship between groups of qubits, and a qubit is the fundamental unit of quantum information. A photon graph state refers to a graph state that represents a relationship between groups of optical qubits. As previously mentioned, an optical qubit refers to the fundamental unit of quantum information stored (or belonging to) one or more photons or electromagnetic fields. For example, a graph state (or a set of graph states) generated from a series of incident optical qubits may represent a relationship between qubits stored (or belonging to) an output photon.

[0208] Generating a photon graph state for quantum computing refers to generating and / or providing a plurality of photons usable in a computation performed through the utilization or application of one or more quantum state properties. The plurality of photons may have a group of associated optical qubits, and the relationships between such groups of associated optical qubits may be represented using graph states. For example, generating a photon graph state for quantum computing may include determining the operating parameters and instructions for generating the photon graph state. In accordance with some embodiments relating to generating a photon graph state for quantum computing, as described below, a photon graph state may be generated, for example, by entangling one or more optical qubits in succession. In this example, the photon graph state may be a plurality of qubit states of a certain type that can be represented by a graph, where each optical qubit may be represented by a vertex of the graph, and the edges between pairs of optical qubits may represent interactions between pairs, e.g., entanglement.

[0209] Some embodiments involve coupling a quantum emitter to a cavity. A cavity, as described above, refers to a structure, housing, or container that can function as a resonator, which is a component that establishes or supports electromagnetic modes. For example, a cavity may correspond to a cavity in a cavity-QED configuration, an optical cavity, a whispering gallery-mode cavity, or a Fabry-Perot cavity. A quantum emitter, as described above, refers to a component configured to couple to electromagnetic modes. For example, a quantum emitter may include a stationary quantum system having an anharmonic spectrum configured to couple to electromagnetic modes. Coupled a quantum emitter to a cavity means enabling interaction between the quantum emitter and the cavity. For example, interaction between the quantum emitter's qubits and the cavity is enabled by allowing the quantum emitter's dipole field to overlap with the cavity's electromagnetic modes. When a quantum emitter is coupled to a cavity (also referred to as a cavity-coupled quantum emitter) at its associated coupling position, the quantum emitter is coupled to the cavity's electromagnetic modes. Therefore, a cavity-coupled quantum emitter can be configured to either release or emit photons when excited (for example, functioning as a photon generator) or to interact with photons passing through the cavity (for example, functioning as an entanglement gate that entangles photons).

[0210] As a non-limiting example, Figures 4A and 4B show source unit 401 implemented as a photon generator (including source unit atom 402 as a quantum emitter), Figures 8-9B show rubidium (87Rb) atom 820 as a quantum emitter coupled to cavity 818 to function as a photon generator, Figures 5A and 5B show entanglement unit 501 implemented as an entanglement gate (including entanglement unit atom 502 as a quantum emitter), and Figures 8 and 9C show rubidium (87Rb) atom 820 as a quantum emitter coupled to cavity 818 to function as an entanglement gate.

[0211] In some embodiments, such coupling may involve positioning a quantum emitter within the internal cavity field of the cavity. As previously stated, positioning a quantum emitter means arranging or setting up the quantum emitter so as to enable interaction between the quantum emitter and the cavity. For example, positioning a quantum emitter within an area configured to enable coupling between the quantum emitter and the cavity, the area may also be referred to as a coupling position or coupling location. As previously stated, quantum emitter positioning may include, for example, arranging a quantum emitter so as to be located at a coupling position or coupling location (e.g., positioning or setting up a quantum emitter at a coupling position or coupling location), positioning a quantum emitter within the internal cavity field of the cavity, trapping a quantum emitter in the vicinity of the cavity, lithographically setting up a quantum dot in the vicinity of the cavity, or lithographically setting up a cavity in the vicinity of a self-assembled quantum dot. Trapping a quantum emitter in the vicinity of a cavity refers to generating a trap that maintains the quantum emitter within a coupling position associated with the cavity, as described above. For example, electromagnetic field configurations such as electric fields, radio frequency (or microwave) fields, magneto-optical trap (MOT) configurations, and / or non-resonant laser beams (atomic tweezers) can be used to maintain the quantum emitter within the coupling position. Figure 14A shows an unrestricted example of coupling position 1420.

[0212] According to some embodiments, a quantum emitter is a stationary qubit capable of interacting with photons. A stationary qubit may refer to a material quantum system usable for storing and processing quantum information. For example, a stationary qubit may refer to a qubit that (i) reliably stores quantum information on a timescale of nanoseconds or longer, (ii) reliably performs computations and / or operations that can transfer or convert the information to flying qubits (e.g., non-stationary qubits or photons), (iii) is reliably measured or read out, and / or (iv) is capable of operating in a highly entangled manner (or satisfies these conditions). Examples of stationary qubits may include qubits stored in or belonging to a quantum emitter. For example, qubits stored in or belonging to rubidium or cesium atoms can function as sources of stationary qubits. For example, a Rydberg atom can also function as a source of stationary qubits. The use of Rydberg atoms can yield properties advantageous for quantum computing applications, such as (i) a strong response to electromagnetic fields, (ii) a long decay period, and (iii) a large electric dipole moment. A Rydberg atom may refer to an excited atom with one or more electrons having a large principal quantum number n.

[0213] For example, a quantum emitter may include a superconducting qubit. As mentioned above, a superconducting qubit refers to a qubit that is stored in or belongs to a superconducting electronic circuit (e.g., a network of electrical elements using superconductors). For example, a superconducting qubit may refer to a solid-state qubit secured from a superconducting material such as aluminum or a niobium-titanium alloy. A superconducting qubit may include or be coupled to at least one Josephson junction. Examples of superconducting qubits may include charge qubits, flux qubits, phase qubits, and / or hybrids thereof (e.g., transmons).

[0214] In the example, a quantum emitter may include quantum dots. A quantum emitter including quantum dots may refer to a quantum emitter having a substrate (e.g., a solid-state substrate such as semiconductor particles) that exhibits optical and / or electronic properties that demonstrate quantum mechanical principles, as described above. For example, a quantum dot may be a nanoparticle having different optical and electronic properties from its bulk component. In the presence of high-energy photons (e.g., UV light), electrons in a quantum dot may be excited to a high-energy state and emit one or more photons when transitioning to the ground state. For example, a quantum dot may be made from one or more binary compounds such as lead sulfide, lead selenide, cadmium selenide, cadmium sulfide, cadmium telluride, indium arsenide, or indium phosphide. For example, a quantum dot may be self-assembled from indium arsenide in a gallium arsenide substrate. For example, a quantum dot may refer to an atomic defect in a solid-state substrate, such as a nitrogen vacancy center in diamond.

[0215] In the example, the quantum emitter may contain at least one of an atom or an ion. An atom can be neutral. Neutral refers to an atom that has no charge overall, such as an atom with an equal number of protons and electrons. An ion refers to a particle or atom that has a charge overall, such as an atom with an unequal number of photons and electrons. The atom or ion may be secured from rubidium. And / or the atom or ion may be secured from cesium. In the example, the atom or ion may be secured from a Rydberg atom. In the example, the quantum emitter may contain at least one of strontium, erbium, ytterbium, calcium, barium, beryllium, or magnesium atoms.

[0216] Some embodiments involve generating a first dirty photon having a first time profile. As previously mentioned, a dirty photon refers to a photon that is distinguishable from other photons, for example, when performing quantum computation. A dirty photon may include, for example, a propagating photon in a mixed state with respect to multiple space-time modes, e.g., multiple time profiles. For example, a dirty photon exhibits an irregularity that makes it easily distinguishable from other photons (for example, in its time profile) (for example, based on the irregularity of its time profile). The time profile may refer to the envelope of the propagating photon field, as discussed earlier. Examples of time profiles include exponentially decreasing or increasing profiles with specific decay time and initial time, constant profiles with specific initial time and final time, frequency and phase modulation profiles with specific initial and final time and modulation frequency and phase, or Gaussian profiles with specific mean time and time variation.

[0217] As mentioned above, an optical qubit refers to a fundamental unit of quantum information stored (or belonging to) one or more photons or electromagnetic fields. Forming an optical qubit using a dirty photon, or forming a first optical qubit using a first dirty photon, means establishing or providing the dirty photon or the first dirty photon as the source of the optical qubit or the first optical qubit. The optical qubit or the first optical qubit is then stored or belongs to the dirty photon or the first dirty photon, or the electromagnetic field associated with it. For example, establishing or providing a dirty photon or the first dirty photon as a source may involve transporting the dirty photon or the first dirty photon to, through, or from one or more linear optical elements. For example, a linear optical element may include one or more of the following: a channel (e.g., a waveguide), a reflector (e.g., a mirror), a beam splitter, a lens, a phase shifter, or another linear optical instrument capable of manipulating the properties or motion of photons.

[0218] Generating a dirty photon, or generating a first dirty photon, represents providing, releasing, or emitting a photon that can be distinguishable from another photon, for example, a photon for which an offer, release, or emission has been made or is planned. For example, a photon may be "dirty" because the photon generator used to provide, release, or emit the photon was not precisely controlled in terms of the time and / or shape or frequency of its input pulse as described above. A single photon generated in accordance with some embodiments of the present disclosure is fully suitable for a photonic qubit ensemble using a quantum emitter coupled to the cavity described herein, even if the photon exhibits irregularities (e.g., in its temporal profile) that allow the photon to be easily distinguishable.

[0219] The photon source unit that secures the single photon described herein is a non-limiting example of such a photon generator that can optionally provide a dirty photon. As a non-limiting example, FIGS. 4A and 4B show emitted photons 406, which can be dirty photons, and a temporally continuous series of output photons 412 generated by source unit 401 (including source unit atom 402 as a quantum emitter). In another non-limiting example, FIGS. 8-9B also show rubidium coupled to cavity 818 ( 87Rb) shows a single photon, which may be a dirty photon, generated and output by atom 820. Referring to source unit 401 in Figures 4A and 4B, source unit 401 includes a cavity such as the optical cavity 103 in Figure 1 and atom 402 (e.g., a quantum emitter). After an initialization pulse 403 initializes the state of atom 402 to state 111 (Figure 1), a generation pulse 404 brings about transitions 121A and 122A in Figure 2A, and as a result, atom 402 may emit photon 406. By repeating this process, a time-sequential series of output photons 412 in Figure 4B is generated. According to some embodiments relating to generating photon graph states for quantum computation, the generation pulse 404 does not need to be precisely controlled, for example, in terms of its pulse time and / or shape, and therefore the output photons may be dirty. The output photons exhibit irregularity and therefore have a time profile that may be distinguishable in some cases.

[0220] Optical quantum computing refers to calculations performed through the use or application of one or more quantum state properties of one or more photons. Conventional optical quantum computing, which generates photon graph states using linear optical elements, relies on the use of indistinguishable photons (also called clean photons) because these indistinguishable photons exhibit no irregularities (for example, in their time profiles). This is because some of the operations involved in such conventional optical quantum computing require the use of destructive interference between multiple photons, and this destructive interference relies on multiple photons that are indistinguishable from one another. For example, if the photons used in such conventional optical quantum computing are distinguishable, this can lead to a decrease in the fidelity of the generated photon graph state and an increase in calculation errors.

[0221] Symmetrically, dirty photons can be used in quantum computation by performing optical quantum computation using photon entanglement through cavity-enhanced quantum emitter-photon interaction (for example, using a cavity-coupled quantum emitter, also called a cavity-coupled quantum emitter). This is because entangling photons through cavity-enhanced quantum emitter-photon interaction uses a cavity-coupled quantum emitter as an intermediary for entangling the photons. The cavity-coupled quantum emitter generates a photon graph state by mediating interactions between photons. Mediation refers to facilitating, enabling, or otherwise promoting the interaction. The interaction can transfer, transmit, associate, and / or establish correlations between incident optical qubits. For example, a cavity-coupled quantum emitter may facilitate entanglement (e.g., interaction) between incident photons, and the cavity-coupled quantum emitter is a means of achieving such interaction between incident photons. Therefore, optical quantum computing using some embodiments relating to generating photon graph states for quantum computing as described herein does not require the use of indistinguishable photons (also referred to as clean photons), otherwise it would be a case of probabilistic entanglement using linear optics. This means, for example, that the input photon pulses used to generate photons for use in quantum computing (e.g., generated pulse 404 in Figure 4A) do not need to be precisely timed and shaped, and as a result, dirty photons with time profiles that are not precisely controlled or tuned, as described above, may be generated. However, the use of one or more cavity-coupled quantum emitters means that the generated photons are still suitable for use in quantum computing operations.

[0222] Some embodiments involve generating a second dirty photon having a second time profile, and some embodiments involve using the second dirty photon to form a second optical qubit. For example, the second dirty photon may be generated and used to form a second optical qubit in a similar manner to how the first dirty photon is generated and used to form the first optical qubit described above. The example described above regarding generating and using the first dirty photon to form a first optical qubit is also applicable to the second dirty photon.

[0223] Some embodiments involve using a cavity-coupled quantum emitter to entangle a first optical qubit with a second optical qubit to form an entangled optical qubit pair. An entangled optical qubit pair refers to a state in which the states of the optical qubit pair are related, as described above. For example, the states of the optical qubit pair may be related to each other and their states cannot be described independently of each other. The entanglement can, for example, correlate a measurement of the state of one optical qubit with a measurement of the state of another optical qubit to generate a correlation between the measurements of those states, thereby allowing mutual information to be stored or processed using this correlation. The cavity-coupled quantum emitter (or cavity-coupled quantum emitter) can be used to function as an entanglement gate, as described above. The required gate refers to a component or group of components or a control sequence configured to entangle qubits. Therefore, the cavity-coupled quantum emitter can interact with the first and second optical qubits, for example, in a continuous manner, and as a result, the first and second optical qubits become entangled with the cavity-coupled quantum emitter and, therefore, entangled with each other.

[0224] As a non-restrictive example, Figures 5A and 5B show an entangled unit 501 implemented as an entanglement gate to generate a time-sequential series of entangled photons 512 (including an entangled unit atom 502 as a quantum emitter), and Figures 8 and 9C show a rubidium as a quantum emitter coupled to cavity 818 to function as an entanglement gate. 87 Rb) indicates 820 atoms.

[0225] Some embodiments involve the use of pairs of entangled optical qubits for quantum computation. Performing quantum computation may refer to applying operations to optical qubits, and applying operations depends on the use or application of one or more quantum state properties such as superposition, entanglement, and interference. Entangled optical qubits are carried through linear optical elements and / or quantum emitters, or by linear optical elements and / or quantum emitters. Direction This can enable the transport and / or manipulation of the information encoded thereby.

[0226] Some embodiments involve generating a third dirty photon having a third temporal profile different from the first and second temporal profiles and using the third dirty photon to form a third photonic qubit. For example, the third dirty photon can be generated and used to form a third photonic qubit in a manner similar to that used to generate and use the first or second dirty photon to form the first or second photonic qubit, as described above. The examples described above with respect to generating and using the first or second dirty photon to form the first or second photonic qubit are applicable to the third dirty photon as well. The temporal profile refers to the temporal envelope of the propagating photon field, as described above. Examples of temporal profiles include exponentially decreasing or increasing profiles having a specific decay time and an initial time, constant profiles having a specific initial time and a final time, or Gaussian profiles having a specific mean time and a time variation. Thus, the third temporal profile of the third dirty photon, which is different from the first and second temporal profiles of the first and second dirty photons, refers to a field of the third dirty photon having a profile that functions or varies differently from the fields of the first and second dirty photons over time.

[0227] Some embodiments involve using a quantum emitter coupled to a cavity to entangle a third photonic qubit with the first or second photonic qubit to form three entangled photonic qubits. For example, as described above, the cavity-coupled quantum emitter can interact with the third photonic qubit and the first or second photonic qubit, for example, in a continuous manner, such that the third photonic qubit and the first or second photonic qubit become entangled with the cavity-coupled quantum emitter and thus with each other. The examples described above with respect to entangling the first photonic qubit with the second photonic qubit are applicable to entangling the third dirty photon with the first or second photonic qubit as well.

[0228] Some embodiments involve using three entangled optical qubits for quantum computation. For example, as described above with reference to using a pair of entangled optical qubits for quantum computation, the three entangled optical qubits are carried through a linear optical element and / or a quantum emitter, or by a linear optical element and / or a quantum emitter. Direction This can enable the transport and / or manipulation of the information encoded thereby.

[0229] Some embodiments involve using a cavity coupled to a quantum emitter to entangle a plurality of additional photons to generate a photonic graph. The additional photons refer to photons other than the aforementioned first, second, and / or third dirty photons. For example, the additional photons can be generated and used to form additional qubits in a similar manner as the first dirty photon (or the second or third dirty photon) is generated and used to form the first qubit (or the second or third qubit). The examples described above regarding generating and using the first dirty photon (or the second or third dirty photon) to form the first qubit (or the second or third qubit) are applicable to the additional photons as well. Using a cavity coupled to a quantum emitter to entangle a plurality of additional photons means that, as described above regarding forming a pair of entangled qubits that requires the first qubit along with the second qubit, the quantum emitter coupled to the cavity (or cavity-coupled quantum emitter) is used to function as an entangling gate. As each additional photon becomes entangled with the cavity-coupled quantum emitter, the cavity-coupled quantum emitter generates a photonic graph of the entangled photons that includes the additional photons as well as the first and second dirty photons. If the third dirty photon is also entangled using the cavity-coupled quantum emitter, the entangled photons include the third photon. And the said photonic graph of the entangled photons can be used, for example, in quantum computing. The examples described above regarding requiring the first qubit along with the second qubit or entangling the third qubit with the first or second qubit are also applicable to entangling a plurality of additional photons.

[0230] As a non-limiting example, Figures 5A and 5B show an entanglement unit 501 (including an entanglement unit atom 502 as a quantum emitter) implemented as an entanglement gate to generate a time-sequential series of entangled photons 512, and Figure 6 shows the repetition of the entanglement process using the entanglement unit 501 according to one embodiment. As a result of step 602, which repeats the loop of steps 603-606, the entanglement unit atom (such as atom 502) becomes entangled with the states of multiple photons, and thereby can generate a photon graph having n entangled photons, as shown in captions 609, 611.

[0231] In some embodiments, at least some of the additional photons are dirty. The additional dirty photons may be the same as the first dirty photons, the second dirty photons described above, or the third dirty photons described below. For example, the additional dirty photons may be generated and used in the same manner as the first or second dirty photons to form an additional optical qubit. A quantum emitter coupled to the cavity may then be used to entangle the formed additional optical qubit with the first and / or second optical qubit or any other optical qubit to form a plurality of entangled optical qubits, which may then be used for quantum computation. The examples and descriptions described herein with respect to the first, second, or third dirty photons are also applicable to additional dirty photons.

[0232] In some embodiments, a first dirty photon is generated by extraction from an interfering laser pulse using a cavity-coupled quantum emitter. A laser pulse refers to a pulse of light, e.g., a time-confined pulse containing a specific average number of photons. An interfering laser pulse refers to a laser pulse having a wavelength of laser light that is its phase in space and time. A cavity-coupled quantum emitter (also called a cavity-coupled quantum emitter) can be used to extract a photon from the interfering laser pulse. The extracted photon can be considered a first dirty photon generated by extraction from the interfering laser pulse using a cavity-coupled quantum emitter. The cavity-coupled quantum emitter used for extraction may be a different cavity-coupled quantum emitter from the quantum emitter coupled to the cavity to entangle a first optical qubit with a second optical qubit. Thus, the extraction cavity-coupled quantum emitter may be an additional quantum emitter to the quantum emitter used for entanglement.

[0233] As a non-limiting example, Figures 15A–15C illustrate the single-photon Raman interaction (SPRINT) mechanism used in photon extraction from interference laser pulses based on a quantum emitter coupled to a cavity. The photon extraction described herein is based on the single-photon Raman interaction (SPRINT) mechanism described in "A passive photon-atom qubit swap operation" by Bechler O. et al., Nature Physics 14, 996-1000 (2018), "Extraction of a single photon from an optical pulse" by Rosenblum S. et al., Nature Photon 10, 19-22 (2016), and "All-optical routing of single photons by a one-atom switch controlled by a single photon" by Shomroni, I. et al., Science 345.6199, 903-906 (2014). The entire content of these documents, as well as the content related to single-photon extraction and the SPRINT mechanism, are incorporated herein by reference. For example, quantum emitter 1432 is coupled to cavity 1434 at coupling position 1420, as shown in Figure 15A. Two transitions in a multi-level quantum emitter (quantum emitter 1432, or, for example, a single atom such as an Rb atom having at least two ground states and at least one excited state) are coupled in different directions of waveguide 1433a via cavity 1434 (e.g., a micro-resonator). The mechanism of quantum emitter 1432, cavity 1434, and waveguide 1433a is such that light or photons carried within waveguide 1433a are evanescently coupled to cavity 1434 adjacent to waveguide 1433a. Here, evanescent coupling means that interaction or transition is possible due to the evanescent field around the waveguide.

[0234] As shown in Figure 15A, an interference laser pulse containing multiple photons 1436a, 1436b, and 1436c is introduced into waveguide 1443a. Then, as shown in Figure 15B, the first photon 1436a of the interference laser pulse in waveguide 1433a, originating from a certain direction, interacts with quantum emitter 1432 via cavity 1434 through the evanescent coupling 1435 of cavity 1434. This interaction, due to destructive interference in transmission, deterministically reflects the first photon 1436a of the interference laser pulse originating from that direction, as shown by the reflected photon 1439a shown in Figure 15C. This interaction between the first photon 1436a and quantum emitter 1432 is analogous to mapping a quantum emitter qubit to an optical qubit, as previously described with reference to the SWAP gate 201 from Figure 2E. This interaction results in a Raman transfer of quantum emitter 1432 from one ground state to another, causing quantum emitter 1432 to become transparent to the next photon from that direction (e.g., the second photon 1436b and the third photon 1436c from the interfering laser pulse). In other words, as shown in Figure 15C, the next photons (e.g., the second photon 1436b and the third photon 1436c from the interfering laser pulse) are simply transmitted to the other end of waveguide 1433a. The reflected photon 1439a can then function as the first dirty photon, which is generated by extracting it from the interfering laser pulse using quantum emitter 1432 coupled to cavity 1434. Thus, a SPRINT mechanism-based cavity-coupled quantum emitter can be used to extract dirty photons from an interfering laser pulse. The extracted dirty photon from the SPRINT mechanism is the first photon of the interference laser pulse that interacts with the cavity-coupled quantum emitter and is therefore reflected so that the extracted dirty photon is output in the direction from which it originally came. The subsequent photons of the interference laser pulse are simply carried, so the first photon of the interference laser pulse interacting with the cavity-coupled quantum emitter is extracted as a reflected photon, while the remaining photons of the interference laser pulse are carried unaffected.

[0235] In some embodiments, a second dirty photon is generated by extraction from the interference laser pulse using a quantum emitter coupled to the cavity. For example, the second dirty photon may be generated by extraction from the interference laser pulse in a manner similar to how the first dirty photon is generated by extraction from the interference laser pulse described above. The first and second dirty photons may be generated, for example, by extraction from the interference laser pulse using a quantum emitter coupled to the cavity. The example described above for generating the first dirty photon is also applicable to generating the second dirty photon. Similarly, in some embodiments, a third dirty photon and / or additional photons may be generated by extraction from the interference laser pulse using a quantum emitter coupled to the cavity.

[0236] In some embodiments, the first dirty photon is generated from a fluctuating quantum emitter. A fluctuating quantum emitter refers to a quantum emitter whose physical state or properties change over time (at least temporarily), as described above. For example, a quantum emitter may fluctuate because its resonant frequency changes over time due to a stray magnetic field or electric field. Such a fluctuating quantum emitter may be used to generate the first dirty photon. For example, a fluctuating quantum emitter may be used as a quantum emitter coupled to a cavity in a photon source unit (e.g., source unit 401 in Figure 4A) or photon generator (e.g., quantum emitter 820 coupled to cavity resonator 818 in Figure 9B) that secures a single photon as described herein, and as a result, the fluctuating quantum emitter may provide a photon when excited.

[0237] In some embodiments, a second dirty photon is generated from a variable quantum emitter. For example, at least one of the first and second dirty photons may be generated from a variable quantum emitter. In some embodiments, a third dirty photon and / or additional photons are generated from a variable quantum emitter. The examples described above regarding the first dirty photon generated from the variable quantum emitter are also applicable to these embodiments.

[0238] In some embodiments, the spectra of the first and second dirty photons are within the interaction bandwidth of the quantum emitter coupled to the cavity. The spectrum refers to the wavelength range of the electromagnetic radiation. The spectra of the first and second dirty photons refer to the wavelength range of the electromagnetic radiation associated with the first and second dirty photons. The interaction bandwidth of the quantum emitter coupled to the cavity refers to the frequency range at which interaction with the quantum emitter coupled to the cavity is possible. For example, the interaction bandwidth of the quantum emitter may be the absorption spectrum of the quantum emitter, and the electromagnetic field is likely to interact with the quantum emitter at frequencies within the interaction bandwidth range. Similarly, in some embodiments, the spectra of a third dirty photon and / or additional photons may be within the interaction bandwidth of the quantum emitter coupled to the cavity.

[0239] In some embodiments, the second time profile differs from the first time profile. The time profile refers to the envelope of the propagating photon field, as described above. Examples of time profiles include exponentially decreasing or increasing profiles with specific decay times and initial times, constant profiles with specific initial and final times, or Gaussian profiles with specific mean times and time variations. Thus, the second time profile of a second dirty photon, which differs from the first time profile of a first dirty photon, refers to the fields of the second and first dirty photons having profiles that function or change differently over time. Similarly, in some embodiments, the time profiles of a third dirty photon and / or additional photons may differ from the first time profile.

[0240] In some other embodiments, the second time profile is the same as the first time profile. In these other embodiments, the fields of the second and first dirty photons have profiles that function or change in the same way over time. Similarly, in some embodiments, the time profile of additional photons may be the same as the first time profile.

[0241] In some embodiments, at least one of the first and second dirty photons is acquired from an optical delay line. As previously stated, an optical delay line refers to a component or group of components arranged to introduce a time delay for pulses of one or more photons. The optical delay line may have a fixed delay or an adjustable delay. For example, the optical delay line may be controlled by an optical switch that determines whether an optical pulse passes through the delay line. The optical delay line may be implemented, for example, in free space, fiber, and / or on-chip waveguides. In an example, the optical delay line may be configured to synchronize the timing of acquiring at least one of the first and second dirty photons. For example, the optical delay line may be configured to carry at least one of the first and second dirty photons, so that the first and second dirty photons are delivered in a continuous manner to a quantum emitter coupled to a cavity, and the first and second dirty photons are entangled one by one with the quantum emitter coupled to the cavity. Furthermore, an optical switch that selectively entangles an optical delay line may be provided with at least one processor or circuit. This processor or circuit may be configured to control the optical switch so as to lengthen the travel path of at least one of the first and second dirty photons. In another example, once one or more photons are generated, they may be sent through a beam splitter that generates two separate pulses, and one or both pulses may be directed to an optical delay line configured to generate a time delay in one or both pulses carried by the optical delay line. The time delay alters the temporal coherence of the photons, resulting in pulses with different time profiles, and thus potentially outputting one or more dirty photons.

[0242] In some embodiments, the first dirty photon and the second dirty photon are parts of a graph, the graph including optical qubits without quantum emitter qubits. The graph refers to graph states representing entanglement relationships between groups of qubits, the qubit being the fundamental unit of quantum information, as previously stated. This may mean that the graph is a photon graph, and the first dirty photon and the second dirty photon originate from a source other than a quantum emitter, rather than from a quantum emitter. In some embodiments, the first dirty photon and the second dirty photon are parts of a graph, the graph including optical qubits and quantum emitter qubits. This may mean that at least one of the first dirty photon and the second dirty photon originates from a quantum emitter, or a photon generator that uses a quantum emitter to produce photons.

[0243] As a non-limiting example, Figure 14A shows a preferred system 1400 or preferred device according to some embodiments relating to generating photon graph states for quantum computation. The system 1400 in Figure 14A includes a cavity 1404, a quantum emitter 1402 that can be coupled to the cavity 1404, photon generators 1416a, 1416b configured to produce dirty photons, and a circuit 1418 configured to perform a quantum computation method according to an embodiment relating to generating photon graph states for quantum computation as described herein.

[0244] Figure 14A shows two separate photon generators 1416a and 1416b, but it is understood that a single photon generator can produce a first dirty photon 1406a and a second dirty photon 1406b. In some examples of some embodiments relating to generating photon graph states for quantum computation, the photon generators 1416a and 1416b may include a cavity-coupled quantum emitter (e.g., quantum emitter 1432 coupled to cavity 1434 in Figures 15A-15C), and the photon generators 1416a and 1416b may be configured to produce the first dirty photon 1406a and / or the second dirty photon 1406b by extracting from an interfering laser pulse using the cavity-coupled quantum emitter (e.g., quantum emitter 1432 coupled to cavity 1434 in Figures 15A-15C), as described above. In some cases, as mentioned above, the quantum emitters in photon generators 1416a and 1416b may be atoms or fluctuating quantum emitters.

[0245] In the example, circuit 1418 may be configured to control photon generators 1416a, 1416b to produce a first dirty photon 1406a having a first time profile and a second dirty photon 1406b having a second time profile, and circuit 1418 may be configured to use the first dirty photon 1406a to form a first optical qubit and use the second dirty photon 1406b to form a second optical qubit.

[0246] The system 1400 in Figure 14A includes waveguides 1412a and 1412b configured to carry one or more photons or lasers. Waveguides 1412a and 1412b in Figure 14A may serve the same purpose as, for example, waveguides 816, 910, and 930 in Figures 8 to 9C. Circuit 1418 carries one or more photons DirectionThe circuit may include one or more linear optical elements configured to perform various functions relating to or transporting, controlling the flow of one or more photons, manipulating the state of one or more photons, and / or performing quantum computation. For example, the circuit 1418 may be configured to use one or more linear optical elements to couple a quantum emitter 1402 to a cavity 1404, to use the quantum emitter 1402 coupled to the cavity 1404, to entangle a first optical qubit with a second optical qubit to form a pair of entangled optical qubits 1408, and to use the pair of entangled optical qubits 1408 for quantum computation. In some embodiments of the present disclosure relating to generating photon graph states for quantum computation, the controller 1414 controls the flow of input and output photons between the photon generator and the entanglement gate (e.g., Directional between different waveguides also is cut It may be provided to replace it. For example, the controller 1414 may include one or more processors. Memory, circuit components, or circuits may also be provided to perform control.

[0247] Circuit 1418 may, for example, receive a first dirty photon 1406a and a second dirty photon 1406b from photon generators 1416a and 1416b and output the first dirty photon 1406a and the second dirty photon 1406b, which can then be carried as a continuous sequence of photons within waveguides 1412a and 1412b. In the example, circuit 1418 may also include an optical delay line configured to carry at least one of the first dirty photon 1406a and the second dirty photon 1406b, as described above in some embodiments relating to generating photon graph states for quantum computation. The first dirty photon 1406a and the second dirty photon 1406b can then interact with the quantum emitter 1402 via the evanescent coupling 1425 between the first dirty photon 1406a or the second dirty photon 1406b and the cavity 1404, provided by the waveguide 1412a, as previously described with reference to Figures 15A to 15C. This interaction between the quantum emitter 1402 and the first and second dirty photons 1406a and 1406b can result in entanglement of the first optical qubit with the second optical qubit, as previously described with reference to some embodiments relating to generating photon graph states for quantum computation.

[0248] As a non-limiting example, FIG. 14B shows an exemplary process 1450 related to generating a photonic graph state for quantum computing. Since examples of process steps are described throughout this disclosure, the foregoing examples will not be repeated or will be briefly summarized in relation to FIG. 14B. In some embodiments of the present disclosure, the exemplary process 1450 is performed by at least one processor or circuit, such as the control system 1031 and / or the optical chip 1015 of FIG. 10, or the circuit 1418 and / or the controller 1414 of FIG. 14A, to perform the operations or functions described herein. In some embodiments of the present disclosure, some aspects of the process 1450 may be implemented as software (e.g., program code or instructions) stored in a memory provided with at least one processor, or a non-transitory computer-readable medium or a computer-readable medium. In some embodiments, some aspects of the process 1450 may be implemented as hardware (e.g., a dedicated circuit). In some embodiments, the process 1450 may be implemented as hardware or as a combination of software and hardware.

[0249] FIG. 14B includes process steps (or method steps) 1452 to 1464. It will be readily understood that various implementations are possible and any combination of components or devices may be utilized to implement the exemplary process. It will also be readily understood that the process shown may be modified to change the order of steps, delete steps, or further include additional steps such as steps directed to the examples or embodiments described herein.

[0250] In step 1452, the process involves coupling a quantum emitter to a cavity. As described above, FIGS. 14A and 15A - 15C show examples of quantum emitters 1402, 1432 coupled to cavities 1404, 1434.

[0251] In step 1454, the process involves generating a first dirty photon having a first time profile, and in step 1456, the process involves using the first dirty photon to form a first optical qubit. In step 1458, the process involves generating a second dirty photon having a second time profile, and in step 1460, the process involves using the second dirty photon to form a second optical qubit. As previously mentioned, Figure 14A shows examples of the first dirty photon 1406a and the second dirty photon 1406b used to form the first and second optical qubits.

[0252] In step 1462, the process involves using a quantum emitter coupled to the cavity to entangle a first optical qubit with a second optical qubit to form a pair of entangled optical qubits. In step 1464, the process involves using the pair of entangled optical qubits for quantum computation. Figure 14A shows an exemplary pair of entangled optical qubits 1408 as described above.

[0253] As described above, conventional quantum computing relies on linear optics to generate graphs, requiring the photons used to be nearly indistinguishable ("clean") in order to achieve destructive interference. In such conventional quantum computing, any distinguishability between photons leads to a decrease in the fidelity or error of the graph. By using nonlinear elements, for example, by using the interaction between a photon and a quantum emitter coupled to a cavity, quantum computing with distinguishable ("dirty") photons is possible. Embodiments relating to generating photon graph states for quantum computing described herein provide examples of such optical quantum computing in which "dirty" (distinguishable) photons can be used.

[0254] For example, a non-temporary computer-readable medium (or computer-readable medium or computer program) may include instructions, which, when executed by at least one processor (or device), cause at least one processor (or device) to execute a process or quantum computing method described herein. According to embodiments relating to generating photon graph states for quantum computing, instructions may cause at least one processor (or device) to execute a quantum computing method or process 1450 shown in Figure 14B.

[0255] The same examples described above for each process or system feature of embodiments relating to generating photon graph states for quantum computing are also applicable to corresponding features of embodiments of this non-temporary computer-readable medium (or computer-readable medium or computer program).

[0256] According to other embodiments relating to generating photon graph states for quantum computing, an apparatus, device, system, integrated circuit device, or circuit is provided, comprising at least one processor (and memory) configured to perform a quantum computing method or process 1450 shown in Figure 14B. The same examples described above for each process or system feature of the embodiments relating to generating photon graph states for quantum computing are also applicable to the corresponding features of these embodiments.

[0257] According to yet another embodiment relating to generating photon graph states for quantum computing, a layout of an integrated circuit device or circuit comprising layout portions is provided, each layout portion being defined to pattern each feature from a combination of features of system 1400 in Figure 14A, or photon generator 1416a in Figures 15A-15C. For example, accumulationA circuit device or circuit layout includes a cavity layout portion defined to pattern a cavity, a coupling position layout portion defined to pattern coupling positions for coupling quantum emitters into a cavity, a photon generator layout portion defined to pattern a photon generator, or a channel for carrying photons supplied to the cavity by the photon generator, and a circuit layout portion defined to pattern a circuit. In some embodiments of the present disclosure, the photon generator layout portion may be defined to pattern another cavity and another coupling position for coupling another quantum emitter into the other cavity. In some embodiments of the present disclosure, the circuit layout portion includes a waveguide for carrying one or more photons or lasers, and one or more photons Direction It may be determined to pattern one or more of the following: one or more linear optical elements that perform various functions related to or transporting, controlling the flow of one or more photons, manipulating the state of one or more photons, and / or performing quantum computation.

[0258] In some embodiments of this disclosure, the layout of the integrated circuit device or circuit controls the flow of input and output photons between the photon generator and the entanglement gate (for example, Directional between different waveguides also is cut The controller further comprises a controller layout section defined to pattern the controller, and the controller may comprise one or more processors that perform control, and memory, circuit components, or circuits.

[0259] When quantum emitters (e.g., quantum dots) that can be installed by lithography are used, it is understood that the coupling position layout portion may be defined so that the quantum emitters are also patterned. The same examples described above for each process or system feature of embodiments relating to generating photon graph states for quantum computing are also applicable to the corresponding features of this embodiment.

[0260] Some embodiments of this disclosure involve initializing the state of a resonator-coupled quantum emitter. The quantum emitter may include any components configured to couple to electromagnetic modes, the resonator may include any components that establish electromagnetic modes, and the resonator-coupled quantum emitter may include quantum emitters capable of interacting with the resonator. For example, a resonator-coupled quantum emitter may include a component or group of components that confine an electromagnetic field in space and time. The component or group of components may support a discrete set of electromagnetic modes, each associated with a specific resonant frequency and lifetime in the confined field. Initializing the state of a resonator-coupled quantum emitter may involve setting a baseline state for the resonator-coupled quantum emitter. For example, initialization may include establishing an initial adjustment state system for the resonator-coupled quantum emitter. An initialized resonator-coupled quantum emitter may be one of several initialized resonator-coupled quantum emitters. The initialization of several resonator-coupled quantum emitters may occur simultaneously or sequentially.

[0261] As a non-restrictive example, Figure 1 shows a four-state system 101 of atoms 102 contained within an optical cavity 103. This may involve preparing a resonator-coupled quantum emitter in a superposition of first and second ground states. Initialization may involve causing the resonator-coupled quantum emitter to undergo one or more transitions from one state to another.

[0262] In some embodiments of this disclosure, initialization may be such that the state of a resonator-coupled quantum emitter is an equal superposition of two ground states. The ground state may be the lowest energy rest state, and the energy of the ground state may be called the zero-point energy. Superposition may refer to having multiple states simultaneously, for example, until a measurement is taken. Superposition may refer to the sum (or superposition) of two or more quantum states, for example, and equal superposition may refer to having two or more quantum states that have equal probabilities.

[0263] Figures 2E and 3 show examples of the initialized state of a resonator-coupled quantum emitter, where atom 102 (exemplary quantum emitter) is the initial superposition state of the first and second ground states 111, 113 after the initialization process. The frequencies for one or more transitions from one state to another can also be tuned by optical shifting using a laser or by applying a magnetic field.

[0264] As a non-limiting example, embodiments relating to entanglement of a photon graph or those shown in Figures 11A to 11D involve the initialization of the state of a resonator-coupled quantum emitter (e.g., exemplary resonator 1733 and exemplary quantum emitter 1731 shown in Figure 11C or Figure 11D).

[0265] For example, the resonator may include a cavity, photon cavity, optical cavity, whispering gallery mode cavity, Fabry-Perot cavity, or ring (shaped) cavity. As previously mentioned, a resonator-coupled quantum emitter may include a quantum emitter whose dipole field overlaps with the electromagnetic modes of the resonator, such as a quantum emitter or atom located within the internal cavity field of the resonator. As a non-limiting example, Figure 11C shows an example of such a quantum emitter or atom located within the internal cavity field of a resonator, having an exemplary resonator 1733 and an exemplary quantum emitter 1731.

[0266] As a non-restrictive example, a quantum emitter may be a stationary quantum system having an anharmonic spectrum configured to couple to an electromagnetic mode. In other words, as mentioned above, a quantum emitter may be a stationary qubit capable of interacting with photons. For example, a quantum emitter may include a quantum system having one or more of the following: an ion or neutral atom's electronic or nuclear configuration, a defect or quantum dot's electronic or nuclear configuration in a material substrate, or a superconducting circuit configuration including one or more Josephson junctions. For example, a quantum emitter may be one or more of a superconducting qubit, a quantum dot, an atom, a neutral atom, an ion, a rubidium atom, a cesium atom, strontium, erbium, ytterbium, calcium, barium, beryllium, or a magnesium atom (either in neutral or ionic form). For example, a quantum emitter may include a superconducting qubit. For example, a quantum emitter may include a quantum dot. For example, a quantum emitter may include an atom. An atom (e.g., a rubidium atom or a cesium atom) may be neutral. Alternatively, the atom may be an ion. Similarly, if strontium, erbium, ytterbium, calcium, barium, beryllium, or magnesium atoms are used, the atom may be neutral or in ionic form.

[0267] Some embodiments of this disclosure involve taking at least two photon graph states, each of which contains at least two photons, and selecting at least one photon from each graph state. A graph state represents a relationship between groups of qubits, a qubit is the basic unit of quantum information, and a photon graph state refers to a graph state applied to a photon, as described above. For example, a photon graph state may include photon states whose vertices may represent photon states, where a photon state refers to a state of one or more photons. For example, each of the at least two photon graph states may be the aforementioned photon graph states that represent a composite quantum system (e.g., quantum states associated with the degrees of freedom of one or more photons). A composite quantum system may include multiple quantum subsystems. Each subsystem may be represented by a node or vertex of a graph. For example, each photon graph state may have a vertex representing a photon state, where each vertex corresponds to a single-photon qubit. For example, a single-photon qubit may have a single-photon path, a single-photon vertex light This can describe the time position of a single photon, or the frequency of a single photon. Alternatively, each vertex may correspond to a continuous variable optical qubit, where the qubit represents a pair of orthogonal superposition states of photon number states.

[0268] At least two photon graph states may be provided, for example, by a photon graph state generator, such as a deterministic photon graph state generator as described herein, or any other type of generator capable of generating photon graph states containing at least two photons. Selecting at least one photon from each graph state may involve transporting the at least two photons of each graph state within a channel (or waveguide) and separating the at least two photons into individual single photons using a (beam) splitter, thereby selecting at least one photon from each graph state.

[0269] As a non-limiting example, switches such as switches 1735 and 1737 shown in Figure 11D allow at least two photons in the channel (or waveguide) Direction, and / or can be used to separate at least two photons into individual single photons. Additionally or alternatively, at least one photon may be provided, or at least one photon may be made available, by means of a single-photon generator (e.g., a photon source unit as described herein), a resonator-coupled quantum emitter configured to generate the photons described herein, and / or an optical cavity-coupled atom configured to be used as a photon generator as shown in Figures 8 to 9B.

[0270] Then, at least one photon from each photon graph state is selected for supply through the entanglement gate as described below, and as a result, the photons selected from at least two photon graph states can entangle with each other and ultimately entangle at least two graph states. For example, an entangled photon state can form or generate a larger cluster of entangled photons. The supply through the entanglement gate can be continuous, for example.

[0271] As a non-restrictive example, multidimensional clusters of entangled photons may be formed or generated having one time dimension and one or two additional dimensions, such as one or two spatial dimensions. Such cluster states may be represented by a graph, which is a d-dimensional lattice of connected subsets. Non-restrictive examples of such clusters include the photon state cluster 1041 shown in Figure 10, the entangled photon cluster 1748 shown in Figure 11D, the time-sequential cluster state of n entangled photon states in Figure 6, and the time-sequential entangled photon cluster and / or graph state 405 shown in Figure 7.

[0272] As a non-limiting example, embodiments relating to entangling a photon graph or those shown in Figures 11A to 11D include receiving at least two photon graph states, each of which contains at least two photons, and selecting at least one photon from each graph state.

[0273] Some embodiments of the present disclosure involve supplying selected photons through an entanglement gate via a resonator-coupled quantum emitter. For example, such supply through an entanglement gate via a resonator-coupled quantum emitter may involve supplying selected photons sequentially, i.e., one by one, through a waveguide, each selected photon interacting with the resonator-coupled quantum emitter via a resonator, thereby causing the photon state of the selected photon to become entangled with the state of the resonator-coupled quantum emitter, and therefore with each other's states.

[0274] As mentioned above, an entangled gate refers to a component or group of components configured to entangle qubits. For example, an entangled gate may include a quantum circuit configured to entangle qubits. An entangled gate may include the aforementioned resonator-coupled quantum emitter configured to function as an entangled gate. For example, an entangled gate may be one of the following: a controlled Z gate (CZ gate), a controlled NOT gate (CNOT gate), the square root of a SWAP gate, or a virtual SWAP gate (iSWAP gate). A resonator-coupled quantum emitter may be configured to function as one or more of these gates.

[0275] As a non-limiting example, Figure 11C or Figure 11D shows a resonator-coupled quantum emitter (e.g., exemplary resonator 1733 and exemplary quantum emitter 1731) implemented as an entanglement gate. Figure 3 shows a controlled Z-gate implementation. Figures 5A and 5B show an entanglement unit 501 (including entanglement unit atom 502) implemented as an entanglement gate. Figures 8 and 9C show rubidium coupled to cavity 818 within configuration 810 implemented as an entanglement gate. 87 Rb) indicates 820 atoms.

[0276] Non-restrictive examples of waveguides include quantum waveguide 930 in Figures 9A to 9C or channel 1736 in Figures 11C to 11D.

[0277] Figure 11D illustrates the continuous supply of photons through an entanglement gate. In this example, photons 1743 and 1745 from two graph states 1742 and 1744 are continuously supplied to a channel 1736 (e.g., a waveguide) to form or generate an entangled photon cluster 1748. Photon 1743 is selected from photon graph state 1742, and photon 1745 is selected from photon graph state 1744. These selected photons 1743 and 1745 are continuously supplied through an entanglement gate (e.g., a resonator-coupled quantum emitter such as exemplary resonator 1733 and exemplary quantum emitter 1731) to form or generate a cluster of entangled photon states (e.g., an entangled photon cluster 1748). The formed or generated cluster of entangled photon states can then be used to perform quantum computations.

[0278] Figures 5B and 6 also illustrate an exemplary cluster of a temporally continuous cluster state of n entangled photon states, where a temporally continuous series of single photons 412 generated by the single-photon source unit 401 in Figure 4B are supplied one by one through the entanglement unit 501 to generate a temporally continuous series of entangled photons 512 (for example, steps 602 to 606 are repeated n times in step 608).

[0279] As a non-limiting example, embodiments relating to entanglement of a photon graph or those shown in Figures 11A to 11D involve sequentially supplying selected photons through an entanglement gate via a resonator-coupled quantum emitter (for example, via an exemplary quantum emitter 1731 coupled to exemplary resonator 1733 shown in Figure 11C or Figure 11D).

[0280] Some embodiments of this disclosure involve unentangling a resonator-coupled quantum emitter from one or more selected photons. Unentangling means freeing something from entanglement (e.g., removing an entangled state). Unentangling a resonator-coupled quantum emitter from one or more selected photons means freeing the resonator-coupled quantum emitter from the aforementioned photon-quantum emitter entanglement, where the quantum emitter state is also entangled with the state of one or more selected photons (photon state). For example, unentangling may include at least one of detecting the state of the resonator-coupled quantum emitter or mapping the state of the resonator-coupled quantum emitter to the state of additional photons.

[0281] The state of the resonator-coupled quantum emitter is detected, the entanglement with the last photon that the resonator-coupled quantum emitter interacted with is removed, and the entanglement of the resonator-coupled quantum emitter is undone from that photon and any other photons that the resonator-coupled quantum emitter previously interacted with.

[0282] As mentioned above, mapping the state of a resonator-coupled quantum emitter to the state of an additional photon refers to transferring the state of the resonator-coupled quantum emitter qubit to an additional optical qubit. For example, mapping the state of a resonator-coupled quantum emitter to the state of an additional photon may be the result of performing a SWAP gate operation on the quantum emitter qubit and the additional optical qubit, where the state of the resonator-coupled quantum emitter is transferred to the additional photon, and the state of the additional photon is transferred to the resonator-coupled quantum emitter. In other words, the mapping can be achieved by applying a SWAP gate to the quantum emitter and the additional photon. As mentioned above, by supplying an additional photon at a frequency corresponding to a specific transition frequency of the resonator-coupled quantum emitter, the state of the resonator-coupled quantum emitter can be mapped to the additional photon, while simultaneously leaving behind a resonator-coupled quantum emitter that has been untangled from the selected photon. This is because the state of the resonator-coupled quantum emitter has been exchanged with the state of the additional photon.

[0283] Step 610 in Figure 6 involves performing a measurement on the entangled unit atom, in other words, detecting the state of the entangled unit atom (an example of a resonator-coupled quantum emitter such as atom 502). Solve the problem Let's look at an example. For instance, the measurement in question could be measurement 200, schematically shown in Figure 2E. We perform measurement 200 to untangle the entangled unit atoms from a state where quanta are entangled with photons, leaving behind a temporally continuous cluster state of n photon states of the entangled state, which is output for use as a qubit in quantum computing.

[0284] Figure 2E shows an example of untangling an entanglement involving mapping from atom to photon using a SWAP gate 201, which can be used to perform a "read" or "write" operation on the qubit of atom 102. In the example shown, the state of the incident photon is exchanged with the state of the atom (an example of a resonator-coupled quantum emitter, such as atom 502).

[0285] As a non-limiting example, embodiments relating to entanglement of a photon graph or those shown in Figures 11A to 11D involve untangling the entanglement of a resonator-coupled quantum emitter (e.g., exemplary quantum emitter 1731 coupled to exemplary resonator 1733) from selected photons. Untangling, for example, may include at least one of detecting the state of the resonator-coupled quantum emitter or mapping the state of the resonator-coupled quantum emitter to the state of additional photons, as described above.

[0286] As a non-limiting example, Figure 11A shows a quantum computing method 1710 according to an embodiment relating to entangling a photon graph to form or generate clusters of entangled photons. The quantum computing method 1710 shown in Figure 11A includes the steps of: initializing the state of a resonator-coupled quantum emitter 1711; receiving at least two photon graph states 1713, each of the at least two photon graph states including at least two photons; selecting at least one photon from each graph state 1715; supplying the selected photons through an entanglement gate via the resonator-coupled quantum emitter 1717; and unentangling the resonator-coupled quantum emitter from the selected photons 1719. The supply of selected photons through the entanglement gate may be continuous. For example, untangling includes at least one of the steps of detecting the state of a resonator-coupled quantum emitter (step 1721) and / or mapping the state of the resonator-coupled quantum emitter to the state of an additional photon (step 1722), as shown in Figure 11B.

[0287] The same examples described above for each step of the embodiment relating to entangling the photon graph are also applicable to the embodiments shown in Figures 11A and 11B.

[0288] Some embodiments of the present disclosure involve a quantum computing system comprising a resonator-coupled quantum emitter, a plurality of switches, and at least one processor or circuit configured to control the plurality of switches.

[0289] For example, a resonator-coupled quantum emitter may be as described above. The resonator may be a ring-shaped whispering gallery mode cavity. Alternatively or additionally, the resonator may include resonators of different shapes and / or configurations that can be coupled to the quantum emitter to achieve the same effect. The resonator may be capable of interacting with the quantum emitter to facilitate the interaction between the photons carried in the waveguide and the quantum emitter. For example, the resonator may have electromagnetic modes that overlap with the dipole field of the quantum emitter and / or have an internal cavity field in which the quantum emitter can be positioned or located.

[0290] A switch refers to a component or group of components configured to establish or interrupt a connection in a circuit. A switch may be, for example, a component or group of components that can establish or interrupt a connection to a channel (waveguide) to which a photon, a pulse of one or more photons, a laser, or any electromagnetic beam can be carried.

[0291] At least one processor may include any physical device or group of devices having electrical circuits that perform logical operations on one or more inputs. The quantum computing system may also include memory that stores instructions executed by at least one processor.

[0292] The circuit may include one or more functional units (or one or more layout portions), each functional unit (or each layout portion) configured to perform one or more process steps. The one or more functional units (or one or more layout portions) may be arranged (for example, they may be positioned and connected to each other or to other functional units or other layout portions) so that the circuit can perform some or all of the steps of a method or process. For example, the circuit may perform some or all of the steps of a method or process according to some embodiments of this disclosure.

[0293] For example, at least one processor or circuit may be configured to control a plurality of switches to perform one or more steps of the quantum computing method described herein.

[0294] Figure 11C shows an example of a quantum computing system 1730 according to an embodiment relating to the formation or generation of entangled photon clusters by entangling a photon graph. The quantum computing system 1730 may relate to the quantum computing method 1710 shown in Figures 11A and 11B. For example, the quantum computing system 1730 may be configured to perform the quantum computing method 1710. The quantum computing system shown in Figure 11C comprises a resonator-coupled quantum emitter (for example, an exemplary quantum emitter 1731 coupled to an exemplary resonator 1733 shown in Figure 11C), a plurality of switches 1735, 1737, and at least one processor (or controller 1739 shown in Figure 11C) configured to control the plurality of switches 1735, 1737 to initialize the state of the resonator-coupled quantum emitter 1731, receiving at least two photon graph states, each of which contains at least two photons, selecting at least one photon from each graph state, supplying the selected photon through an entanglement gate via the resonator-coupled quantum emitter 1731, and unentangling the resonator-coupled quantum emitter 1731 from the selected photon. The supply of the selected photon through the entanglement gate may be continuous. Untangling may involve at least one of the following: detecting the state of the resonator-coupled quantum emitter 1731, or mapping the state of the resonator-coupled quantum emitter 1731 to the state of additional photons.

[0295] The quantum computing system 1730 in Figure 11C may also include a plurality of channels 1736 (e.g., waveguides) that carry a laser (or pulse), or a resonator-coupled quantum emitter 1731, a magnetic field injector (e.g., a magnetic field generator or solenoid) that initializes the state of at least two photons and / or additional photons. The quantum emitter 1731 may be coupled to a resonator that may be a ring-shaped whispering gallery mode cavity 1733, as shown in Figure 11C. It is understood that another resonator of a different shape and / or configuration may be coupled to the quantum emitter 1731 to achieve the same effect, provided that the other resonator can be coupled to the quantum emitter as described above.

[0296] The multiple switches include switches such as switches 1735 and 1737 shown in Figure 11D, which allow at least two photons to enter the channel (or waveguide). Direction , and / or when separating at least two photons into individual single photons, at least two photons Direction It can be used for that purpose.

[0297] Figure 11D shows an example of an embodiment relating to entangling a photon graph, and the quantum computing system 1730 shown in Figure 11C is used to entangle photon graphs 1742, 1744 to form or generate a cluster of entangled photons 1748. As described above, the selected photon 1743 (from photon graph state 1742) and the selected photon 1745 (from photon graph state 1744) can be continuously supplied through the channel 1736 (e.g., a waveguide) via an entanglement gate (e.g., a resonator-coupled quantum emitter such as the exemplary resonator 1733 and exemplary quantum emitter 1731 shown in Figure 11C or Figure 11D), thereby causing the selected photons 1743 and 1745 to interact with the resonator-coupled quantum emitters 1733 and 1731 and become entangled, ultimately forming or generating an entangled photon cluster 1748 when all photons from photon graph states 1742 and 1744 have passed through the entanglement gate. The entangled photon cluster 1748 can then be used to perform quantum computations.

[0298] The same examples described above for each step of the embodiment relating to entangling the photon graph are also applicable to the corresponding system features of the embodiment shown in Figures 11C and 11D.

[0299] Some embodiments of the present disclosure involve a non-temporary computer-readable medium (or computer-readable medium or computer program) containing instructions, which, when executed by at least one processor (or device), cause at least one processor (or device) to execute a method or process according to some embodiments of the present disclosure.

[0300] For example, a non-temporary computer-readable medium (or computer-readable medium or computer program) may include instructions, which, when executed by at least one processor (or device), cause at least one processor (or device) to execute the quantum computing method described herein. According to an embodiment relating to entangling a photon graph to form or generate clusters of entangled photons, the instructions may cause at least one processor (or device) to execute the quantum computing method 1710 shown in Figure 11A or Figure 11B.

[0301] The same examples described above for each step of the embodiment relating to entanglement of a photon graph are also applicable to the corresponding features of this non-temporary computer-readable medium (or computer-readable medium or computer program).

[0302] According to other embodiments relating to entangling a photon graph to form or generate clusters of entangled photons, there exists an apparatus, device, system, integrated circuit device, or circuit comprising at least one processor (and memory) configured to perform the quantum computing method 1710 shown in Figure 11A or Figure 11B. The same examples described above for each step of the embodiments relating to entangling a photon graph are also applicable to the corresponding features of these embodiments.

[0303] According to yet another embodiment relating to entangling photon graphs to form or generate clusters of entangled photons, there exists an integrated circuit device or circuit layout comprising layout portions, each layout portion being configured to pattern each feature from a combination of features of the quantum computing system 1730 shown in Figure 11C or Figure 11D. For example, a resonator-coupled quantum emitter layout portion configured to pattern one or more resonators and at least one coupling position for positioning resonator-coupled quantum emitters (e.g., exemplary resonator 1733 and exemplary quantum emitter 1731 in Figure 11C or Figure 11D), a switch layout portion configured to pattern a plurality of switches 1735, 1737, and initializing the state of the resonator-coupled quantum emitter 1731, receiving at least two photon graph states, each of the at least two photon graph states being at least two There exists an integrated circuit device or circuit layout comprising: a controller layout portion defined to pattern a controller layout portion configured to control a plurality of switches 1735, 1737 to include photons, select at least one photon from each graph state, supply the selected photon through an entanglement gate via a resonator-coupled quantum emitter 1731, and untangle the resonator-coupled quantum emitter 1731 from the selected photon. The supply of selected photons through the entanglement gate may be continuous. Untangling may involve at least one of detecting the state of the resonator-coupled quantum emitter 1731 or mapping the state of the resonator-coupled quantum emitter 1731 to the state of an additional photon. The layout of the integrated circuit device or circuit may also include channel layout portions defined to pattern a plurality of channels 1736 (e.g., waveguides) that carry a laser (or pulse), or a resonator-coupled quantum emitter 1731, a magnetic field injector (e.g., a magnetic field generator or solenoid) that initializes the state of at least two photons and / or additional photons.

[0304] When quantum emitters (e.g., quantum dots) that can be installed by lithography are used, it is understood that the resonator-coupled quantum emitter layout portion may be defined to pattern one or more resonators and resonator-coupled quantum emitters (e.g., quantum dots). The same examples described above for each step of the embodiment relating to entangling the photon graph are also applicable to the corresponding features of this embodiment.

[0305] According to yet another embodiment relating to entangling a photon graph to form or generate clusters of entangled photons, there exists a method for controlling or initializing the quantum computing system 1730 shown in Figure 11C, the method comprising a corresponding method step of the quantum computing method 1710 shown in Figure 11A or Figure 11B. According to yet another embodiment relating to entangling a photon graph to form or generate clusters of entangled photons, there exists a signal or data carrier signal that carries a cluster, graph state, or optical qubit generated using the quantum computing system 1730 shown in Figure 11C or Figure 11D or the quantum computing method 1710 shown in Figure 11A or Figure 11B. The same examples described above for each step of the embodiments relating to entangling a photon graph are also applicable to the corresponding features of these embodiments.

[0306] Embodiments relating to entangling a photon graph described herein can be used to entangle a photon graph using a quantum emitter-photon entanglement gate. For example, the quantum computing system 1730 shown in Figure 11C or Figure 11D or the quantum computing method 1710 shown in Figure 11A or Figure 11B may be used to form or generate clusters of photon states (e.g., the cluster of entangled photons 1748 shown in Figure 11D). The quantum emitter-photon entanglement gate, for example, the atomic-photon controlled Z(CZ) gate, may be used to entangle a photon graph to form larger clusters of entangled photon states. The method of entangling a photon graph may result in clusters of dirty (distinguishable) photons, where dirty photons refer to distinguishable photons that are distinguishable from other photons. For example, as mentioned above, dirty photons may include, for example, propagation photons of mixed states with respect to multiple space-time modes, for example, multiple time profiles. However, it is understood that the use of such quantum emitter-photon entanglement gates (e.g., resonator-coupled quantum emitters) when performing quantum logic gate operations means that quantum computation operations can be performed using such clusters of dirty (distinguishable) photons, even if the photons exhibit disorder that makes them distinguishable.

[0307] Some embodiments of this disclosure involve a resonator-coupled quantum emitter having at least four energy levels arranged in an N configuration, the N configuration having a first ground state, a second ground state, a first excited state, and a second excited state. Excited states and ground states are relative terms in that an excited state has a higher energy level than a ground state. For example, the ground state may refer to the lowest energy rest state, and the energy of the ground state may be called the zero-point energy. An excited state refers to any quantum state having a higher energy than a ground state. Excitation refers to an increase in energy level above a chosen starting point, which is usually the ground state, but can sometimes be an already excited state. Spontaneous or induced emission of energy quanta (such as photons or tones) can occur immediately after a system (e.g., a quantum emitter or atom) is prompted to an excited state and returns to a lower energy state, e.g., a lower excited state or ground state. An N configuration refers to an arrangement that can be represented by the shape of the letter "N". The at least four levels arranged in the N configuration refer to each of the at least four levels represented by the endpoints or vertices of the "N" shape, and transitions connecting lower levels to higher levels, represented by the edges of the "N" shape. For example, the at least four levels could refer to at least four energy levels of a resonator-coupled quantum emitter, each energy level corresponding to one of a first ground state, a second ground state, a first excited state, or a second excited state, and each edge of the N configuration could represent a transition between a ground state and an excited state.

[0308] According to some embodiments of N-configuration resonator-coupled quantum emitters, such as those shown in Figures 16A to 16D (e.g., exemplary resonators 1833, 1863 and exemplary quantum emitter 1831 shown in Figures 16B to 16D), the resonator-coupled quantum emitter can be configured to perform various types of operations by controlling or setting the frequencies relating to the first ground state, second ground state, first excited state, second excited state, and transitions between any two of these states. This allows the resonator-coupled quantum emitter to be controlled to perform various operations. For example, the same resonator-coupled quantum emitter can be controlled to be used for SWAP gate operation or controlled Z(CZ) gate operation. A controlled magnetic field having a specific frequency and amplitude may, for example, allow control or manipulation of energy levels associated with those states, thereby allowing specific types of photons to be generated, released, or emitted from the resonator-coupled quantum emitter.

[0309] As previously stated, a quantum emitter includes any component configured to couple to an electromagnetic mode, a resonator includes any component that establishes an electromagnetic mode, and a resonator-coupled quantum emitter may include a quantum emitter capable of interacting with the resonator. For example, a resonator-coupled quantum emitter may include a component or group of components that confine an electromagnetic field in space and time. The component or group of components may support a discrete set of electromagnetic modes, each associated with a specific resonant frequency and lifetime in the confined field. The resonator may include, for example, a cavity, photon cavity, optical cavity, whispering gallery mode cavity, Fabry-Perot cavity, or ring (shaped) cavity. As previously stated, a resonator-coupled quantum emitter may include a quantum emitter whose dipole field overlaps with the electromagnetic modes of the resonator, for example, a quantum emitter or atom located within the internal cavity field of the resonator. As a non-limiting example, Figures 16B to 16D show an example of a quantum emitter located within the internal cavity field of an exemplary resonator 1833, 1863 and an exemplary quantum emitter 1831.

[0310] A quantum emitter may be, for example, a stationary quantum system having an anharmonic spectrum configured to couple to the electromagnetic modes of a resonator. As mentioned above, a quantum emitter may be a stationary qubit capable of interacting with photons. For example, a quantum emitter may include a quantum system having one or more of the following: an electronic or nuclear configuration of an ion or neutral atom, an electronic or nuclear configuration of a defect or quantum dot in a material substrate, or a configuration of a superconducting circuit including one or more Josephson junctions. For example, a quantum emitter may include one or more of the following: a superconducting qubit, a quantum dot, an atom, a neutral atom, an ion, a rubidium atom, a cesium atom, a strontium, an erbium, a ytterbium, a calcium, a barium, a beryllium, or a magnesium atom (either in neutral or ionic form). For example, a quantum emitter may include either a superconducting qubit or a quantum dot. For example, a quantum emitter may include an atom. For example, a quantum emitter may include at least one of a rubidium atom or a cesium atom. The atom (or rubidium atom or cesium atom) may be neutral. Alternatively, the atom (or rubidium atom or cesium atom) may be an ion. In another example, a quantum emitter may contain at least one of strontium, erbium, ytterbium, calcium, barium, beryllium, or magnesium atoms, and similarly, the atom may be neutral or in ionic form.

[0311] In some embodiments of this disclosure, a resonator-coupled quantum emitter includes a quantum emitter coupled to at least one resonator. For example, a resonator-coupled quantum emitter may be one quantum emitter coupled to one resonator. In another example, a resonator-coupled quantum emitter may be one quantum emitter coupled to two resonators, or a resonator-coupled quantum emitter may include two resonators coupled to a single quantum emitter. In yet another example, a resonator-coupled quantum emitter may include more than two resonators coupled to a single quantum emitter.

[0312] As a non-restrictive example, Figure 1 shows a four-state system 101 of an atom 102 (an example of a quantum emitter) contained within an optical cavity 103 (an example of a resonator), having a first ground state 111, a first excited state 112, a second ground state 113, and a second excited state 114; Figure 16B shows a quantum emitter 1831 coupled to a resonator 1833, the resonator-coupled quantum emitter 1831 having a first ground state 1821, a second ground state 1823, a first excited state 1822, and a second excited state 1824 arranged in an N configuration 1801; and Figure 16D shows two resonators 1833, 1863 coupled to a single quantum emitter 1831.

[0313] Some embodiments of this disclosure involve initializing the state of a resonator-coupled quantum emitter. The state of a resonator-coupled quantum emitter refers to the state or configuration of the quantum emitter, as described above. For example, the state of a resonator-coupled quantum emitter may be an electronic state, a nuclear state, or a combination thereof. Initializing the state of a resonator-coupled quantum emitter may refer to setting a baseline state for the resonator-coupled quantum emitter. For example, initialization may include establishing an initial adjustment state system for the resonator-coupled quantum emitter. The initial adjustment state system may refer to the resonator-coupled quantum emitter being in a specific state or superposition state from its N configuration of a first ground state, a second ground state, a first excited state, and a second excited state.

[0314] In some embodiments of this disclosure, the initialization of the state of a resonator-coupled quantum emitter includes preparing the resonator-coupled quantum emitter in a superposition state of a first ground state and a second ground state. Superposition can refer to, for example, multiple states being simultaneously until a measurement is taken. Superposition can refer to, for example, the sum (or superposition) of two or more quantum states. For example, initializing the state of a resonator-coupled quantum emitter, setting a baseline state, establishing an initial adjustment state system, and / or preparing the resonator-coupled quantum emitter may involve using a pulse (e.g., a laser pulse or a group of photons) having a suitable superposition of modes so that when the resonator-coupled quantum emitter interacts with the pulse, a desired state associated with a suitable superposition of modes is mapped to the resonator-coupled quantum emitter.

[0315] In some examples, a superposition state is an equal superposition of a first ground state and a second ground state. An equal superposition can mean having two or more quantum states with equal probabilities.

[0316] As a non-limiting example, Figures 2E and 3 show an example of an initialized state of a resonator-coupled quantum emitter, where atom 102 (an exemplary quantum emitter) is in an initial superposition state of first and second ground states 111, 113 after the initialization process, and Figure 1 shows a four-state system 101 of atom 102 contained within an optical cavity 103. Initializing this four-state system may involve preparing the resonator-coupled quantum emitter in a superposition of the first and second ground states. This initialization may involve causing the resonator-coupled quantum emitter to undergo one or more transitions from one state to another. For example, if an entangled unit atom 502 having a four-state system similar to atom 102 is used in the entangled unit 501 in Figures 5A and 5B described herein, initializing the entangled unit atom 502 may involve bringing atom 502 into a superposition state

number

[0317] Some embodiments of this disclosure involve tuning a frequency related to a transition between two states. A transition refers to a change in energy level, for example, a change from one state to another. The frequency related to the transition refers to the energy difference between the energy levels of the two states. A transition can occur when one or more photons having frequencies corresponding to the transition frequency interact with a resonator-coupled quantum emitter. Tuning a frequency related to a transition refers to fine-tuning, adjusting, and / or setting the frequency for that transition. For example, tuning a frequency related to a transition between two states may involve using one or more of the following: a magnetic field and / or a laser. For example, tuning a frequency related to a transition may occur by an optical shift using a laser and / or by a Zeeman shift using a magnetic field.

[0318] Some embodiments of this disclosure involve tuning the frequency of a first transition between a first ground state and a first excited state, tuning the frequency of a second transition between a second ground state and a second excited state, and tuning the frequency of a third transition between a second ground state and a first excited state. In the example, the tuning of the frequencies of the first, second, and third transitions is initiated before initialization. One or more of the transition frequencies may be produced by optical shifts using a laser. Optical shifts may refer to AC-Stark shifts, which are perturbation effects that shift the atomic energy levels of the laser field. One or more of the transition frequencies may be produced by applying a magnetic field. For example, one or more of the transition frequencies may be produced by applying a Zeeman shift using a magnetic field.

[0319] As a non-limiting example, Figure 1 shows a laser source 151 that provides pulses to change the state of an atom 102 (an example of a quantum emitter coupled to a resonator), a magnet 141 that generates a magnetic field configured to ensure that the transitions are within the bandwidth of an optical cavity 103 (an example of a resonator) and / or to set the energy levels of the excited or ground state, and transitions 121, 122, 123 having specific energies associated with specific interacting optical modes 1, 2, and 3, as also shown in Figures 2A and 2B.

[0320] As a non-limiting example, Figure 16B shows transitions 1841, 1842, and 1843, and Figure 16C shows a laser source 1851 and a magnetic field generator 1853 configured to provide a laser or magnetic field that can be used for such adjustment of the frequency related to the transitions.

[0321] Some embodiments of this disclosure involve supplying a plurality of photons at a frequency corresponding to the frequency of a second transition, thereby entangling the plurality of photons with a resonator-coupled quantum emitter. For example, supplying a plurality of photons includes supplying a plurality of single photons in sequence. Such a sequence supply may involve supplying the plurality of photons one by one through a waveguide such that each photon interacts with the resonator-coupled quantum emitter through the resonator, thereby entangling the plurality of photons one by one with the resonator-coupled quantum emitter. The second transition lies between a second ground state and a second excited state. In an example, the resonator-coupled quantum emitter may be prepared / initialized in a superposition state of a first ground state and a second ground state, and when photons at a frequency corresponding to the frequency of the second transition are supplied to the waveguide, the photons interact with the resonator-coupled quantum emitter through the resonator (due to the evanescent field around the waveguide). This interaction results in a second transition from the second ground state to the second excited state of the resonator-coupled quantum emitter. heightThe resonator-coupled quantum emitter then transitions back to its second ground state, releasing or emitting an output photon. This sequence of events results in a pi phase shift for the emitted photon, provided the resonator-coupled quantum emitter is in its second ground state. Therefore, the emitted photon can also become entangled with the resonator-coupled quantum emitter.

[0322] As a non-restrictive example, Figure 16B shows a second transition 1842 between the second ground state 1823 and the second excited state 1824 of the quantum emitter 1831. As a non-restrictive example, Figure 3 shows an incident photon 301 in mode 3 (optical mode 3 associated with transition 123 between the second ground state 133 and the second excited state 114), which gives rise to transition 123A, then transition 123B, thereby emitting an exit photon 302 entangled with atom 102 (an example of a resonator-coupled quantum emitter).

[0323] For example, entanglement may involve using a resonator-coupled quantum emitter to function as an entanglement gate. As previously mentioned, an entanglement gate refers to a component or group of components or a control sequence configured to entangle qubits, for example, optical qubits of multiple photons. For example, an entanglement gate may include a quantum circuit configured to entangle qubits. An entanglement gate may include the aforementioned resonator-coupled quantum emitter configured to function as an entanglement gate. An entanglement gate may be, for example, one of the controlled Z gate (CZ gate), controlled NOT gate (CNOT gate), the square root of a SWAP gate, or a virtual SWAP gate (iSWAP gate). A resonator-coupled quantum emitter may be configured to function as one or more of these gates.

[0324] As a non-limiting example, Figure 3 shows a controlled Z-gate implementation, Figures 5A and 5B show an entangled unit 501 (including entangled unit atom 502) implemented as an entangled gate, and Figures 8 and 9C show rubidium coupled to cavity 818 within configuration 810 implemented as an entangled gate. 87 Rb) indicates 820 atoms.

[0325] Non-restrictive examples of waveguides from which photons may be supplied include quantum waveguide 930 in Figures 9A to 9C or waveguides 1838 and 1868 in Figures 16B to 16D. Photons may be supplied continuously.

[0326] Some embodiments of this disclosure involve supplying photons at frequencies corresponding to the frequency of at least one of the first or third transitions, thereby mapping the state of a resonator-coupled quantum emitter to the photons. As described above, mapping the state of a resonator-coupled quantum emitter to photons means transferring the state of a resonator-coupled quantum emitter qubit to a photon qubit. For example, mapping the state of a resonator-coupled quantum emitter to photons may be the result of performing a SWAP gate operation on the quantum emitter qubit and the photon qubit, where the state of the resonator-coupled quantum emitter is transferred to the photon and the state of the photon is transferred to the resonator-coupled quantum emitter. In other words, the mapping can be achieved by applying a SWAP gate to the quantum emitter and the photon.

[0327] As mentioned above, by supplying photons at frequencies corresponding to specific transition frequencies of the resonator-coupled quantum emitter, it is possible to map the state of the resonator-coupled quantum emitter to the photons, while simultaneously leaving behind a resonator-coupled quantum emitter that has been untangled from previously interacting photons. This is because the state of the resonator-coupled quantum emitter is exchanged with the state of the supplied photons.

[0328] Since the state of the supplied photons is transferred to the resonator-coupled quantum emitter, the resonator-coupled quantum emitter can also be initialized to an initial state, such as a first ground state or a second ground state, by supplying photons at a frequency corresponding to a specific transition of the resonator-coupled quantum emitter. The first transition lies between the first ground state and the first excited state, and the third transition lies between the second ground state and the first excited state. Therefore, for example, the resonator-coupled quantum emitter can be further initialized to correspond to at least one of the first ground state or the second ground state by supplying photons at a frequency corresponding to at least one of the first or third transition. In the example, a resonator-coupled quantum emitter may be prepared / initialized in a superposition state of a first and a second ground state, and when photons at frequencies corresponding to the superposition of the frequencies for the first and third transitions are supplied to the waveguide, the photons interact with the resonator-coupled quantum emitter through the resonator (due to the evanescent field around the waveguide). This interaction causes the superposition state of the photons to be exchanged with the superposition state of the resonator-coupled quantum emitter.

[0329] As a non-restrictive example, Figure 16B shows a first transition 1841 between a first ground state 1821 and a first excited state 1822, and a third transition 1843 between a second ground state 1823 and a first excited state 1822. As a non-restrictive example, Figure 2E shows a SWAP gate 201, in which an incident photon 202 of superposition of optical modes 1 and 2 (optical modes 1 and 2 associated with transitions 121 and 122, respectively) produces transition 121A in Figure 2A, then transition 122A, and transition 122B in Figure 2B, then transition 121B. The exit photon 204 is left in the state of atom 102, and atom 102 is left in the state of incident photon 202.

[0330] Figure 16A shows a quantum computation method 1810 according to an embodiment relating to an N-configuration resonator-coupled quantum emitter. The quantum computation method 1810 shown in Figure 16A is a step 1811 for initializing the state of a resonator-coupled quantum emitter having at least four levels arranged in an N configuration, wherein the N configuration has a first ground state, a second ground state, a first excited state, and a second excited state; a step 1813 for adjusting the frequency relating to a first transition between the first ground state and the first excited state; and a step 18 for adjusting the frequency relating to a second transition between the second ground state and the second excited state. The process includes steps 15, 1817 of adjusting the frequency for a third transition between a second ground state and a first excited state, 1818 of supplying a plurality of photons at a frequency corresponding to the frequency for the second transition, thereby entangling the plurality of photons to a resonator-coupled quantum emitter, and 1819 of supplying a plurality of photons at a frequency corresponding to the frequency for at least one of the first or third transition, thereby mapping the state of the resonator-coupled quantum emitter to the photons. In the example, in step 1818, the plurality of photons may be supplied sequentially.

[0331] The same examples described above for each step of the embodiment relating to an N-configuration resonator-coupled quantum emitter are also applicable to the embodiment shown in Figure 16A. For example, initializing the state of a resonator-coupled quantum emitter may include preparing the resonator-coupled quantum emitter in a superposition state of a first ground state and a second ground state. In the example, tuning of the frequencies relating to the first, second, and third transitions may occur before initialization. In the example, tuning of one or more of the frequencies relating to the transitions is caused by optical shifting using a laser or by applying a magnetic field. In the example, supplying multiple photons may include supplying multiple single photons in sequence. The resonator-coupled quantum emitter may be further initialized to correspond to at least one of the first ground state or the second ground state by supplying photons at frequencies corresponding to the frequencies relating to at least one of the first or third transitions.

[0332] Some embodiments of the present disclosure are associated with a quantum computing system comprising a resonator-coupled quantum emitter having at least four levels arranged in an N configuration, the N configuration having a first ground state, a second ground state, a first excited state, and a second excited state, and at least one processor or circuit. For example, the resonator-coupled quantum emitter may be configured as described above. The resonator may be a ring-shaped whispering gallery mode cavity. Alternatively or additionally, the resonator may include resonators of different shapes and / or configurations that can be coupled to the quantum emitter to achieve the same effect. The resonator may be capable of interacting with the quantum emitter to facilitate the interaction between photons carried in the waveguide and the quantum emitter. For example, the resonator may have electromagnetic modes that overlap with the dipole field of the quantum emitter and / or have an internal cavity field in which the quantum emitter can be positioned or located.

[0333] At least one processor may include any physical device or group of devices having electrical circuits that perform logical operations on one or more inputs. The quantum computing system may also include memory that stores instructions executed by at least one processor.

[0334] The circuit may include one or more functional units (or one or more layout portions), each functional unit (or each layout portion) configured to perform one or more process steps. The one or more functional units (or one or more layout portions) may be arranged (for example, they may be positioned and connected to each other or to other functional units or other layout portions) so that the circuit can perform some or all of the steps of a method or process. For example, the circuit may perform some or all of the steps of a method or process according to some embodiments of this disclosure relating to an N-configuration resonator-coupled quantum emitter.

[0335] For example, Figure 16B shows a quantum computing system 1830 according to a certain embodiment relating to an N-configuration resonator-coupled quantum emitter. The quantum computing system 1830 may relate to the quantum computing method 1810 shown in Figure 16A. For example, the quantum computing system 1830 may be configured to perform the quantum computing method 1810. The quantum computing system shown in Figure 16B is a resonator-coupled quantum emitter having at least four levels arranged in an N configuration 1801 (for example, an exemplary quantum emitter 1831 coupled to an exemplary resonator 1833 shown in Figures 16B to 16D), wherein the N configuration 1801 includes a resonator-coupled quantum emitter having a first ground state 1821, a second ground state 1823, a first excited state 1822, and a second excited state 1824, and at least one processor or circuit 1839 configured to perform a quantum computing method described herein, for example, the quantum computing method 1810.

[0336] The quantum computing system 1830 in Figure 16B may also include multiple channels (e.g., waveguides 1836, 1838) for carrying a laser (or pulse), or a magnetic field injector (e.g., a magnetic field generator or solenoid) for initializing the state of the resonator-coupled quantum emitter 1831. Waveguide 1836 may perform the same function as the utility waveguide 910 in Figures 9A to 9C, and waveguide 1838 may perform the same function as the quantum waveguide 930 in Figures 9A to 9C. The quantum emitter 1831 may be coupled to a resonator that may be a ring-shaped whispering gallery mode cavity 1833, as shown in Figures 16B to 16D. The quantum emitter 1831 may be coupled to two resonators 1833, 1863, as shown in Figure 16D. It is understood that another resonator of a different shape and / or configuration may be coupled to the quantum emitter 1831 to achieve the same effect, provided that the other resonator can be coupled to the quantum emitter as described above.

[0337] Figure 16C shows a quantum computing system 1850 according to a subset embodiment relating to an N-configuration resonator-coupled quantum emitter. Compared to quantum computing system 1830, quantum computing system 1850 further includes at least one of a laser source 1851 or a magnetic field generator 1853 configured to provide a laser or magnetic field that can be used to tune frequencies relating to the initialization and / or transitions of the resonator-coupled quantum emitter. The laser source 1851 may provide a laser that is optically shifted (e.g., AC-Stark shift) and thereby tunes at least one of the frequencies relating to the transitions. The magnetic field generator 1853 may provide a magnetic field and provide the application of a magnetic field that tunes at least one of the frequencies relating to the transitions.

[0338] Figure 16D shows a quantum computing system 1860 according to one embodiment relating to an N-configuration resonator-coupled quantum emitter. Compared to quantum computing systems 1830 or 1850, quantum computing system 1850 further includes an additional resonator 1863 and an additional waveguide 1868. In quantum computing system 1850, two resonators 1833, 1863 are coupled to a single quantum emitter 1831, and each resonator 1833, 1863 is provided with its own waveguides 1838, 1868, which couple the photons carried within them to the associated resonators 1833, 1863 by an evanescent field established around the waveguides 1838, 1868. It is also understood that a plurality of upper waveguides 1836 may be provided so that each resonator has its own utility waveguide.

[0339] The same examples described above for each step of the embodiment relating to the N-configuration resonator-coupled quantum emitter, or for each step of the quantum computation method 1810, are also applicable to these embodiments shown in Figures 16B to 16D.

[0340] Some embodiments of the present disclosure involve a non-temporary computer-readable medium (or computer-readable medium or computer program) containing instructions, which, when executed by at least one processor (or device), cause at least one processor (or device) to execute a method or process according to some embodiments of the present disclosure.

[0341] For example, a non-temporary computer-readable medium (or computer-readable medium or computer program) may include instructions, which, when executed by at least one processor (or device), cause at least one processor (or device) to execute the quantum computation method described herein. According to embodiments relating to an N-configuration resonator-coupled quantum emitter or those shown in Figures 16A to 16D, the instructions may cause at least one processor (or device) to execute the quantum computation method 1810 shown in Figure 16A.

[0342] The same examples described above for each step of embodiments relating to an N-configuration resonator-coupled quantum emitter or those shown in Figures 16A to 16D are also applicable to corresponding features of embodiments of this non-temporary computer-readable medium (or computer-readable medium or computer program).

[0343] Other embodiments relating to an N-configuration resonator-coupled quantum emitter include an apparatus, device, system, integrated circuit device, or circuit comprising at least one processor (and memory) configured to perform the quantum computation method 1810 shown in Figure 16A. The same examples described above for each step of the embodiments relating to the N-configuration resonator-coupled quantum emitter are also applicable to the corresponding features of these embodiments.

[0344] Further embodiments relating to an N-configuration resonator-coupled quantum emitter include a layout of an integrated circuit device or circuit having layout portions, each layout portion being configured to pattern each feature from combinations of features of the quantum computing systems 1830, 1850, 1860 shown in Figures 16B to 16D. For example, some embodiments may include a layout of an integrated circuit device or circuit having a resonator-coupled quantum emitter layout portion configured to pattern one or more resonators and at least one coupling position for positioning resonator-coupled quantum emitters (e.g., exemplary resonators 1833, 1863 and exemplary quantum emitter 1831 in Figures 16B, 16C, or 16D), and a circuit layout portion configured to pattern a circuit (e.g., at least one processor or circuit 1839 in Figures 16B to 16D) configured to perform a quantum computing method described herein, e.g., quantum computing method 1810.

[0345] The resonator-coupled quantum emitter layout portion may be defined to pattern two or more resonators (e.g., exemplary resonators 1833, 1863 and exemplary quantum emitter 1831 in Figure 16D) associated with one coupling position that positions one resonator-coupled quantum emitter. If quantum emitters that can be installed by lithography (e.g., quantum dots) are used, it is understood that the resonator-coupled quantum emitter layout portion may be defined to pattern the resonator-coupled quantum emitters (e.g., quantum dots). The same examples described above for each step of embodiments relating to an N-configuration resonator-coupled quantum emitter or those shown in Figures 16A to 16D are also applicable to the corresponding features of this embodiment.

[0346] The layout of the integrated circuit device or circuit may also include channel layout portions defined to pattern multiple channels (e.g., waveguides 1836, 1838) that carry a laser (or pulse),...

Claims

1. A quantum computing system, Multiple photon cavities, A plurality of coupling positions for quantum emitter positioning, each coupling position associated with a different photon cavity among the plurality of photon cavities, and the quantum emitter associated with each coupling position is configured to generate a graph state by mediating the interaction between consecutive incident light qubits, A photon generator configured to supply photons to a plurality of photon cavities, wherein the photon cavities are configured to couple optical qubits to quantum emitters, Multiple photon output channels located downstream of the multiple cavities that output the graph state, A quantum computing system equipped with [the following features].

2. The system according to claim 1, wherein the quantum emitter includes a stationary qubit capable of interacting with photons.

3. The system according to claim 1, wherein the quantum emitter includes a superconducting qubit.

4. The system according to claim 1, wherein the quantum emitter includes a quantum dot.

5. The system according to claim 1, wherein the quantum emitter includes an atom.

6. The system according to claim 5, wherein the atom is neutral.

7. The system according to claim 5, wherein the atom is an ion.

8. The system according to claim 5, wherein the quantum emitter includes a rubidium atom.

9. The system according to claim 5, wherein the quantum emitter includes a cesium atom.

10. The system according to claim 5, wherein the quantum emitter comprises at least one of strontium, erbium, ytterbium, calcium, barium, beryllium, or magnesium atoms.

11. The system according to any one of claims 1 to 10, wherein the photon generator includes at least one additional photon cavity.

12. The system according to claim 11, wherein the photon generator includes at least one additional quantum emitter and at least one additional coupling position for quantum emitter positioning, each additional coupling position being associated with a different photon cavity among the at least one additional photon cavity.

13. The system according to claim 12, wherein the at least one additional quantum emitter includes a stationary qubit capable of interacting with photons.

14. The system according to claim 12, wherein the at least one additional quantum emitter includes a superconducting qubit.

15. The system according to claim 12, wherein the at least one additional quantum emitter includes a quantum dot.

16. The system according to claim 12, wherein the at least one additional quantum emitter includes an atom.

17. The system according to claim 16, wherein the at least one additional quantum emitter comprises a rubidium atom.

18. The system according to claim 16, wherein the at least one additional quantum emitter comprises at least one of strontium, erbium, ytterbium, calcium, barium, beryllium, or magnesium atoms.

19. A quantum computation method for generating a graph state, wherein the method is This involves coupling quantum emitters at each of multiple coupling positions, resulting in each of the multiple quantum emitters being associated with a different coupling position, each coupling position being associated with a different photon cavity among multiple photon cavities, and the quantum emitters associated with each coupling position being configured to generate a graph state by mediating the interaction between consecutive incident optical qubits. The method involves supplying photons to the plurality of photon cavities, wherein the photon cavities are configured to couple optical qubits to the quantum emitters. The graph state is output via a plurality of photon output channels located downstream of the plurality of cavities, A quantum computing method that includes this.

20. A non-temporary computer-readable storage medium containing instructions, wherein, when the instructions are executed by at least one processor, the at least one processor causes the quantum computing method to execute, and the quantum computing method is This involves coupling quantum emitters at each of multiple coupling positions, resulting in each of the multiple quantum emitters being associated with a different coupling position, each coupling position being associated with a different photon cavity among multiple photon cavities, and the quantum emitters associated with each coupling position being configured to generate a graph state by mediating the interaction between consecutive incident optical qubits. The method involves supplying photons to the plurality of photon cavities, wherein the photon cavities are configured to couple optical qubits to the quantum emitters. The graph state is output via a plurality of photon output channels located downstream of the plurality of cavities, Non-temporary computer-readable storage media, including [specific type of storage medium].

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