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 to U.S. Provisional Application No. 63 / 320,454, filed March 16, 2022, and Israeli Patent Application No. 282705, filed April 27, 2021, the entire contents of both of which are incorporated herein by reference.

[0002] The present disclosure relates generally to quantum computing using cavity quantum electrodynamics (cavity QED), and related devices, systems, computer-readable media, and methods. Some embodiments involve the generation of photonic graph states. [Background technology]

[0003] Building a commercially useful quantum computer (QC) can be challenging for many reasons, including scalability issues resulting from the increased complexity, noise, and crosstalk that result when more qubits are added. Quantum computing algorithms can also utilize entangled states, and some quantum computing architectures may use a source of entangled states (also referred to as a resource state generator) to obtain such entangled states. This disclosure relates to mechanisms for or with such a source of entangled states. Currently, quantum computing remains limited to the proof-of-concept stage, using a relatively small number of qubits, sufficient merely to demonstrate that quantum computing is feasible in principle. To make quantum computing practical for handling real-world problems, current devices require 10 qubits, including qubits for error correction. 6 It needs to be scaled up to handle a large number of qubits beyond that.

[0004] Qubits for quantum computing are often organized on one of three physical platforms (or domains): superconductors (superconducting state), atoms (ionic state), and photons (photonic state).

[0005] Optical platforms offer a number of significant practical advantages over other platforms: photons are relatively easy to generate, do not require cryogenic or ultra-high vacuum environments, and the construction of highly miniaturized and reliable optical devices and their communication infrastructure is achieved using readily available fabrication techniques. Thus, optical platforms are currently prime candidates for achieving the high levels of scaling required for practical quantum computing devices.

[0006] However, the full potential of optical platforms is not currently realized, primarily due to the current high inefficiency of generating entangled photon states for use as entanglement resources in optical quantum computing. Conventional mechanisms rely on nonlinear effects in crystals to generate single photons. To generate photon graph states, linear optical elements are used to probabilistically entangle the photons. To achieve this, the generated photons must be indistinguishable and generated according to perfectly timed, identically shaped pulses. Unfortunately, this requirement comes at the expense of generation efficiency. Furthermore, to arrive at a photon graph state with a specific number of qubits, the probabilistic entanglement process requires a much larger number of initial single photons and, therefore, a larger number of elements. These cumulative inefficiencies significantly limit efforts to scale optical platforms to meaningful numbers of qubits.

[0007] It would therefore be highly desirable to have an apparatus and method for generating photonic graph states that reduces or eliminates stochastic processes and the inefficiencies inherent in such processes, and instead deterministically generates photonic graph states with maximum or improved efficiency for use as qubits. Such objectives are met or furthered by embodiments of the present disclosure. Summary of the Invention

[0008] The source of entangled states used in quantum computing architectures may use matter-based or light-based mechanisms. Matter-based quantum computing mechanisms, such as those using trapped ions, superconducting qubits, or quantum dots, are sometimes thought to achieve entangled states more efficiently than light-based mechanisms. Light-based quantum computing mechanisms, such as silicon photonics, are thought to be much more scalable and modular. Thus, light-based mechanisms may be useful in addressing the scalability issues discussed above.

[0009] Using embodiments consistent with the present disclosure, a source of entangled states for use in quantum computing with a large number of qubits may be possible, for example, for optical quantum computing. The architecture may also provide a scalable architecture that can be fabricated in a standard silicon fabrication lab. The cavity quantum electrodynamics (cavity QED)-based mechanism used in embodiments consistent with the present disclosure can exploit the properties of both light and matter and therefore can serve as a source of entangled states in the architecture, leading to a scalable architecture that can be fabricated, possibly even in a standard silicon fabrication lab, at a reasonable cost.

[0010] For example, some embodiments consistent with the present disclosure include novel entangled photon cluster state generators. More specifically, the present disclosure includes a description of chip implementations of cavity QED systems. Entangled photons can be used as the basic building blocks for quantum computers.

[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 states of photons. The building blocks of an optical quantum computer can include entangled photons. Therefore, there is a need to efficiently generate entangled photons.

[0012] Embodiments of the present disclosure may provide or enable deterministic apparatus and methods for generating single-photon, multi-photon, and photon graph states and their entanglement that can be used in quantum computing. By avoiding stochastic processes, the present disclosure can achieve high efficiency and enable highly generated photons to be used in qubits.

[0013] According to aspects of the present disclosure, there are provided systems, methods, devices, integrated circuit devices, circuits, integrated circuit device layouts, computer-readable storage media, non-transitory computer-readable storage media, and signals as described herein. Other features of embodiments of the present disclosure will become apparent from the following dependent claims, clauses, accompanying drawings, and description of preferred embodiments with reference to the accompanying drawings.

[0014] Some embodiments of the present disclosure involve coupling a quantum emitter at each of a plurality of coupling locations, such that each of the plurality of quantum emitters is associated with a different coupling location, and each coupling location is associated with a different photon cavity of a plurality of photon cavities, the quantum emitter associated with each coupling location being configured to mediate interactions between successive incoming optical qubits to generate a graph state; providing photons to the plurality of photon cavities, the photon cavities being configured to couple the optical qubits to the quantum emitters; and outputting the graph state via a plurality of photon output channels 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 a state of a quantum emitter qubit associated with each of the plurality of quantum emitters; transmitting the optical qubit toward the plurality of quantum emitters in at least one first instance of transmission to create 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 of transmissions, transmitting the optical qubit toward the plurality of quantum emitters in at least one second instance of transmission to create a SWAP gate between the optical qubit and the quantum emitter qubit, 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 first dirty photons having a first temporal profile, using the first dirty photons to form a first optical qubit, generating second dirty photons having a second temporal profile, using the second dirty photons to form a second optical qubit, using the quantum emitter coupled to the cavity to entangle the first optical qubit with the second optical qubit to form an entangled optical qubit pair, and using the entangled optical qubit pair to perform quantum computation.

[0017] According to aspects of the present disclosure, a quantum computing system, method, and computer-readable medium (or non-transitory computer-readable medium) are provided that involve initializing a state of a resonator-coupled quantum emitter; receiving at least two photon graph states, each of the at least two photon graph states including at least two photons; selecting at least one photon from each graph state; feeding the selected photon through an entanglement gate via the resonator-coupled quantum emitter; and disentangling the resonator-coupled quantum emitter from the selected photon, wherein the disentangling 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 a state of an additional photon.

[0018] According to aspects of the present disclosure, a quantum computing system, method, and computer-readable medium (or non-transitory computer-readable medium) are provided that involve initializing a state of 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; tuning a frequency associated with a first transition between the first ground state and the first excited state; tuning a frequency associated with a second transition between the second ground state and the second excited state; tuning a frequency associated with a third transition between the second ground state and the first excited state; providing a plurality of photons at a frequency corresponding to the frequency associated with the second transition, thereby entanglement of the plurality of photons in the resonator-coupled quantum emitter; and providing photons at a frequency corresponding to the frequency associated with at least one of the first transition or the third transition, thereby mapping the state of the resonator-coupled quantum emitter to the photons.

[0019] Some embodiments of the present disclosure involve a plurality of optical processing stages, each optical processing stage including at least two of an optical switch, a beam splitter, a waveguide, or a photon generator; a plurality of messengerless connections, each connection located between adjacent optical processing stages; and circuitry configured to regulate the flow of photons between adjacent stages such that there is no input from a previous stage in decisions regarding stage setting or flow between adjacent stages.

[0020] According to aspects of the presently disclosed subject matter, a deterministic photon graph state generator and related methods are provided in which deterministic single-photon generation is combined with deterministic cavity-enhanced photon-atom entanglement to generate temporally continuous entangled photons, and in related embodiments, the generation and entanglement units are integrated into an integrated array that emits multidimensional cluster states of entangled photons with one time dimension and one or two additional dimensions, such as one time dimension and one or two spatial dimensions.

[0021] Single-photon generation, atom-photon entanglement, and photon-photon entanglement can be achieved with a four-state atomic system within an optical cavity, whose transitions can be independently manipulated according to the energy and polarity of the incident photons. Types of operations include single-photon capture, atom-photon entanglement, multiple-photon entanglement, and atomic qubit preparation and measurement.

[0022] According to one aspect, there is provided a method for ensuring a graph state of quantum entangled photons (a photon source unit may also be referred to as a photon generator), the method comprising: providing a photon source unit for securing single photons, the photon source unit comprising a source unit atom disposed within an internal cavity field of a source optical cavity; Providing a photon entanglement unit for quantum entanglement of photon states, wherein the photon entanglement unit atoms are disposed within an internal cavity field of an entanglement optical cavity; A photon pulse is sent to the photon entanglement unit to place the entanglement unit atoms in an atomic quantum superposition state.

number

[0023] Making a measurement on an entangled unit atom may include making a measurement in the xy plane of the Bloch sphere.

[0024] According to another aspect, there is provided a device for ensuring a graph state of quantum entangled photons, the device comprising: a plurality of single photon source units; a first stage linear optical element; a first plurality of entanglement units; Equipped with the plurality of single-photon source units, the first stage linear optical element, and the first plurality of entanglement units are correspondingly offset along a predetermined spatial axis; each single-photon source unit of the plurality of photon source units outputs a single photon to the first stage linear optical element and from there into a respective entanglement unit of the first plurality of entanglement units; The first plurality of entanglement units outputs a one-dimensional spatial array of entangled photons sequentially in the time dimension.

[0025] The single photon source unit and / or the entanglement unit may each comprise an atom in a first ground state, a first excited state, a second ground state, a second excited state, or a superposition thereof, wherein the atom is a first transition between a first ground state and a first excited state; a second transition between the first excited state and a second ground state, and further configured to selectively undergo a third transition between the second ground state and the second excited state; The device includes an optical cavity defining an internal cavity field disposing atoms therein, an optical waveguide coupled to the optical cavity, a magnet configured to generate a magnetic field at the atoms, and a laser source configured to generate pulses of photons in an interference state, the device configured such that each of the transitions is within a resonance of the optical cavity.

[0026] The first and second transitions may be selected to be orthogonally polarized relative to each other.

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

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

[0029] The laser source is a photon initiating pulse configured to initialize the 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 The photon capture pulse may be configured to selectively generate a photon-capturing pulse configured to capture a single photon from the atom by causing the atom to undergo a second and first transition from a second ground state to the first ground state via a first excited state.

[0030] The laser source may be configured to selectively generate preparation photons configured to set the state of the atom to a quantum superposition state, the preparation photons being in a superposition of first and second preparation modes, and as a result of the preparation photon's interaction with the atom, its first and second ground states are in a superposition corresponding to the superposition of the first and second preparation modes, i.e., as a result of the interaction, the first and second ground states of the atom are in a superposition with probability amplitudes equal to the probability amplitudes of the first and second preparation modes of the incident preparation photon.

[0031] The atom can be a rubidium atom.

[0032] The magnet may be a solenoid.

[0033] The first stage linear optics may include phase control.

[0034] The device is a second stage linear optic; a second plurality of entanglement units; and the second stage linear optical element and the second plurality of entanglement units are correspondingly offset along a predetermined spatial axis relative 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 an entangled state output from each entanglement unit of the first plurality of entanglement units are input to a linear optical element of a second stage, and from there are input into each entanglement unit of the second plurality of entanglement units.

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

[0036] The device may be configured to generate entangled qubits for use in a quantum computer.

[0037] The device may be configured to perform the methods of any of the aspects of the presently disclosed subject matter.

[0038] The foregoing summary provides specific examples of embodiments of the present disclosure to provide characterization of the disclosure and is not intended to encompass all aspects of embodiments of the present disclosure. Additional features and advantages of embodiments of the present disclosure will be set forth in part in the description that follows, and in part will be obvious from the description, or may be learned by practice of embodiments of the present disclosure. The features and advantages of embodiments of the present disclosure will be realized and attained by means of the elements and combinations particularly pointed out in the appended claims.

[0039] It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the embodiments of the present disclosure as claimed. The accompanying drawings constitute a part of this specification. The drawings illustrate several embodiments of the present disclosure and, together with the description, serve to explain the principles of the embodiments of the disclosure as set forth in the appended claims. [Brief explanation of the drawings]

[0040] The disclosed subject matter can be best understood by reference to the following detailed description when read in conjunction with the accompanying drawings. [Figure 1] FIG. 1 illustrates a schematic diagram of a device for use in quantum computing according to an embodiment of the present disclosure. [Figure 2A] FIG. 2A is a state diagram for the process of the device shown in FIG. [Figure 2B] FIG. 2B is a state diagram for another process of the device shown in FIG. [Figure 2C] FIG. 2C is a state diagram illustrating the no-interaction state of the device shown in FIG. [Figure 2D] FIG. 2D is a state diagram illustrating another no-interaction state of the device shown in FIG. [Figure 2E] FIG. 2E illustrates a schematic diagram of performing measurements on atoms of the device shown in FIG. 1 according to an embodiment of the present disclosure. [Figure 3] FIG. 3 shows a schematic diagram of entanglement of atoms with photons using the device shown in FIG. [Figure 4A] FIG. 4A illustrates a schematic diagram of a single photon source unit according to an embodiment of the present disclosure. [Figure 4B] FIG. 4B shows a schematic representation of the generation of a continuous train of single photons from the photon source unit of FIG. 4A. [Figure 5A] FIG. 5A illustrates a schematic diagram of an entanglement unit for quantum entanglement of a photon state with an atomic state, according to an embodiment of the present disclosure. [Figure 5B] FIG. 5B schematically illustrates the quantum entanglement of a continuous series of photon states with an atomic state, according to an embodiment of the present disclosure. [Figure 6] FIG. 6 is a flowchart of a method for securing a photon graph state according to an embodiment of the present disclosure. [Figure 7] FIG. 7 illustrates a schematic diagram of an apparatus for ensuring a multidimensional cluster state of quantum entangled photon states according to an embodiment of the present disclosure. [Figure 8] FIG. 8 shows a schematic diagram of atoms bound to a cavity consistent with some embodiments of the present disclosure. [Figure 9A] FIG. 9A illustrates a schematic of a waveguide that can be used for atoms coupled to a cavity according to some embodiments of the present disclosure. [Figure 9B] FIG. 9B illustrates a schematic diagram of photon generation according to some embodiments of the present disclosure. [Figure 9C] FIG. 9C illustrates a schematic diagram of an entanglement gate according to some embodiments of the present disclosure. [Figure 10] FIG. 10 shows a schematic diagram of a system including a vacuum chamber that can be used for atomic and optical chips according to some embodiments of the present disclosure. [Figure 11A] FIG. 11A illustrates schematically a quantum computing method according to some embodiments relating to entangling photon graphs. [Figure 11B] FIG. 11B illustrates schematically a quantum computing method according to some embodiments relating to entangling a photon graph. [Figure 11C] FIG. 11C illustrates a schematic diagram of a quantum computing system according to some embodiments involving entanglement of photon graphs. [Figure 11D] FIG. 11D illustrates a schematic diagram of 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] FIG. 12A illustrates a schematic of a preferred implementation of a quantum computing system for providing multiple cavities that generate graph states consistent with some embodiments of the present disclosure. [Figure 12B] FIG. 12B illustrates a schematic diagram of a photon generator providing multiple cavities consistent with some embodiments of the present disclosure. [Figure 12C] FIG. 12C is a block diagram of an example process involved in providing multiple cavities to generate a graph state, according to some embodiments of the present disclosure. [Figure 12D] FIG. 12D illustrates a schematic diagram of a preferred implementation of a quantum computing system for providing multiple cavities that generate graph states, according to some embodiments of the present disclosure. [Figure 13A]FIG. 13A illustrates a schematic diagram of a preferred implementation of a system according to some embodiments for generating a photon graph state. [Figure 13B] FIG. 13B illustrates a schematic diagram of a preferred implementation of a system according to some embodiments for generating a photon graph state. [Figure 13C] FIG. 13C illustrates a schematic diagram of a preferred implementation of a system according to some embodiments for generating a photon graph state. [Figure 13D] FIG. 13D is a block diagram of an example process according to some embodiments for generating a photon graph state. [Figure 14A] FIG. 14A illustrates a schematic diagram of a preferred implementation of a system or device according to some embodiments for generating photonic graph states for quantum computation. [Figure 14B] FIG. 14B is a flowchart of an exemplary process according to some embodiments for generating a photon graph state for quantum computation. [Figure 15A] FIG. 15A illustrates a schematic diagram of a single-photon Raman interaction (SPRINT) mechanism using a quantum emitter coupled to a resonator (or cavity), according to some embodiments of the present disclosure. [Figure 15B] FIG. 15B illustrates a schematic diagram of a single-photon Raman interaction (SPRINT) mechanism using a quantum emitter coupled to a resonator (or cavity), according to some embodiments of the present disclosure. [Figure 15C] FIG. 15C illustrates a schematic diagram of a single-photon Raman interaction (SPRINT) mechanism using a quantum emitter coupled to a resonator (or cavity), according to some embodiments of the present disclosure. [Figure 16A] FIG. 16A is a flow diagram of a quantum computing method according to some embodiments for an N-configuration of resonator-coupled quantum emitters. [Figure 16B] FIG. 16B illustrates a schematic representation of a quantum computing system according to some embodiments for an N-configuration of resonator-coupled quantum emitters. [Figure 16C]FIG. 16C illustrates a schematic diagram of a quantum computing system according to some embodiments for an N-configuration of resonator-coupled quantum emitters. [Figure 16D] FIG. 16D illustrates a schematic representation of a quantum computing system according to some embodiments for an N-configuration of resonator-coupled quantum emitters. [Figure 17A] FIG. 17A illustrates a schematic diagram of a preferred implementation of a system or device according to some embodiments involving the use of a heralding-less connection. [Figure 17B] FIG. 17B shows a schematic representation of a preferred implementation of the optical processing stage according to some embodiments involving the use of a messenger-less connection. [Figure 17C] FIG. 17C illustrates a schematic representation of a preferred implementation of the optical processing stage according to some embodiments involving the use of a messenger-less connection. [Figure 17D] FIG. 17D is a flowchart of an example process according to some embodiments for using messenger-less connections.

[0041] For simplicity and clarity of illustration, elements shown in the figures have not necessarily been drawn to scale, the dimensions of some elements may be exaggerated relative to other elements, and reference numerals may be repeated among the figures to indicate corresponding or similar elements.

[0042] In the following description, various operational examples are provided for illustrative purposes. However, it should be understood that the present disclosure may be practiced without one or more of these detailed descriptions. Reference will now be made in detail to non-limiting examples of the present disclosure, examples of which are illustrated in the accompanying drawings. The examples are described below with reference to the drawings, in which like reference numerals refer to like elements. Where like reference numerals are shown, corresponding descriptions will not be repeated and readers are referred to previously described figures for descriptions of like elements, if interested.

[0043] Various embodiments are described herein with reference to systems, methods, devices, or computer-readable media. A disclosure of one is intended to be a disclosure of all. For example, it should be understood that the disclosure of a computer-readable medium described herein also constitutes a disclosure of a method implemented by the computer-readable medium, as well as systems and devices that perform the method, e.g., via at least one processor or circuit. It should be understood that this disclosure is for ease of explanation only, and that one or more aspects of one embodiment herein may be combined with one or more aspects of other embodiments herein within the intended scope of the disclosure. DETAILED DESCRIPTION OF THE INVENTION

[0044] Preferred embodiments will be described with reference to the accompanying drawings. The figures are not necessarily drawn to scale. While examples and features of the principles of the present disclosure are described herein, modifications, variations, and other implementations are possible without departing from the spirit and scope of the embodiments of the present disclosure. Additionally, the words "comprising," "having," "containing," and "including," and other similar forms, are intended to be equivalent and are intended to be open-ended in that the item or items following any one of these words do not imply an exhaustive listing of the item or items or are limited to only the listed item or items. It should also be noted that, as used in this specification and the appended claims, the singular forms "a," "an," and "the" include plural references unless the context clearly dictates otherwise. Furthermore, relational terms used herein, such as "first" and "second," are used only to distinguish one entity or operation from another and do not require or imply any actual relationship or order between those entities or operations.

[0045] Unless specifically stated otherwise, the term "or" as used herein includes all possible combinations unless impracticable. For example, if it is stated that a component may include A or B, the component may include A, B, or A and B, unless specifically stated otherwise or impracticable. As a second example, if it is stated that a component may include A, B, or C, the component may include A, B, C, A and B, A and C, B and C, or A, B, and C, unless specifically stated otherwise or impracticable.

[0046] The embodiments described herein may refer to a non-transitory computer-readable medium or computer-readable media containing instructions that, when executed by at least one processor (or system, circuit, or device), cause the at least one processor (or system, circuit, or device) to perform a method according to embodiments of the present disclosure. A non-transitory 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 a method or any other instructions stored in the memory. A non-transitory computer-readable medium (or computer-readable medium) may be implemented as hardware, firmware, software, or any combination thereof. Furthermore, software may preferably be implemented as an application program tangibly 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 circuitry). Preferably, the machine may be implemented on a computer platform having hardware (or circuitry) such as one or more central processing units ("CPU"), a memory, and input / output interfaces. The computer platform may also include an operating system and microinstruction code. The various processes and functions described in this disclosure may be part of the microinstruction code or part of the application program, or any combination thereof, and may be executed by a CPU whether or not the computer or processor is explicitly shown. In addition, various other peripheral units may be connected to the computer platform, such as an additional data storage unit and a vacuum chamber. Furthermore, a non-transitory computer-readable medium may be any computer-readable medium except a transitory, propagating signal.

[0047] Memory may include random access memory (RAM), read-only memory (ROM), hard disk, optical disk, magnetic media, solid-state storage device, flash memory, other persistent, fixed, volatile, or non-volatile memory, or any other mechanism capable of storing instructions. Memory may include one or more separate storage devices, collocated or distributed, capable of storing data structures, instructions, or any other data. Memory may further include memory portions containing instructions for the processor to execute. Memory may also be used as an operating scratchpad for the processor or as temporary storage.

[0048] Some embodiments involve at least one processor. "At least one processor" may include any physical device or group of devices having electrical circuitry that performs logical operations on an input or multiple inputs. For example, the 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), a graphics processing unit (GPU), a digital signal processor (DSP), a field-programmable gate array (FPGA), a server, a virtual server, or other circuitry suitable for executing instructions or performing logical operations. The instructions executed by the at least one processor may be preloaded, for example, into memory integrated or embedded in the controller, or may be stored in a separate memory. The memory may include random access memory (RAM), read-only memory (ROM), a hard disk, an optical disk, a magnetic medium, a solid-state storage device, flash memory, other persistent, fixed, or volatile memory, or any other mechanism capable of storing instructions. In some embodiments, the at least one processor may include multiple processors. Each processor may have a similar structure, or the processors may be different structures that are electrically connected or separated from one another. For example, the processors may be separate circuits or integrated into a single circuit. When multiple processors are used, the processors may be configured to operate independently or cooperatively and may be located side by side or remote from one another. The processors may be connected electrically, magnetically, optically, acoustically, mechanically, or by other means that allow the processors to interact.

[0049] Alternatively or additionally, some embodiments involve a circuit (or an 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 (e.g., positioned and connected to each other or to other functional units or other layout portions) such that the circuit (or integrated circuit or integrated circuit device layout) can perform some or all of the steps of a method or process. For example, a circuit (or integrated circuit or integrated circuit device layout) can perform some or all of the steps of a method or process according to some embodiments of the present disclosure.

[0050] In examples or embodiments described herein, at least some of the features of a system, device, apparatus, integrated circuit device, or circuit, e.g., an optical chip or photonic integrated circuit (PIC), are formed using a manufacturing method such as lithography, e.g., using lithographic processing 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 using lithographic processes to form the features thereon. It is also understood that other techniques, 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 a substrate, and that the other techniques enable the fabrication of the features having a structure capable of providing the functionality of the features described herein.

[0051] The following paragraphs provide definitions of terms employed in this disclosure and examples associated with those terms. When a feature is described functionally using that term, it should be understood that that feature may be replaced with another feature sharing equivalent functionality. The embodiments and examples described herein may refer to the following:

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

[0053] As a non-limiting example, FIGS. 6 and 7 illustrate methods and apparatus for securing a photon graph state (eg, n photons 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 a quantum state associated with one or more photon degrees of freedom. Examples of photon states include single-photon states, which correspond to the presence of exactly one photon in a specified mode. As a non-limiting example, FIGS. 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 whose vertices represent photon states. Examples of photon graph states include graph states where each vertex corresponds to a single-photon qubit, where the qubit describes the path of the single photon, the polarization of the single photon, the time bin of the single photon, or the frequency of the single photon, or graph states where each vertex corresponds to a continuous variable qubit, where the qubit represents a pair of orthogonal superpositions of photon number states.

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

[0057] Some embodiments involve optical qubits. An optical qubit refers to a fundamental unit of quantum information stored in (or residing in) one or more photons or electromagnetic fields. For example, an optical qubit includes a qubit encoded with degrees of freedom associated with a propagation or stationary mode of an electromagnetic field. Examples of optical qubits include qubits encoded with polarization, photon number, phase, time bin, frequency, or position in an 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 that can interact with photons. A stationary qubit can refer to a material quantum system that can be used to store and process quantum information. For example, a stationary qubit can refer to a qubit that (i) reliably stores quantum information on nanosecond or longer timescales, (ii) reliably performs calculations and / or operations, including operations that can transfer or convert information to flying qubits (e.g., non-stationary qubits or photons), (iii) can be reliably measured or read out, and / or (iv) can be operated to be highly entangled (or meets these conditions). Examples of stationary qubits can include qubits stored in or residing in a quantum emitter. For example, qubits stored in or residing in rubidium or cesium atoms can serve as a source of stationary qubits. For example, Rydberg atoms can also serve as sources of stationary quantum bits. The use of Rydberg atoms can provide advantageous properties 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 can 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 configurations: an ion or neutral atom, a defect or quantum dot in a material substrate, or a superconducting circuit including one or more Josephson junctions. A quantum emitter can be a superconducting quantum bit, a quantum dot, an atom, a neutral atom, an ion, a rubidium atom, a cesium atom, a strontium, an erbium, an ytterbium, a calcium, a barium, a beryllium, or a magnesium atom. The atom or ion can be secured from a Rydberg atom. A superconducting quantum bit can refer to a solid-state quantum bit 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). A quantum dot may refer to a quantum emitter having a substrate (e.g., a solid-state substrate such as a semiconductor particle) with optical and / or electronic properties that exhibit quantum mechanical principles, as described above. For example, a quantum dot may be a nanoparticle with optical and electronic properties different from its bulk component. In the presence of high-energy photons (e.g., UV light), electrons in the quantum dot may be excited to a higher energy state and emit one or more photons upon transitioning to the ground state. For example, quantum dots 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, quantum dots may self-assemble 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 FIGS. 1 and 3, atom 402 in FIGS. 4A and 4B, atom 502 in FIGS. 5A and 5B, rubidium ( 87 The Rb) atom 820, as well as one or more atoms 1020 in FIG. 10, are non-limiting examples of quantum emitters.

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

[0060] Some embodiments involve the state of a quantum emitter qubit. The state of a quantum emitter qubit refers to a state or configuration of the quantum emitter. For example, the state of a quantum emitter includes a configuration of the quantum emitter that corresponds to a superposition of eigenstates of a Hamiltonian that describes the quantum emitter. An example of a state of a quantum emitter qubit includes the ground state of the quantum emitter, which corresponds to the lowest energy eigenstate.

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

[0062] Some embodiments involve a quantum emitter coupled to a resonator (or a resonator-coupled quantum emitter). A quantum emitter coupled to a resonator (or a resonator-coupled quantum emitter) refers to a quantum emitter that can interact with a resonator. For example, a quantum emitter coupled to a resonator (or a 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 particular resonant frequency and lifetime in the confined field. Such a quantum emitter coupled to a resonator (or a resonator-coupled quantum emitter) may also be referred to as a quantum emitter coupled to a cavity, a quantum emitter coupled to a photonic cavity, or a quantum emitter coupled to an optical cavity, and accordingly the component functions as a resonator. Thus, a quantum emitter coupled to a resonator (or resonator-coupled quantum emitter) may include a quantum emitter whose dipole field overlaps with an electromagnetic mode of the resonator (eg, a cavity, a photonic cavity, or an optical cavity).

[0063] For example, a quantum emitter (or atom) placed within the internal cavity field of a cavity (or photonic cavity, resonator, or optical cavity) is a quantum emitter coupled to the cavity (or a quantum emitter coupled to a photonic cavity, or a quantum emitter coupled to a resonator, or a quantum emitter coupled to an optical cavity). The atom 102 confined within the optical cavity 103 in FIG. 1, the rubidium ( 87 Rb) atoms 820 and rubidium ( 87 The Rb) atom 820 is a non-limiting example of a quantum emitter coupled to a resonator (or a resonator-coupled quantum emitter).

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

[0065] Some embodiments involve quantum emitter positioning, which refers to placing or positioning a quantum emitter to allow interaction between the quantum emitter and a resonator (or cavity, or photonic cavity, or optical cavity). Examples of such quantum emitter positioning include one or more of: positioning a quantum emitter to be located at a binding position or binding location (e.g., positioning or placing a quantum emitter at a binding position or binding location); coupling a quantum emitter to a resonator (or cavity, photon cavity, or optical cavity); placing a quantum emitter within the internal cavity field of a resonator (or cavity, photon cavity, or optical cavity); trapping a quantum emitter near a resonator (or cavity, photon cavity, or optical cavity); lithographically placing a quantum dot near a resonator (or cavity, photon cavity, or optical cavity); or lithographically placing a resonator (or cavity, photon cavity, or optical cavity) near 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 creating a trap that maintains the quantum emitter in a binding position. 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 (atom tweezers). As non-limiting examples, FIG. 9A shows a utility waveguide 910 carrying a pulse or field that creates a trap, and FIG. 10 shows a magneto-optical trap (MOT) trapping one or more atoms 1020. The pulse or field in FIG. 9A is configured to trap a Rb atom 820 next to a binding position, e.g., a cavity 818 (or resonator or ring shape in the figure). The pulse or field may be configured to create and / or contain an evanescent field around the waveguide 910, so that an evanescent field trap can be used to maintain the Rb atoms 820 at or within the binding position. The magneto-optical trap in Figure 10 is configured to trap one or more atoms 1020 at or within the binding position.

[0067] Some embodiments involve being in the vicinity of a photonic cavity (or cavity, resonator, or optical cavity). Being in the vicinity of a photonic cavity (or cavity, resonator, or optical cavity) refers to being within an electromagnetic mode of the photonic cavity (or cavity, resonator, or optical cavity). Examples of being in the vicinity of a photonic cavity (or cavity, resonator, or optical cavity) include being between two reflecting surfaces of a Fabry-Perot cavity, being in or at a coupling location as described above, being in the internal cavity field of such a resonator (or cavity, photonic cavity, or optical cavity), being in or at a coupling location that allows the dipole field of the quantum emitter to overlap with the electromagnetic mode of such a resonator (or cavity, photonic cavity, or optical cavity), and / or being in the evanescent field of such a whispering gallery cavity.

[0068] Some embodiments involve coupling an optical qubit to a quantum emitter or coupling a qubit to an atomic qubit. Coupling an (optical) qubit to a quantum emitter (atomic qubit) refers to enabling interaction between the 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 the quantum emitter). For example, coupling an (optical) qubit to a quantum emitter (atomic qubit) may include enabling interaction between the qubit (or optical qubit) and the 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 that is stored in or resides in a superconducting electronic circuit (e.g., a network of electrical elements using superconductors). For example, a superconducting qubit may include an electrical circuit made of superconducting material that includes one or more Josephson junctions or is coupled to one or more Josephson junctions. Examples of superconducting qubits include a superconducting transmon qubit, a superconducting fluxonium qubit, or a superconducting bosonic qubit.

[0070] Some embodiments involve quantum emitters that include quantum dots. A quantum emitter that includes quantum dots may refer to a quantum emitter that includes a substrate (e.g., a solid-state substrate, such as semiconductor particles) with 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 that includes quantum dots may include a stationary quantum system with an anharmonic spectrum configured to couple with electromagnetic degrees of freedom, where the quantum system includes a spatially defined region within a solid-state substrate to confine charge carriers within the substrate in all three dimensions. Examples of quantum emitters that include 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, where the spatial region is composed of a material with a smaller bandgap than the surrounding region. For example, quantum dots may be self-assembled from indium arsenide within 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 refers to a state in which the state of one or more photons is associated with the state of one or more quantum emitters. For example, the state of one or more photons may be associated with the state of one or more quantum emitters, and these states cannot be described independently of one another. Such entanglement may involve, for example, correlating 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 these states, whereby mutual information can be stored or processed using the correlation. For example, photon-quantum emitter entanglement may involve non-separable states of a composite quantum system composed of at least one photon and at least one quantum emitter, where at least one quantum emitter is entangled with a photon state (e.g., the photon state of at least one photon). As a non-limiting example, FIG. 3 illustrates entanglement between atom 102 and photon 302 with 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, photonic 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, mapping two quantum emitter qubits to an optical qubit may produce a three-photon entangled state (i.e., a Greenberger-Horn-Zeilinger state). Examples of entanglement gates include a controlled-Z entanglement gate (CZ gate), a controlled-NOT entanglement gate (CNOT gate), a square root of a SWAP entanglement gate, or a virtual SWAP entanglement gate (iSWAP gate).

[0073] As a non-limiting example, FIGS. 8 and 9C show rubidium ( 87 Rb) atoms 820, and rubidium ( 87 Rb) atom 820, implemented as an entanglement (CZ) gate, and Figures 5A-5B show an entanglement unit 501 (including an entanglement unit atom 502) implemented as an entanglement gate.

[0074] A controlled Z gate (CZ gate) refers to a quantum gate operable on two qubits, whose combined quantum state experiences a conditional phase shift (e.g., a phase shift of pi). For example, the combined quantum state of the two qubits may experience a phase shift of pi if both qubits are in a state associated with logic 1, and no phase shift otherwise. As non-limiting examples, FIG. 3 illustrates a controlled Z gate implementation, and FIGS. 8 and 9C illustrate a rubidium ( 87 Rb) atom 820 is shown.

[0075] A SWAP gate refers to a quantum gate operable on two qubits, where the quantum state of a first qubit is transferred to a second qubit and the quantum state of the second qubit is transferred to the first qubit. For example, if the 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-limiting example, Figure 2E shows a SWAP gate 201 that performs qubit "read" and "write" operations on atoms 102.

[0076] Some embodiments involve mapping a quantum emitter qubit to an optical qubit. Mapping a quantum emitter qubit to an optical qubit refers to transferring the quantum emitter qubit to an optical qubit. For example, the mapping may include transferring quantum information stored in the quantum emitter qubit to one or more photon qubits. In one example, mapping a quantum emitter qubit to an optical qubit may be the result of performing a SWAP gate operation on the quantum emitter qubit and the optical qubit, as described above. For example, the state of the resonator-coupled quantum emitter may be mapped to a photon by providing photons at a frequency corresponding to the frequency of a particular transition of the resonator-coupled quantum emitter. As a non-limiting example, FIG. 2E illustrates a mapping using a SWAP gate 201 in which an initial superposition of atom 102 (which is a non-limiting example of a quantum emitter) of first and second basis states 111, 113 with probability amplitudes γ and δ is transferred to an outgoing photon 204 (whose superposition of modes 1 and 2 is shown with probability amplitudes δ and γ), and an incoming photon 202 superposition of optical modes 1 and 2 with probability amplitudes α and β is transferred to atom 102 (where atom 102 remains in a superposition of first and second basis states 111, 113 is shown with probability amplitudes β and α).

[0077] Some embodiments involve optical chips. Optical chips refer to devices that integrate elements or components operating at visible or infrared wavelengths. For example, the devices 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: integrated lasers, channels or waveguides that carry lasers, pulses of photons, and / or one or more single photons, waveguides, switches, phase modulators, resonators, interferometers, beam splitters, optical amplifiers, nonlinear waveguides, nonlinear resonators, amplitude modulators, integrated magnetic field generators such as solenoids, detectors, and one or more controllers (or circuits) configured to control or receive output from any one or more of the above elements or components of the chip.

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

[0079] Some embodiments involve a jet of atoms. A jet of atoms refers to a stream or beam of atomic vapor. The stream or beam of atomic vapor may be provided or dispensed by an atom dispenser as described above. For example, the jet of atoms may include a directed beam of high-temperature atomic vapor emerging from an atom dispenser.

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

[0081] Some embodiments involve cavities (or resonators) formed in silicon nitride layers. For example, cavities (or resonators) such as those described above formed in silicon nitride layers may involve planar layers incorporating connecting regions comprising silicon nitride. The connecting regions may be incorporated with a different material whose refractive index is lower than that of silicon nitride. Cavities (or resonators) formed in silicon nitride layers may be formed in silicon nitride regions surrounded by silica, and the silicon nitride regions may include straight or curved lines, or the silicon nitride regions may include rings. As non-limiting examples, optical cavity 103 in FIGS. 1 and 3 and cavity 818 in FIGS. 8 through 9C may be formed in silicon nitride regions.

[0082] Some embodiments involve dirty photons. Dirty photons refer to photons that can be distinguished from other photons, for example, when performing quantum computation. Dirty photons can include, for example, propagating photons in a mixed state with respect to multiple space-time modes, e.g., multiple temporal profiles. Entangling photons through cavity-enhanced atom-photon interactions (e.g., using a quantum emitter coupled to the resonator or a resonator-coupled quantum emitter) enables the use of dirty photons in quantum computation operations. This is because entangling photons through cavity-enhanced atom-photon interactions (e.g., using a quantum emitter coupled to the resonator or a resonator-coupled quantum emitter) does not require the use of indistinguishable photons (clean photons), which would otherwise be the case with probabilistic entanglement using linear optics. For example, this means that the input photon pulse (e.g., pulse 404 in FIG. 4A ) does not need to have precise timing and shape. Single photons generated according to some embodiments of the present disclosure are perfectly suitable for qubit entanglement using the aforementioned resonator-coupled quantum emitters or resonator-coupled quantum emitters, even if the photons exhibit irregularities that make them easily distinguishable.

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

[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 incorporating an optical waveguide that functions to delay the arrival time of an incident pulse relative to a pulse that does not enter the optical waveguide. An optical delay line that may utilize the visible portion of the electromagnetic spectrum is an example of a photon delay line. An optical delay line 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 waveguides.

[0085] Some embodiments involve manipulating alkali atoms (or manipulating quantum emitters). Manipulating alkali atoms (or manipulating 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, the nuclear configuration, or a combination thereof. The external state may correspond to, for example, the movement of the alkali atoms in their bonding positions.

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

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

[0088] The embodiments, clauses, claims, or examples described herein relate to the use of one or more cavities (e.g., resonators as described herein) coupled with quantum emitters (e.g., ions, atoms, or quantum dots) for use in quantum computing, and their associated systems, devices, apparatus, methods, (non-transitory) computer-readable media, or computer-readable medium, which 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 atomic and optical cavities (or cavity-QED) used in the devices for the deterministic photon graph state generator described herein, where the optical cavity (or resonator) and atom (or quantum emitter) are arranged such that coupling between them occurs at the atomic or other particle trap of the exemplary configuration (also referred to as the coupling position or location, or the location (location) where the internal cavity field of the source optical cavity or entangled optical cavity resides). In the exemplary configuration for the deterministic photon graph state generator of the present disclosure, the cavity corresponds to the optical cavity 103, and the quantum emitter corresponds to the atom 102 shown in FIGS. 1 and 3, the atom 402 in FIGS. 4A and 4B, and the atom 502 in FIGS. 5A and 5B. In another non-limiting example, the cavity corresponds to cavity 818 in FIGS. 8 through 9C and the quantum emitter corresponds to rubidium ( 87 Rb) atom 820, or one or more atoms 1020 in FIG.

[0090] For example, the coupled cavity and quantum emitter (or cavity-coupled quantum emitter) described herein may be used in one of the exemplary configurations of a photonic-cavity-coupled quantum emitter, e.g., in embodiments relating to providing multiple cavities that generate graph states, or those shown in Figures 12A through 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 shown in Figures 12A, 12B, and 12D).

[0091] For example, the coupled cavities and quantum emitters (or cavity-coupled quantum emitters) described herein may be used in embodiments relating to generating one of the exemplary configurations of cavity-coupled quantum emitters, such as photon graph states, or those shown in Figures 13A through 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 one of the exemplary configurations of cavity-coupled quantum emitters, such as those shown in Figures 14A, 15A-15C, for generating photonic graph states for quantum computing (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 an embodiment involving entanglement of one of the exemplary configurations of resonator coupled quantum emitters, such as a photon graph, or those 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 an embodiment relating to one of the exemplary configurations of a resonator coupled quantum emitter, such as an N-configuration resonator coupled quantum emitter, or those shown in Figures 16A through 16D (e.g., the exemplary resonators 1833, 1863 and exemplary quantum emitter 1831 shown in Figures 16B through 16D).

[0095] For example, the coupled cavity and quantum emitter (or cavity coupled quantum emitter) described herein may be used in one of the exemplary configurations of resonator coupled quantum emitters, such as a messengerless connection, or in an embodiment involving the use of those shown in Figures 17A through 17D (e.g., the 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, whereby that optical cavity-coupled atom can be used as a photon generator as shown in Figures 8-9B, or as an atom with which an input photon can establish an entangled state as shown in Figures 8, 9A, and 9C.

[0097] For example, rubidium ( 87 Rb) atoms can be used in conjunction with a waveguide (e.g., formed using a fiber 816, nanofiber, or on-chip waveguide) to generate photons (a "single-photon source" 812 or "photon generator") or to entangle passing photons (an "entanglement gate" 814, e.g., a controlled Z gate (CZ gate)).

[0098] 9A , the waveguide may include a utility waveguide 910 that carries a trap-generating pulse that traps the Rb atom 820 at the coupling location, for example, next to the cavity 818 (or resonator or ring shape in the figure). The pulse may be configured to generate an evanescent field around the waveguide 910, such that the evanescent field trap can be used to trap the Rb atom 820 at the coupling location. The parameters of the evanescent field-generating pulse may be determined based on the specific mechanics of the Rb atom 820 (or any other quantum emitter used in that location), the cavity 818, the coupling location, and / or the waveguides 816, 910, 930. The pulse may be configured such that it can trap a cold atom (Rb atom 820 or quantum emitter) 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 fiber-guided light propagates in the evanescent field in the surrounding vacuum. Optical dipole traps can then be generated in the evanescent field when pulses having two wavelengths are injected into the guided mode of the nanofiber. The first pulse can be red-detuned to pull atoms toward the nanofiber, where the evanescent field is stronger. The second pulse can be blue-detuned to provide a repulsive potential that prevents (or hinders) atoms from colliding with the surface of the nanofiber. The combination of the two contributions can result in a potential minimum at a binding site located, for example, approximately 200 nm from the surface of the nanofiber. In one embodiment, the red-detuned pulse can have a wavelength of 850 nm (or, for example, 980 nm), and the blue-detuned pulse can have a wavelength of 690 nm (or, for example, 720 nm). Detector 951 may be located at the end of utility waveguide 910 carrying the pulse that generates the trap, so that the pulse can be detected at detector 951 and appropriate control of the pulse can be performed based on measurements from detector 951.

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

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

[0101] 9C , when the configuration is used for an entanglement (CZ) gate 814, a utility waveguide 910 may carry blue and red lasers that trap the atom 820 at the coupling point between the waveguide 910 and the cavity 818 (resonator). Another waveguide (e.g., quantum waveguide 930) may be provided within the interaction distance of the cavity 818 (resonator) such that one or more single photons may be carried therein and through the cavity 818 (resonator) to facilitate an interaction between the carried photon and the trapped atom 820, whereby the interaction results in the carried photon becoming entangled with the atom 820 and being output as an entangled photon.

[0102] According to an embodiment of the present disclosure, the perforated vacuum chamber 1013 may be used in an exemplary mechanism 1011 shown in FIG. 10 , which includes a combination of one or more optical chips 1015 with a cold atom 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 the optical chip 1015, which controls its operation, or a magneto-optical trap (MOT) that traps one or more atoms 1020 from the cold atom source 1017, and a photon detector 1035 connected to the optical chip 1015 detects photons at or from the optical chip 1015, so that 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, where the circuitry and / or at least one processor are configured to perform some or all of the steps of the quantum computing methods described herein according to some embodiments of the present disclosure.

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

[0104] When a quantum emitter is coupled to a photon cavity (also referred to as a photon-cavity-coupled quantum emitter) at its associated coupling location, the quantum emitter is coupled to the electromagnetic mode of the photon cavity. Thus, the quantum emitter has its dipole field overlapping with the electromagnetic mode of the photon cavity, and the 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, each photon cavity associated with a coupling location and quantum emitter, it is possible to release or emit multiple photons, interact with multiple photons, or interact with a photon 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 mentioned, a photon generator refers to a source of individual photons, and an entanglement gate refers to a component or group of components or control sequence configured to entangle qubits, in this case photons or qubits belonging to optical qubits. For example, an entanglement gate can include a quantum circuit configured to entangle optical qubits.

[0106] As non-limiting examples, Figures 4A and 4B show source unit 401 (including source unit atom 402 as a quantum emitter) implemented as a photon generator, 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 (including entanglement unit atom 502 as a quantum emitter) implemented as an entanglement gate, 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 an entanglement gate, each quantum emitter (e.g., associated with one of the coupling locations and the photonic cavity) may mediate interactions between successive incoming optical qubits, e.g., to generate a graph state (or multiple graph states) as output. As previously described, a graph state represents a relationship between a group of qubits, and a qubit is the basic unit of quantum information. Thus, the graph state (or multiple graph states) generated from successive incoming optical qubits represents a relationship between the qubits stored in (or belonging to) an output photon. A photon generator may be provided to provide photons toward each of the multiple photonic cavities, e.g., to enable interactions between the successive incoming optical qubits via the quantum emitter. In some embodiments of the present disclosure, the photon generator may include one or more photonic-cavity-coupled quantum emitters configured to provide photons. Each of the multiple photonic cavities may facilitate interactions between an optical qubit and an associated quantum emitter. Multiple output channels may also be positioned downstream of the multiple photonic cavities to output a graph state after an interaction between an optical qubit and an associated quantum emitter. For example, each photonic cavity may have an associated output channel that outputs a graph state. Alternatively, some or all of the multiple photonic cavities may share an output channel that outputs a graph state.

[0108] As a non-limiting example, FIG. 12A illustrates a preferred implementation of a quantum computing system 1100 that provides multiple cavities for generating graph states. The quantum computing system 1100 in FIG. 12A is intended merely to facilitate conceptualization of one preferred implementation of a quantum computing system and is not intended to limit the present disclosure to any particular implementation. The output graph state or states may be, for example, one or more time-contiguous series of entangled photons, which may be used as qubits in quantum computing applications. The system 1100 may include multiple entanglement gates 1102_1 through 1102_n, each including a configuration suitable for entangling optical qubits as described above, where n is any integer greater than 1. The entanglement gates 1102_1 through 1102_n may each receive a series of input photons 1106_1 through 1106_n, respectively, from a photon generator 1104. Each of the entanglement gates 1102_1 to 1102_n may output a time-contiguous series of entangled photons 1108_1 to 1108_n, respectively, to form a photon graph state 1110_1 to 1110_n or 1122. Figure 12A depicts the input photons 1106_1 to 1106_n as separate photons with no connectors between them, showing the state of the input photons 1106_1 to 1106_n before being input to the entanglement gates 1102_1 to 1102_n. Before the input photons 1106_1-1106_n are input to the entanglement gates 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 unentangled and there is no correlation between the input photons 1106_1-1106_n. In contrast, the time-sequential series of output photons 1108_1-1108_n are connected via double lines 1108a to indicate their entanglement. Photon entanglement refers to a state in which the states of two or more photons are related to each other. For example, the states of two or more photons may be related to each other, and their states cannot be described independently of each other. The entanglement, for example, generates a correlation between measurements of their states, so that mutual information can be stored or processed using the correlation.

[0109] 12A 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, entanglement gate 1102_n in FIG. 12A 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, details provided for entanglement gate 1102_1 may apply to entanglement gate 1102_n as well.

[0110] Some embodiments involve quantum computing. Quantum computing may refer to computations performed through the utilization or application of one or more quantum state properties, such as superposition, entanglement, and interference. Some embodiments involve quantum computing systems, which may thus include a component or group of components configured to facilitate the performance of a computation or operation via quantum computing. For example, a quantum computing system may generate a graph state that may include multiple, time-contiguous series of entangled photons for use as qubits in a quantum computation.

[0111] 12A illustrates a preferred implementation of a quantum computing system 1100 consistent with some embodiments of the present disclosure. The quantum computing system 1100 in FIG. 12A includes a plurality of entanglement gates 1102_1 through 1102_n. The entanglement gates 1102_1 through 1102_n may each receive a series of consecutive input photons 1106_1 through 1106_n from a photon generator 1104. The entanglement gates 1102_1 through 1102_n may collectively generate, from the input photons 1106_1 through 1106_n, any of graph states 1110_1 through 1110_n and / or 1122 associated with a time-sequential series of entangled photons 1108_1 through 1108_n.

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

[0113] 12A and 12B illustrate preferred implementations of multiple photon cavities 1112_1-1112_n and 1138_1-1138_n according to some embodiments related to providing multiple cavities for generating graph states. Photon cavities 1112_1-1112_n may be included in entanglement gates 1102_1-1102_n, respectively, and may facilitate generating any of graph states 1110_1-1110_n or 1122 associated with a time-contiguous series of entangled photons 1108_1-1108_n. Photon cavities 1138_1-1138_n may be included in photon generation units 1132_1-1132_n, respectively, and may facilitate generating one or more photons.

[0114] Some embodiments involve multiple coupling locations for quantum emitter positioning. A coupling location includes an area configured to allow coupling between a quantum emitter and a photon cavity, as described above. For example, by positioning a quantum emitter at a coupling location, the quantum emitter can couple with the photon cavity, whereby the quantum emitter interacts with an established or supported electromagnetic mode of the photon cavity. A quantum emitter, as described above, refers to a component configured to couple with an electromagnetic mode. A quantum emitter positioning, as described above, refers to arranging or placing a quantum emitter to allow interaction between the quantum emitter and the photon cavity. Thus, a quantum computing system may include multiple coupling locations for positioning multiple quantum emitters, thereby forming multiple coupling pairs of quantum emitters and photon cavities. This allows, for example, multiple simultaneous (e.g., parallel) interactions between multiple quantum emitters and multiple photon cavities.

[0115] 12A and 12B illustrate a preferred implementation of multiple coupling locations 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 locations (1116_1-1116_n and 1142_1-1142_n), respectively. The coupling locations (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 corresponding waveguides (1120_1-1120_n and 1134_1-1134_n). Positioning (e.g., confinement or trapping) the quantum emitters (1114_1 to 1114_n and 1140_1 to 1140_n) at their respective coupling locations (1116_1 to 1116_n and 1142_1 to 1142_n), for example, between corresponding waveguides (1120_1 to 1120_n and 1134_1 to 1134_n) and corresponding photonic cavities (1112_1 to 1112_n and 1138_1 to 1138_n), enables interactions between the quantum emitters (1114_1 to 1114_n and 1140_1 to 1140_n) and the corresponding photonic cavities (1112_1 to 1112_n and 1138_1 to 1138_n).

[0116] In some embodiments, each binding location is associated with a different photonic cavity of the plurality of photonic cavities. Association refers to associating or corresponding. Thus, each binding location may be associated with or correspond to a different photonic cavity such that each photonic cavity can couple with one or more quantum emitters positioned at its associated or corresponding binding location (e.g., only its corresponding binding location).

[0117] As a non-limiting example, Figure 12A illustrates a preferred implementation of each coupling position associated with a different one of the photon cavities: coupling position 1116_1 is associated with photon cavity 1112_1, and coupling position 1116_n is associated with photon cavity 1112_n, where each of photon cavities 1112_1 and 1112_n is a different, e.g., separate, photon cavity; Figure 12B also illustrates a preferred implementation of each coupling position associated with a different one of the photon cavities: coupling position 1142_1 is associated with photon cavity 1138_1, and coupling position 1142_n is associated with photon cavity 1138_n, where each of photon cavities 1138_1 and 1138_n is a different, e.g., separate, photon cavity.

[0118] In some embodiments of the present disclosure, a quantum emitter associated with each binding site is configured to mediate interactions between successive incoming optical qubits to generate a graph state. Mediating refers to facilitating, enabling, or otherwise promoting the interaction. The interaction may transfer, convey, associate, and / or establish correlations between the incoming optical qubits. For example, a quantum emitter may facilitate entanglement (e.g., interaction) between the incoming photons, and the quantum emitter is a means for achieving that interaction between the incoming photons. Successive refers to following or successive, e.g., coming one after the other in temporal succession. An optical qubit refers to a basic unit of quantum information stored in (or residing in) one or more photons or electromagnetic fields, as previously described. For example, an optical qubit includes a qubit encoded with degrees of freedom associated with propagation or stationary modes of an electromagnetic field. Optical qubits may exhibit properties unique to quantum mechanical systems, such as superposition with respect to degrees of freedom (e.g., one or both of vertical and horizontal polarization states) and / or entanglement (e.g., among multiple optical qubits or with a quantum emitter qubit). Thus, each binding site may have a corresponding (e.g., associated) quantum emitter positioned thereto to facilitate interaction (e.g., entanglement) between successive incoming optical qubits by the corresponding (e.g., associated) quantum emitter to generate a graph state. For example, each quantum emitter may facilitate entanglement of multiple optical qubits.

[0119] 12A illustrates a preferred implementation of quantum emitters associated with each coupling site and configured to mediate interactions between successive input optical qubits to generate a graph state, consistent with some embodiments of the present disclosure. Entanglement gate 1102_1 includes quantum emitter 1114_1 associated with coupling site 1116_1. Photon generator 1104 provides multiple single photons to entanglement gate 1102_1 via waveguide 1118_1, e.g., as successive individual input photons 1106_1. Input photons 1106_1 are not entangled (or disentangled) with one another, as indicated by the absence of connecting double lines between them. Entanglement gate 1102_1 is configured such that each photon of input photon 1106_1 interacts with quantum emitter 1114_1 through photon cavity 1112_1, thereby entangling the photon's optical quantum bit with the quantum bit of quantum emitter 1114_1. As multiple photons from input photon 1106_1 undergo this interaction with quantum emitter 1114_1, the multiple photons become entangled with one another. As a result, successive input optical quantum bits become entangled and are output as entangled output photon 1108_1. In other words, quantum emitter 1114_1 mediates the interaction between successive input optical quantum bits. As a result of this interaction, output photons 1108_1 become entangled with one another, as indicated by the interconnecting double lines 1108a. Similarly, entanglement gate 1102_n includes quantum emitter 1114_n associated with binding site 1116_n. Entanglement gate 1102_n may similarly receive input photons 1106_n and mediate interactions therebetween to produce entangled output photons 1108_n, as indicated by interconnecting line 1108a.

[0120] According to some embodiments of the present disclosure, a quantum emitter can be a stationary qubit capable of interacting with photons. When the two are aligned, the stationary qubit can be capable of interacting with protons. As a non-limiting example, a quantum emitter can be a stationary quantum system having an anharmonic spectrum configured to couple to an electromagnetic mode. For example, a quantum emitter can include a quantum system having one or more of the following configurations: an ion or neutral atom electron or nuclear configuration, a defect or quantum dot in a material substrate, or a superconducting circuit including one or more Josephson junctions. Figure 12A shows a non-limiting example of such a quantum emitter according to some embodiments relating to providing multiple cavities that generate graph states. Quantum emitter 1114_1 may be suspended (e.g., trapped) between photon cavity 1112_1 and waveguide 1120_1, allowing quantum emitter 1114_1 in coupling position 1116_1 to interact with photons (e.g., incident optical quantum bits) carried by waveguide 1118_1 via photon cavity 1112_1.

[0121] For example, a quantum emitter may include a superconducting qubit. As previously mentioned, 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). With reference to Figure 12A or 12B, one or more of quantum emitters 1114_1 to 1114_n or 1140_1 to 1140_n may include a superconducting electronic circuit or a superconducting qubit.

[0122] The 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 has optical and / or electronic properties that exhibit quantum mechanical principles, as described above. Referring to FIG. 12A or 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] The quantum emitter may include, for example, an atom. With reference to FIG. 12A or 12B , one or more of quantum emitters 1114_1-1114_n or 1140_1-1140_n may include an atom, such as atom 102 of FIG. 1 . According to some embodiments of the present disclosure, the atom is neutral. Neutral refers to an atom with no overall charge, 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, the atom is an ion. An ion refers to a particle or atom with an overall charge, such as an atom with an unequal number of protons and electrons. According to some embodiments of the present disclosure, the quantum emitter includes a rubidium atom, as described above. The rubidium atom may be neutral or ionic. According to some embodiments of the present disclosure, the quantum emitter includes a cesium atom, as described above. According to some embodiments of the present disclosure, the quantum emitter includes at least one of a strontium, erbium, ytterbium, calcium, barium, beryllium, or magnesium atom, as described above.

[0124] According to some embodiments, a photon generator is configured to provide photons to a plurality of photonic cavities, where the provided photons may serve as incident photons to which an incident optical quantum bit belongs or to which it is associated. 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 FIGS. 8-9B. As another example, a photon generator may correspond to photon source unit 401 of FIG. 4A. Thus, a photon generator may provide one or more photons, e.g., provide multiple consecutive individual photons to each of multiple photon cavities. As a non-limiting example, FIGS. 12A, 12B, and 12D illustrate preferred implementations of a photon generator configured to provide or generate photons, according to some embodiments related to providing multiple cavities that generate graph states. The photons may then be provided to multiple photon cavities to provide input optical qubits consistent with some embodiments of the present disclosure. Photon generators 1104 and 1130 may provide input photon 1106_1 (or photon 1146_1 in FIG. 12D) to photon cavity 1112_1 via waveguide 1118_1. Photon generators 1104 and 1130 may also provide input photons 1106_n (or photons 1146_1 in FIG. 12D) to photon cavity 1112_n via waveguide 1118_n. It is understood that there may be multiple photon generators, and each photon generator may provide input photons to one or more photon cavities.

[0126] In some embodiments of the present disclosure, the photonic cavity is configured to couple an optical quantum bit to a quantum emitter. Coupling an optical quantum bit to a quantum emitter refers to facilitating an interaction between the optical quantum bit and the quantum emitter. For example, the interaction may be facilitated in the absence of physical contact between the optical quantum bit and the quantum emitter. The photonic cavity may, for example, serve as a means to enable the interaction between the optical quantum bit and the quantum emitter. The interaction may, for example, result in a statistical correlation or correspondence between the physical behavior of the optical quantum bit and the physical behavior of the quantum emitter. Thus, by coupling the optical quantum bit to the quantum emitter, the photonic cavity may result in a statistical correlation between the physical behavior of the optical quantum bit and the physical behavior of the quantum emitter. For example, a change in the state of the optical quantum bit may occur simultaneously with a corresponding change in the state of the quantum emitter quantum bit coupled to it. The photonic cavity may, for example, serve as a means for allowing an optical qubit to become entangled with a quantum emitter qubit, which may be achieved by such coupling between the optical qubit and the quantum emitter. For example, the coupled optical qubit may correspond to or be related to an input photon (or incident photon) received from a photon generator.

[0127] 12A and 12D illustrate preferred implementations of photonic cavities configured to couple optical qubits to quantum emitters, according to some embodiments related to providing multiple cavities that generate graph states. Each of photonic cavities 1112_1-1112_n may allow an optical qubit (e.g., associated with input photons 1106_1-1106_n in FIG. 12A or photon 1146_1 in FIG. 12D) to become coupled with quantum emitters 1114_1-1114_n. Such coupling then enables, for example, entanglement between input photons 1106_1-1106_n in FIG. 12A or photon 1146_1 in FIG. 12D and quantum emitters 1114_1-1114_n.

[0128] Some embodiments of the present disclosure involve multiple photon output channels downstream of multiple cavities that output a graph state. Downstream refers to occurring subsequent to, after, or following. For example, downstream may refer to being positioned to follow a direction of temporal or spatial flow or progression. The upstream cavity may be a multiple photon cavity as described above. The multiple photon output channels may, for example, be positioned following a direction of spatial flow of input photons. For example, the multiple photon output channels may be positioned between the multiple cavities and the output graph state. The photon output channels may carry or transport a temporally consecutive series of entangled photons (e.g., entangled using a photon-cavity coupled quantum emitter) to an output to output a graph state formed from the entangled photons.

[0129] As a non-limiting example, Figure 12A illustrates a preferred implementation of multiple photon output channels downstream of multiple cavities that output graph states according to some embodiments related to providing multiple cavities that generate graph states. The multiple photon output channels, each carrying or transporting a series of entangled photons 1108_1 through 1108_n, are located subsequent to (e.g., after or downstream from) photon cavities 1112_1 through 1112_n, respectively. The entangled photons 1108_1 through 1108_n may form one or more graph states that are output of 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, where the graph is a d-dimensional lattice of connected subsets) formed from a combination of entangled photons 1108_1-1108_n. Note that graph states 1110_1-1110_n and cluster state 1122 are merely intended as preferred conceptual illustrations and are not intended to limit the present disclosure to any particular graph state or any particular cluster.

[0130] Some embodiments involve a photon generator that includes at least one additional photon cavity. In embodiments that include an entanglement gate that entangles photons, the additional photon cavity may be provided to feed 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 mentioned above, with respect to a photon cavity, the additional photon cavity may similarly be coupled to a quantum emitter, which may interact with an established 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 upon excitation. Excitation may occur, for example, using a laser carried in a nearby waveguide 910 as shown in FIG. 9B. This allows the additional photon cavity and quantum emitter to function as a photon generator. For example, some embodiments that provide multiple cavities to generate graph states may involve that photon generator functioning as photon generator 1104 of FIG. 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 location for the quantum emitter positioning, each additional coupling location associated with a different one of the at least one additional photon cavity. The additional quantum emitter may be in addition to the quantum emitter already provided in the entanglement or photon generator. The quantum emitter may have a configuration similar to that described above. When an additional photon cavity is employed as described above, an additional coupling location may be provided. The additional coupling location, which may have a configuration similar to that described above, may enable the additional quantum emitter to couple to the additional photon cavity and thereby function as a photon generator.

[0132] The photon source unit for securing a single photon described herein is a non-limiting example of such a photon generator. For example, FIGS. 8-9B show that rubidium (Rb) atoms 820 as quantum emitters coupled to cavity 818 can function as a photon generator. As another example, FIGS. 4A and 4B show a 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 of FIG. 1, and atom 402 (e.g., a quantum emitter). After initialization pulse 403 initializes the state of atom 402 to state 111 (FIG. 1), generation pulse 404 can cause transitions 121A and 122A of FIG. 2A, which can cause atom 402 to emit photon 406. Repeating this process generates a temporally continuous series of output photons 412 in FIG. 4B. The output photon may then be provided to any one of the entanglement gates 1102_1 to 1102_n, enabling the entanglement gate to generate a graph state 1110_1 to 1110_n.

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

[0134] Although the following description refers to multiple photon generation units 1132_1-1132_n, 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_1-1132_n in FIG. 12B are arranged similarly to the entanglement gates 1102_1-1102_n in FIG. 12A. Each photon generation unit 1132_1-1132_n includes a first waveguide 1134_1-1134_n, a second waveguide 1136_1-1136_n, a photon cavity 1138_1-1138_n, and a quantum emitter 1140_1-1140_n. The quantum emitters 1140_1 to 1140_n may be positioned (eg, suspended or trapped) at their associated coupling locations 1142_1 to 1142_n located between their associated photonic cavities 1138_1 to 1138_n and the first waveguides 1134_1 to 1134_n. For example, as described above with respect to the single-photon source 812 of FIG. 9B, the first waveguides 1134_1 to 1134_n may carry a laser (e.g., a pulse of photons 1144_1 to 1144_n) that positions or traps the quantum emitters 1140_1 to 1140_n at their binding locations 1142_1 to 1142_n, and further, the first waveguides 1134_1 to 1134_n may carry a laser (e.g., a pulse of photons 1144_1 to 1144_n) that excites the quantum emitters 1140_1 to 1140_n to generate output photons 1146_1 to 1146_n that are output via the second waveguides 1136_1 to 1136_n.

[0135] For example, the pulses of photons 1144_1 to 1144_n may alternate between initialization photons (eg, photon 403) and generation photons (eg, photon 404) as described above with respect to FIGS. 4A and 4B.

[0136] The photonic cavities 1138_1 to 1138_n are coupled to corresponding quantum emitters 1140_1 to 1140_n, allowing the (additional) photonic cavity coupled quantum emitters 1140_1 to 1140_n to release or generate one or more photons 1146_1 to 1146_n upon excitation.

[0137] The released or generated photons 1146_1 through 1146_n may be provided to entanglement gates 1102_1 through 1102_n of Figure 12A as input photons 1106_1 through 1106_n, as shown in Figure 12D. In other words, in some embodiments relating to providing multiple cavities to generate graph states, successive output photons 1146_1 through 1146_n in Figure 12B may correspond to input photons 1106_1 through 1106_n of Figure 12A and therefore may be provided to entanglement gates 1102_1 through 1102_n via waveguides 1118_1 through 1118_n, as shown in Figure 12D.

[0138] 12D illustrates multiple cavities for generating a graph state, where photon generation unit 1132_1 (having photon cavity 1138_1) is used as photon generators 1130 and 1104 to supply photon 1146_1 to entanglement gate 1102_1 (having photon cavity 1112_1) to generate graph state 1110_1 associated with entangled output photon 1108_1. In some embodiments of the present disclosure relating to providing multiple cavities for generating a graph state, a quantum computing system includes multiple such combinations of photon generation unit 1132_1 and entanglement gate 1102_1, each combination configured to generate a graph state. In some embodiments of the present disclosure relating to providing multiple cavities for generating a graph state, multiple photon generation units may supply photons to one entanglement gate. In some other embodiments of the present disclosure related to providing multiple cavities to generate graph states, one photon generating unit may feed photons to multiple entanglement gates. In these embodiments of the present disclosure related to providing multiple cavities to generate graph states, a controller may be provided to control (e.g., direct or switch between different waveguides) the flow of input and output photons between the photon generating units and the entanglement gates. For example, the controller may include one or more processors. Memory, circuit components, or circuits may also be provided to perform the control.

[0139] The second waveguides 1136_1 to 1136_n may carry a field that couples to a particular electromagnetic mode or modes of the photonic cavities 1138_1 to 1138_n to generate output photons 1146_1 to 1146_n.

[0140] As mentioned above, some embodiments of the present disclosure involve a photon generator that includes at least one additional quantum emitter. The quantum emitter examples described above in some embodiments related to providing multiple cavities for generating graph states are also applicable to the at least one additional quantum emitter of the photon generator. For example, the at least one additional quantum emitter may include a stationary qubit that can interact with photons. With reference to FIGS. 12A and 12B , each of quantum emitters 1114_1 through 1114_n may be associated with a stationary qubit that interacts with photons 1106_1 through 1106_n via a corresponding photon cavity 1112_1 through 1112_n, and each of quantum emitters 1140_1 through 1140_n may be associated with a stationary qubit that can interact with input photons 1144_1 through 1144_n. For example, the at least one additional quantum emitter may include a superconducting qubit, or in another example, the at least one additional quantum emitter may include a quantum dot. The at least one additional quantum emitter may include an atom, such as atom 402 in FIG. 4A or atom 820 in FIG. 9B. In another example, the at least one additional quantum emitter may include a rubidium atom, as described above. In yet another example, the at least one additional quantum emitter may include at least one of a strontium, erbium, ytterbium, calcium, barium, beryllium, or magnesium atom, as described above.

[0141] As a non-limiting example, FIG. 12C illustrates an exemplary process 1150 for generating a graph state, according to some embodiments related to providing multiple cavities for generating a graph state. The exemplary process 1150 may be part of a quantum computational method for generating a graph state. While the block diagram in FIG. 12C may be described below in conjunction with specific implementation embodiments presented in other figures, the implementations are provided solely for illustrative purposes and are not intended to serve as limitations on the block diagram. Because example steps of the process are described throughout this disclosure, such examples will not be repeated or briefly summarized in conjunction with FIG. 12C . In some embodiments of the present disclosure, the exemplary process 1150 may be performed by at least one processor or circuitry, e.g., in the control system 1031 and / or optical chip 1015 of FIG. 10 , to perform the operations or functions described herein. In some embodiments of the present disclosure, some aspects of the process 1150 may be implemented as software (e.g., program code or instructions) stored in memory provided with at least one processor, or in a non-transitory computer-readable medium or computer-readable medium. In some embodiments, some 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] 12C includes process steps (or method steps) 1152-1156. In step 1152, the process or method involves coupling a quantum emitter at each of a plurality of coupling locations, such that each of the plurality of quantum emitters is associated with a different coupling location, each coupling location being associated with a different one of a plurality of photonic cavities, and the quantum emitter associated with each coupling location is configured to mediate interactions between successive incoming optical qubits to generate a graph state. For example, FIG. 12A shows a preferred implementation of multiple quantum emitters (e.g., quantum emitters 1114_1-1116_n) coupled at multiple coupling locations (e.g., coupling locations 1116_1-1116_n) such that each quantum emitter is associated with a different coupling location (e.g., quantum emitter 1114_1 is associated with coupling location 1116_1, quantum emitter 1114_n is associated with coupling location 1116_n). Further, each coupling site is associated with a different one of the photonic cavities (e.g., coupling site 1116_1 is associated with photonic cavity 1112_1, and coupling site 1116_n is associated with photonic cavity 1112_n). Each of quantum emitters 1114_1 through 1114_n associated with corresponding coupling site 1116_1 through 1116_n is configured to mediate interactions between successive incoming optical qubits (e.g., associated with input photons 1106_1 through 1106_n) to generate one of graph states (e.g., graph states 1110_1 through 1110_n and 1122).

[0143] At step 1154, the process involves providing photons to a plurality of photonic cavities, the photonic cavities configured to couple optical qubits to quantum emitters. For example, Figure 12A shows a preferred implementation of providing photons to a plurality of photonic cavities configured to couple optical qubits to quantum emitters. Photon generator 1104 is configured to provide input photons 1106_1 through 1106_n toward photonic cavities 1112_1 through 1112_n via waveguides 1118_1 through 1118_n. Similarly, photon generator 1130 or photon generation unit 1132_1 of Figure 12B may provide output photons 1146_1 to 1146_n as input photons 1106_1 to 1106_n via waveguides 1118_1 to 1118_n of entanglement gates 1102_1 to 1102_n toward photonic cavities 1112_1 to 1112_n, as shown in Figure 12D. Photonic cavities 1112_1 to 1112_n may then couple optical quantum bits (e.g., associated with the input photons) to quantum emitters 1114_1 to 1114_n. In other words, photonic cavities 1112_1 through 1112_n may then facilitate interactions between optical quantum bits (eg, associated with input photons) and quantum emitters 1114_1 through 1114_n.

[0144] At step 1156, the process involves outputting the graph state via multiple photon output channels downstream of the multiple cavities, consistent with some embodiments of the present disclosure. For example, FIG. 12A illustrates a preferred implementation that outputs the graph state via multiple photon output channels downstream of the multiple cavities. Each entanglement gate 1102_1-1102_n outputs a graph state 1110_1-1110_n of entangled photons 1108_1-1108_n. Additionally, the combination of entanglement gates 1102_1-1102_n may collectively output a cluster state 1122.

[0145] Some embodiments of the present disclosure involve a non-transitory computer-readable medium (or computer-readable medium or computer program) containing instructions that, when executed by at least one processor (or device), cause the at least one processor (or device) to perform a method or process in accordance with some embodiments of the present disclosure.

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

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

[0148] According to other embodiments relating to providing a plurality of cavities for generating graph states, there is 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 provided above for each system feature of the embodiments relating to providing a plurality of cavities for generating graph states are also applicable to the corresponding features of these embodiments.

[0149] According to yet another embodiment relating to providing multiple cavities for generating graph states, there is an integrated circuit device or circuit layout comprising layout portions, each layout portion defined to pattern a feature from a combination of features of quantum computing system 1100 in Figure 12A, photon generator 1130 in Figure 12B, or photon generator 1130 and entanglement gate 1102_1 in Figure 12D. For example, there is an integrated circuit device or circuit layout including: a photon cavity layout portion defined to pattern a plurality of cavities; a coupling location layout portion defined to pattern a plurality of coupling locations for quantum emitter positioning, each coupling location associated with a different one of the plurality of photon cavities; a photon generator layout portion defined to pattern a photon generator or a channel carrying photons provided by the photon generator to the plurality of photon cavities; 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 defined to pattern at least one additional photon cavity. In those embodiments of the present disclosure, the photon generator layout portion may also be defined to pattern at least one additional coupling location for the quantum emitter positioning, each additional coupling location being associated with a different one of the at least one additional photon cavity. In some embodiments of the present disclosure, the layout of the integrated circuit device or circuit further comprises a controller layout portion defined to pattern the photon generator and the plurality of photon cavities and a controller that controls (e.g., directs or switches between different waveguides) the flow of input and output photons among the plurality of photon output channels, and the controller may comprise one or more processors to perform the control, and memory, circuit components, or circuitry.

[0150] It will be appreciated that if lithographically deposited quantum emitters (e.g., quantum dots) are used, the binding site layout portion can be defined to also pattern the quantum emitters. 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 the present embodiment.

[0151] Some embodiments of the present disclosure involve generating a photonic graph state using one or more interactions of optical qubits with quantum emitters, each quantum emitter coupled to a cavity. Such embodiments may involve a quantum computing method for generating a photonic graph state. In such a quantum computing method for generating a photonic graph state, multiple quantum emitters may be positioned at multiple coupling locations associated with multiple different cavities (e.g., photonic or optical cavities, whispering gallery mode cavities, Fabry-Perot cavities, or cavities functioning as resonators, such as ring-shaped cavities). The states of the quantum emitter qubits associated with each of the multiple quantum emitters may be initialized so that the quantum emitters are configured to perform a specific function when generating the photonic graph state. Such initialization refers to setting a baseline state for a quantum emitter coupled to a cavity (also referred to as a cavity-coupled quantum emitter). For example, initialization may include establishing a starting coordinated state system for the cavity-coupled quantum emitter. A system in an initial adjusted state may refer, for example, to a cavity-coupled quantum emitter being in a particular state or superposition of states. For example, the initialization may involve using a laser or applying a magnetic field to the quantum emitter. An optical qubit may then be transmitted toward multiple quantum emitters in at least a first instance to generate an entanglement gate (e.g., a controlled Z quantum gate or a 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 FIGS. 3, 5A-5B, and 9C. After at least one of the first instance transmissions, the optical qubit may be transmitted toward multiple quantum emitters in at least one second instance transmission to generate a SWAP gate between the optical qubit and the quantum emitter qubit, which may serve to 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 FIG. 2E.For example, the entanglement gate of FIG. 3 may be performed multiple times (e.g., n times to entangle n optical qubits with a quantum emitter qubit, as described with reference to FIG. 6), followed by the SWAP gate of FIG. 2E (e.g., to disentangle the quantum emitter qubit from the entangled optical qubits) to generate a photon graph state (e.g., of the entangled optical qubit) (in which 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 a quantum emitter coupled to the cavity at a coupling location. Each configuration may be initialized to operate in one of multiple modes of operation, such as an entanglement mode in which one or more optical qubits may become entangled with the quantum emitter qubit associated with the quantum emitter, and a swap mode in which the state of the quantum emitter qubit is swapped with the state of the optical qubit, thereby disentangling the quantum emitter qubit from the entangled optical qubit. In an example, because the swap mode involves swapping qubit states, an initialization pulse of one or more photons (having a particular desired state) may be used in a cavity-coupled quantum emitter operating in the swap mode to initialize the cavity-coupled quantum emitter. By combining these configurations in different modes of operation in a particular order, a quantum computing method can generate a photon graph state as an output. For example, a cavity-coupled quantum emitter can be initialized by operating the cavity-coupled quantum emitter in SWAP mode and interacting the cavity-coupled quantum emitter with an initialization pulse. Photons can then be introduced to interact with the initialized cavity-coupled quantum emitter operating in entanglement mode to entangle the photons with the cavity-coupled quantum emitter. The cavity-coupled quantum emitter can then again be operated in SWAP mode, and photons from another pulse can exchange their state with the cavity-coupled quantum emitter, thereby disentangling the cavity-coupled quantum emitter from the entangled photons. This results in a photon graph state of entangled photons. As a non-limiting example, FIG. 6 illustrates this process.

[0153] 13A-13C illustrate a preferred implementation of a quantum computing system 1200 that generates photon graph states consistent with some embodiments of the present disclosure. Quantum computing system 1200 is intended merely to facilitate conceptualization of one preferred implementation of a quantum computing system that generates photon graph states and is not intended to limit the present disclosure to any particular implementation. Quantum computing system 1200 may include multiple configurations (1214_1-1214_n), each including a cavity (e.g., cavities 1202_1-1202_n) that functions as a resonator capable of establishing or supporting an electromagnetic mode, and a quantum emitter (e.g., quantum emitter 1206_1-1206_n) positioned at a coupling location (e.g., coupling location 1204_1-1204_n), where n is any integer greater than 1. Each of the coupling locations 1204_1 to 1204_n may be associated with a different one of the cavities (1202_1 to 1202_n) and a different one of the quantum emitters (1206_1 to 1206_n); for example, quantum emitter 1206_1 may be positioned at coupling location 1204_1 associated with cavity 1202_1, and quantum emitter 1206_n may be positioned at coupling location 1204_n associated with cavity 1202_n.

[0154] The quantum computing system 1200 may further include a controller 1208, waveguides 1210_1 through 1210_n and 1212_1 through 1212_n, and at least one photon generator 1230. The waveguides 1210_1 through 1210_n may be configured to facilitate positioning (e.g., trapping) of the quantum emitters 1206_1 through 1206_n at the coupling locations 1204_1 through 1204_n, for example, by establishing an evanescent field at or around the coupling location around a surface thereof.

[0155] The controller 1208 may include circuitry or at least one processor for controlling the operation of the configurations 1214_1-1214_n. For example, the controller 1208 may include a switch for alternating between operational phases or configurations 1214_1-1214_n operating in different modes. For example, at a given time, each configuration 1214_1-1214_n may be in an initialization phase (e.g., FIG. 13A), an entanglement phase (e.g., FIG. 13B), or a SWAP phase (e.g., FIG. 13C), described in more detail herein below. The controller 1208 may control aspects of operation for any of the waveguides 1210_1-1210_n and 1212_1-1212_n, for example, by controlling the timing, phase, frequency, intensity, amplitude, polarity, and any other characteristics of pulses or lasers carried by the waveguides that may affect the operation of the configurations 1214_1-1214_n. For example, the controller 1208 may control characteristics of trapping lasers (e.g., blue and red lasers) that trap or position quantum emitters at coupling locations, which may be carried within the waveguides 1210_1 through 1210_n, as shown by non-limiting example in Figures 9A-9C. The controller 1208 may, for example, control characteristics of magnetic fields or lasers that may be used during initialization to produce desired states in one or more quantum emitters (1206_1 through 1206_n). The controller 1208 may also control the coupling (e.g., confinement) between the quantum emitters (1206_1 through 1206_n) and the cavities (1202_1 through 1202_n) at the coupling locations (1204_1 through 1204_n), respectively.

[0156] The controller 1208 may control operational aspects of the photon generator 1230, described in more detail herein below. The controller 1208 may control synchronization and timing aspects of the operation of the configurations (1214_1-1214_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 cause the output from configuration 1214_n to be conveyed within a channel to serve 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 phase, the entanglement phase, and the SWAP phase for each of the configurations (1214_1-1214_n). As another non-limiting example, the controller 1208 may include a clock for synchronizing operation among different ones of the configurations (1214_1-1214_n), optionally with additional components and / or circuits. As another non-limiting example, the controller 1208 may include at least one processor for controlling operation of the configurations (1214_1-1214_n), e.g., for synchronizing or otherwise monitoring or managing operation of different ones of the configurations (1214_1-1214_n).

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

[0158] As a non-limiting example, at least one photon generator 1230 (e.g., controlled 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 (e.g., each operating similarly to single photon source unit 401 or single photon source 812). The first photon generator provides photons for an initialization phase (e.g., initializing quantum emitters 1206_1 to 1206_n), the second photon generator provides photons (1226_1 to 1226_n) for an entanglement phase (e.g., generating or operating associated configurations as entanglement gates 1216_1 to 1216_n), and the third photon generator provides photons (1228_1 to 1228_n) for a SWAP phase (e.g., generating or operating associated configurations as SWAP gates 1218_1 to 1218_n). Alternatively, the controller 1208 may control the operational aspects of the photon generator 1230 (e.g., a single-photon generator) to emit any one or more of photons 1224_1 to 1224_n for the initialization phase, photons 1226_1 to 1226_n for the entanglement phase, and photons 1228_1 to 1228_n for the SWAP phase. As mentioned, the controller 1230 may control the operation of the photon generator 1230 and the components (1214_1 to 1214_n) to cycle through and synchronize operation between the different phases.

[0159] Controller 1208 may facilitate controlling any of the operational aspects of quantum computing system 1200. For example, controller 1208 may control a component or group of components of quantum computing system 1200 to facilitate positioning of quantum emitters (1206_1-1206_n) at coupling locations (1204_1-1204_n), e.g., by controlling one or more operational characteristics of waveguides (1210_1-1210_n) related to the wavelength, phase, amplitude, polarity, and modality of pulses or lasers carried within the waveguides. Controller 1208 may facilitate initialization of states for quantum emitter qubits, each state and quantum emitter qubit associated with each of quantum emitters 1206_1-1206_n in FIG. 13A . Controller 1208 may further facilitate the transfer of optical quantum bits associated with photons (1226_1 through 1226_n) for entanglement gates 1216_1 through 1216_n in Figure 13B. Controller 1208 may further facilitate the transfer of respective optical quantum bits associated with photons (1228_1 through 1228_n) for SWAP gates 1218_1 through 1218_n in Figure 13C, such that photonic graph states such as photonic graph states 1220_1 through 1220_n and / or cluster state 1222 may be generated as described herein in more detail below. Note that entanglement gates 1216_1 through 1216_n and SWAP gates 1218_1 through 1218_n may each be generated from configurations 1214_1 through 1214_n, respectively, in Figure 13A after an appropriate initialization process. For example, depending on the mode of operation controlled by the controller 1208, the configurations (1214_1 to 1214_n) may alternatively operate in an entanglement mode for the entanglement phase and in a swap mode for the swap phase.

[0160] Some embodiments involve quantum computing 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 one or more photon degrees of freedom, as described above. For example, a photon graph state may represent relationships between groups of optical qubits, and each optical qubit may represent a basic unit of quantum information. For example, a photon graph state may include states whose vertices may represent photon states, and a photon state may refer to the state of one or more photons, and an edge may represent entanglement between photon states. A photon graph state may refer to, for example, multiple entangled photons or their states.

[0161] 13A-13C collectively illustrate a preferred implementation of a quantum computing system 1200 for generating photonic graph states (1220_1-1220_n and 1222) consistent with certain embodiments of the present disclosure. Quantum computing system 1200 includes quantum emitters (1206_1-1206_n) positioned at coupling locations (1204_1-1204_n) between respective waveguides (1210_1-1210_n) and cavities (1202_1-1202_n).

[0162] Referring to FIG. 13A, the controller 1208 may control the operation of the photon generator 1230 to provide successive photons (1224_1 to 1224_n) (e.g., initialization photons) to the waveguides (1212_1 to 1212_n) to initialize the quantum emitters (1206_1 to 1206_n) of the configurations (1214_1 to 1214_n), respectively. Referring to FIG. 13B, controller 1208 may control the operation of photon generator 1230 to provide multiple photons (1226_1 to 1226_n) to waveguides (1212_1 to 1212_n), respectively, as sources of optical quantum bits for entanglement gates (1216_1 to 1216_n), thereby generating entanglement gates between optical quantum bits and quantum emitter quantum bits, as shown by quantum emitter quantum bits (1234_1 to 1234_n) entangled with two optical quantum bits. Referring to FIG. 13C, controller 1208 may control the operation of photon generator 1230 to provide one or more photons (1228_1 to 1228_n) for SWAP gates (1218_1 to 1218_n) to waveguides (1212_1 to 1212_n), thereby generating SWAP gates (1218_1 to 1218_n) and mapping quantum emitter qubits (e.g., associated with quantum emitters 1206_1 to 1206_n) to optical qubits associated with reflected output photons 1236_1 to 1236_n. This leaves entangled photons 1231_1 to 1232_n, which may form photon graph states 1220_1 to 1220_n and / or clusters 1222 depending on how the inputs and outputs of the entanglement gates are connected.

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

[0164] Some embodiments involve positioning multiple quantum emitters at multiple coupling locations associated with multiple cavities. Quantum emitter, as previously described, refers to a component configured to couple to an electromagnetic mode. Coupling location, as previously described, includes an area or region configured to allow coupling between a quantum emitter and a cavity (which is an example of a resonator). Cavity, as previously described, refers to a structure, housing, or container that functions as a resonator to establish or support vibrational or normal modes. A photonic cavity is an example of a cavity that can establish or support electromagnetic modes associated with photons.

[0165] Positioning multiple quantum emitters at multiple binding locations refers to positioning or installing the quantum emitters to allow interactions between the quantum emitters and one or more cavities associated with each quantum emitter, as described above. Examples of such quantum emitter positioning include one or more of: positioning the quantum emitters to be located at the binding locations (e.g., positioning or installing the quantum emitters at the binding locations), coupling the quantum emitters to the cavities, placing the quantum emitters within the internal cavity field of the cavities, trapping the quantum emitters near the cavities, lithographically placing quantum dots near the cavities, or lithographically placing the cavities near self-assembled quantum dots. For example, positioning quantum emitters at multiple binding locations. Trapping the quantum emitters refers to creating traps that maintain the quantum emitters within the binding locations, as described above. As non-limiting examples, FIG. 9A shows a utility waveguide 910 carrying a pulse or field that generates a trap, and FIG. 10 shows a magneto-optical trap (MOT) trapping one or more atoms 1020. The pulse or field in FIG. 9A is configured to trap Rb atoms 820 (exemplary quantum emitters) next to a binding location, e.g., a cavity 818 (or resonator or ring shape in the figure). The pulse or field may be configured to generate and / or contain an evanescent field around the waveguide 910, such that the evanescent field trap can be used to maintain the Rb atoms 820 at or within the binding location. The magneto-optical trap in FIG. 10 is configured to trap one or more atoms 1020 at or within the binding location.

[0166] Thus, 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., photonic cavities). This may enable, for example, multiple simultaneous (e.g., parallel) interactions between multiple quantum emitters and multiple photons via multiple cavities. It will be understood that multiple quantum emitters may be coupled to a single cavity, or multiple cavities may be coupled to a single quantum emitter and function simultaneously (e.g., in parallel) in a similar manner, and the interactions provided between each quantum emitter and each cavity may be enabled from the couplings.

[0167] 13A-13C illustrate, by way of non-limiting example, multiple quantum emitters positioned at multiple coupling locations associated with multiple cavities, according to some embodiments relating to generating photonic graph states. The structures 1214_1-1214_n, entanglement gates 1216_1-1216_n, and swap gates 1218_1-1218_n each include a coupling location 1204_1-1204_n associated with a cavity 1202_1-1202_n. Each coupling location 1204_1-1204_n is located between the cavity 1202_1-1202_n associated with the respective coupling location and the waveguide 1210_1-1210_n associated with the respective coupling location. 9A-9C, blue and red lasers for trapping quantum emitters at coupling sites may be carried by waveguides (1210_1-1210_n). The blue and red lasers generate evanescent fields around the waveguides (1210_1-1210_n), which may be used, for example, to trap or maintain associated quantum emitters (1206_1-1206_n) at or within their associated coupling sites (1204_1-1204_n). Controller 1208 may control circuitry or optical elements for positioning quantum emitters at coupling sites. For example, controller 1208 may control lasers used to trap quantum emitters at coupling sites. Controller 1208 may control characteristics of the blue and red lasers used for trapping. For example, positioning (e.g., confinement or trapping) quantum emitters (1206_1 to 1206_n) at respective coupling locations (1204_1 to 1204_n) between corresponding waveguides (1210_1 to 1210_n) and cavities (1202_1 to 1202_n) enables interaction between the quantum emitters (1206_1 to 1206_n) and the cavities (1202_1 to 1202_n) associated with the quantum emitters, for example, by allowing the dipole field of each quantum emitter to overlap with the electromagnetic mode of the associated cavity, thereby coupling the quantum emitter to the cavity.For example, photon generator 1230 may include multiple photon generators, one configured to generate photons 1224_1 through 1224_n for configurations 1214_1 through 1214_n, another configured to generate photons 1226_1 through 1226_n for entanglement gates 1216_1 through 1216_n, and another configured to generate photons 1228_1 through 1228_n for SWAP gates 1218_1 through 1218_n. Controller 1208 may switch between the photon generators as needed to generate graph states 1220_1 through 1220_n and 1222. Alternatively, the controller 1208 may control the operation of the photon generator 1230 (e.g., as a single photon generator) to generate photons (1224_1 to 1224_n), photons (1226_1 to 1226_n) (e.g., in the first transfer case), and photons (1228_1 to 1228_n) (e.g., in the second transfer case) for the initialization phase, the entanglement phase, and the SWAP phase, 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, as previously described, refers to a fundamental unit of quantum information stored in or belonging to a quantum emitter. Initializing a 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 a starting coordinated state system for the quantum emitter. As a non-limiting example, FIG. 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 basis 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 the present disclosure, initialization may cause the state of a quantum emitter qubit to correspond to an equal superposition of the quantum emitter's two basis states. 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 state, e.g., zero-point energy. Superposition may refer to multiple states simultaneously, e.g., until a measurement is made. Superposition may refer to, e.g., a sum (or superposition) of two or more quantum states, and equal superposition may refer to having the two or more quantum states with equal probability. For example, FIG. 1 shows a four-state system 101 of atom 102 (an exemplary quantum emitter) coupled to optical cavity 103, where atom 102 may be initialized in a superposition of first and second basis states 111 and 113, respectively. 2E and 3 show examples of such initialized states of a quantum emitter coupled to a cavity, with atom 102 (an exemplary quantum emitter) being in an initial superposition of first and second ground states 111, 113 after an 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 Zeeman shifting through the application of a magnetic field.

[0170] As one non-limiting 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, e.g., using pulses 403 and 503, respectively. As another non-limiting example, the quantum emitter may be initialized to any of the states or any superposition of the states shown in Figure 1.

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

[0172] Some embodiments involve transmitting optical qubits toward multiple quantum emitters in at least one first instance of transmission to create an entanglement gate between the optical qubit and the quantum emitter qubit so as to entangle the quantum emitter qubit and the optical qubit. An optical qubit, as previously described, refers to a fundamental unit of quantum information stored in (or residing in) one or more photons or electromagnetic fields. An entanglement gate, as previously described, 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 entanglement gate (CZ gate) relates to one type of entanglement gate. As non-limiting examples of entanglement gates, FIG. 3 shows a controlled-Z entanglement gate implementation, and FIGS. 8 and 9C show examples of controlled-Z entanglement gates using rubidium ( 87 5A and 5B show photon entanglement unit 501, which is implemented with a controlled Z entanglement gate. As another example, photon entanglement unit 501 in FIGS. 5A and 5B is a type of entanglement gate. Transmission refers to transporting or conveying, for example, through a channel or waveguide. Thus, for example, transmitting an optical quantum bit toward multiple quantum emitters in at least one first instance of transmission to generate an entanglement gate between the optical quantum bit and the quantum emitter quantum bit refers to first conveying a photon (to which the optical quantum bit belongs) toward the quantum emitter, for example, through a channel or waveguide, to create entanglement between the optical quantum bit and the quantum emitter quantum bit (e.g., as described with reference to captions 602-609 in FIG. 6 ).

[0173] In an example, a controller (e.g., controller 1208) may control a component, group of components (e.g., optical elements), or circuit to transmit an optical quantum bit toward multiple quantum emitters in a first case, thereby generating an entanglement gate between the optical quantum bit and the quantum emitter quantum bit, and the quantum emitter quantum bit and the optical quantum bit become entangled. The controller may, for example, control a photon generator or photon source unit to provide a photon belonging to the optical quantum bit. The controller may also control one or more of a switch, a beam splitter, and a waveguide to direct and convey the provided photon to a quantum emitter that has been initialized to be in a desired state for the entanglement gate, to effect entanglement between the optical quantum bit and the quantum emitter quantum bit.

[0174] 13B illustrates quantum computing system 1200 including waveguides 1212_1 through 1212_n that transmit optical qubits toward multiple quantum emitters to create entanglement gates between the optical qubits and the quantum emitter qubits to entangle the quantum emitter qubits, according to some embodiments relating to generating photonic graph states. For example, controller 1208 may control the operation of photon generator 1230 to provide photons 1226_1 through 1226_n to waveguides 1212_1 through 1212_n during, e.g., entanglement phases of entanglement gates 1216_1 through 1216_n of quantum computing system 1200. The controller 1208 may further control how the cavities (1202_1-1202_n) function or interact with the quantum emitters (1206_1-1206_n), for example, by controlling the frequency and / or other characteristics of the optical pulses input to the cavities (1202_1-1202_n) so as to cause photons 1226_1-1226_n (e.g., transported via the waveguides 1212_1-1212_n) to interact with the quantum emitters (1206_1-1206_n) via the cavities 1202_1-1202_n associated with the quantum emitters, the association being such that the quantum emitters and the cavities are coupled to enable interaction therebetween. This, in turn, causes the optical quantum bit (e.g., associated with photon 1226_1-1226_n) to become entangled with the quantum emitter quantum bit (e.g., associated with the associated quantum emitter 1206_1-1206_n). Accordingly, controller 1208 may control the operation of system 1200 such that the cavities (1202_1-1202_n), waveguides (1210_1-1210_n and 1212_1-1212_n), and quantum emitters (1206_1-1206_n) positioned at coupling locations (1204_1-1204_n) collectively operate as entanglement gates (1216_1-1216_n) to output an optical quantum bit that is entangled with the quantum emitter quantum bit (1234_1-1234_n).

[0175] Some embodiments involve, after at least one of the first instance transfers, transferring the optical quantum bit to multiple quantum emitters in at least one second instance transfer to map the quantum emitter quantum bit to the optical quantum bit to generate a SWAP gate between the optical quantum bit and the quantum emitter quantum bit. A SWAP gate, as described above, refers to a quantum gate operable on two quantum bits, where the quantum state of the first quantum bit is transferred to the second quantum bit and the quantum state of the second quantum bit is transferred to the first quantum bit. For example, SWAP gate 201 of FIG. 2E may be a preferred implementation of a SWAP gate.

[0176] Thus, in an example, after a first instance transmission of a photon that entangles an optical quantum bit (e.g., associated with the photon transmitted in the first instance transmission) with a quantum emitter quantum bit (e.g., from a quantum emitter positioned in the cavity and coupling location acting as an entanglement gate), a controller (e.g., controller 1208) may control a component, group of components (e.g., optical elements), or circuit to effect a second instance transmission (e.g., of another successive photon). The controller may control a component, group of components (e.g., optical elements), or circuit to transmit the optical quantum bit toward multiple quantum emitters at a second time (after the first instance), thereby creating a SWAP gate between the optical quantum bit of the first photon interacting with the quantum emitter and the quantum emitter quantum bit, and the quantum emitter quantum bit is mapped to that optical quantum bit. The controller may, for example, control a photon generator or photon source unit to provide one or more photons belonging to one or more optical quantum bits. The controller may also control one or more of the switches, beam splitters, and waveguides to direct and convey one or more donor photons to the quantum emitter initialized to the desired state for the SWAP gate, thereby mapping the quantum emitter qubit to one or more optical qubits. Mapping or transferring the state of the quantum emitter qubit from the quantum emitter to the photon's optical qubit leaves the quantum emitter with the state of the optical qubit before the mapping or transfer. This effectively disentangles the quantum emitter qubit from the entangled optical qubit with which it previously interacted as an entanglement 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. This then leaves only the previously interacting optical qubits entangled with each other, forming a photon graph state or cluster state (e.g., as described with reference to caption 611 in FIG. 6 ).The mapping may also free the quantum emitter to be initialized again to a desired state for the entanglement gate, causing the quantum emitter qubit to become entangled with the optical qubit of another incoming photon.

[0177] The SWAP gate operation may be based on the single-photon Raman interaction (SPRINT) mechanism described in Bechler O. et al., "A passive photon-atom qubit swap operation," Nature Physics 14, 996-1000 (2018), Rosenblum S. et al., "Extraction of a single photon from an optical pulse," Nature Photonics 10, 19-22 (2016), and Shomroni, I. et al., "All-optical routing of single photons by a one-atom switch controlled by a single photon," Science 345.6199, 903-906 (2014), the entire contents of which, as well as the contents relating to single-photon extraction and the SPRINT mechanism, are incorporated herein by reference. For example, a quantum emitter is coupled to a cavity at a coupling location. Two transitions in a multilevel quantum emitter (e.g., a single atom such as a Rb atom having at least two ground states and at least one excited state) are coupled to different directions of a waveguide via a cavity (e.g., a microresonator). The quantum emitter, cavity, and waveguide arrangement (e.g., as shown in FIG. 13C with quantum emitters 1206_1 to 1206_n, cavities 1202_1 to 1202_n, and waveguides 1212_1 to 1212_n) is such that light or photons carried in the waveguide are evanescently coupled to the cavity beside the waveguide. Here, evanescent coupling refers to the ability to interact or be transferred by the evanescent field surrounding the waveguide.When a pulse containing multiple photons (e.g., photons 1228_1 to 1228_n in FIG. 13C ) is introduced into a waveguide (e.g., 1212_1 to 1212_n in FIG. 13C ), the first photon of the pulse in the waveguide originating from a certain direction interacts with a quantum emitter (e.g., quantum emitter 1206_1 to 1206_n) via a cavity (e.g., cavity 1202_1 to 1202_n) coupled to the quantum emitter by evanescent coupling of the cavity. The interaction causes the first photon of the pulse originating from that direction to be deterministically reflected by destructive interference in transmission, as shown by reflected photons 1236_1 to 1236_n shown in FIG. 13C . This interaction between the first photon and the quantum emitter is similar to mapping a quantum emitter qubit to an optical qubit as described above with reference to SWAP gate 201 from FIG. 2E or SWAP gates 1218_1-1218_n in FIG. 13C. This interaction also results in a Raman transfer of the quantum emitter (e.g., quantum emitters 1206_1-1206_n) from one basis state to another, rendering the quantum emitter transparent to the next photon from that direction (e.g., the next second photon from that pulse of photons, such as photons 1228_1-1228_n in FIG. 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 to interact with the cavity-coupled quantum emitter and thus be reflected back to be output in the direction from which the mapping photon originally came. 15A-15C illustrate the SPRINT mechanism, which is described in more detail below.

[0178] 13C illustrates a system 1200 according to some embodiments of the present disclosure for generating a photon graph state, where, after a first instance of transmission, system 1200 transmits optical qubits toward multiple quantum emitters in a second instance to generate a SWAP gate between the optical qubits and the quantum emitter qubits to map the quantum emitter qubits to optical qubits. For example, controller 1208 may control the operation of photon generator 1230 to provide photons (1228_1 through 1228_n) to waveguides (1212_1 through 1212_n), respectively, during the SWAP phase of system 1200. Controller 1208 may further control optical elements or circuits, such as switches and waveguides, to direct the optical qubits (e.g., associated with photons 1228_1 through 1228_n) of the second instance of transmission toward quantum emitters (1206_1 through 1206_n). The interaction between the optical quantum bits from the second instance transmission (e.g., associated with photons 1228_1 to 1228_n) through the cavities (1202_1 to 1202_n) and the quantum emitters (1206_1 to 1206_n) functions as SWAP gates (1218_1 to 1218_n), causing the cavities (1202_1 to 1202_n) and the quantum emitters (1206_1 to 1206_n) positioned at the coupling locations (1204_1 to 1204_n) to operate as SWAP gates, respectively, as described with respect to Figure 2E. As a result, the states of the quantum emitters (1206_1-1206_n) may be transferred (e.g., swapped) or mapped to the states of the optical qubits (e.g., associated with the photons 1228_1-1228_n of the second instance transmission), respectively. Thus, the second instance transmission may result in entanglement between, for example, the quantum emitter qubits associated with the quantum emitters (1206_1-1206_n) and the already entangled optical qubits (e.g., generated by the first instance transmission during the entanglement phase).Each of the SWAP gates (1218_1 to 1218_n) may output mutually entangled photons (1232_1 to 1232_n), depicted as entangled by connecting double lines, or cluster states 1222, corresponding to photon graph states 1220_1 to 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 series to produce multiple photon-quantum emitter entanglements, and the transmission in the second instance follows the first instance to output a photon graph state. Sequential order may refer to a particular order, progression arranged in a particular sequence, or succession in the sense of coming one after the other. Thus, the multiple optical qubits for the first transmission instance (e.g., providing multiple photons during the entanglement step) may be transmitted in a sequential manner, e.g., optical qubit-by-photon or photon-by-photon (e.g., as described with reference to captions 602-609 in FIG. 6 ). This then allows the quantum emitter to interact with the photons in series, with the quantum emitter qubit becoming entangled with each optical qubit in series, resulting in multiple photon-quantum emitter entanglements. As a result, the multiple optical qubits become entangled with the quantum emitter qubit. To output a photon graph state that does not have one of the entangled qubits, the quantum emitter qubit must become disentangled from its multiple optical qubits. Thus, the transfer in the second case, which results in a mapping of the state of the quantum emitter qubit from the quantum emitter to the photon optical qubit, and thus disentangles the quantum emitter qubit from the other entangled optical qubits, follows the first case, leaving only optical qubits entangled with each other (e.g., as described with reference to captions 610-612 in FIG. 6 ), forming the output photon graph state.

[0180] As a non-limiting example, a combination or sequence of an entanglement gate in Figure 13B followed by a SWAP gate in Figure 13C may be used to sequentially transfer a first instance of optical qubits to result in multiple photon-quantum emitter entanglements, and then transfer a second instance of optical qubits 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 optical and phase control elements 702, 705 connecting different stages, each stage including at least one of a photon generator, an entanglement gate, and / or a SWAP gate. Further details regarding how the array may operate to generate photon graph states or cluster states are provided below with reference to Figure 7.

[0181] For example, as described above with reference to the first case transfer and entanglement gate, a controller (e.g., controller 1208) may first control a component, group of components (e.g., optical elements), or circuit to transfer an optical quantum bit toward multiple quantum emitters in the first case, thereby entangling the quantum emitter quantum bit and the optical quantum bit. The controller may, for example, control a photon generator or photon source unit to provide a photon belonging to the optical quantum bit in the first case transfer. The controller may also control one or more of a switch, a beam splitter, and a waveguide to direct and transport the provided photon to a quantum emitter that has been initialized to a desired state for the entanglement gate (e.g., under control of the controller as described above with reference to initializing the state of the quantum emitter quantum bit) to effect entanglement between the optical quantum bit and the quantum emitter quantum bit.

[0182] As described above with reference to the second instance transfer and the SWAP gate, a controller (controller 1208) may control a component, group of components (e.g., optical elements), or circuit to effect a second instance transfer (e.g., of another series of photons). The controller may also control a component, group of components (e.g., optical elements), or circuit to transfer optical qubits toward 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 photons from the first instance transfer. This effectively disentangles the quantum emitter qubits from the entangled optical qubits, leaving only the previously interacting optical qubits entangled with each other, which form an output photon graph state or cluster state (e.g., as described with reference to caption 611 in FIG. 6 ). The controller may, for example, control a photon generator or photon source unit to provide one or more photons belonging to one or more optical qubits. The controller may also control one or more of the switches, beam splitters, and waveguides to direct and convey one or more donor photons to a quantum emitter that has been initialized to a desired state for the SWAP gate (e.g., under the control of the controller as described above with reference to initializing the state of the quantum emitter qubit).

[0183] According to some embodiments, the initialization involves using a SWAP gate. As previously mentioned, a SWAP gate refers to a quantum gate operable on two qubits, where the quantum state of a first qubit is transferred to a 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 onto the optical qubit, while the state of the optical qubit is mapped onto the quantum emitter qubit. Thus, by controlling the properties of photons 1228_1 through 1228_n (which are input into waveguides 1212_1 through 1212_n and exchange photon states with the quantum emitter qubits) so that they correspond to the desired state, a SWAP gate can be used between the quantum emitter qubit and the optical qubit of photon 1228_1 through 1228_n to map a desired state onto the quantum emitter qubit as part of the initialization step. The desired state may be, for example, that of an entanglement gate. For example, the controller (or controller 1208) may control a component, a group of components such as optical elements, or a circuit to control or set the properties of the photons 1228_1-1228_n. For example, an initialization photon may be provided to or transmitted toward the cavity to interact with a quantum emitter to effect a swap (e.g., exchange) of quantum states between the quantum emitter and an optical qubit associated with the initialization photon.

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

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

[0186] According to some embodiments, initialization includes applying a light beam. A light beam may refer to an electromagnetic wave that remains focused around a mean axis during free propagation or an electromagnetic wave that is guided by a structure such as a waveguide. With reference to FIG. 13A , controller 1208 may control the operational aspects of photon generator 1230 to apply the light beam to structures 1214_1 through 1214_n via any of waveguides 1210_1 through 1210_n and 1212_1 through 1212_n, respectively.

[0187] According to some embodiments, the plurality of quantum emitters include atoms, and the positioning includes trapping the atoms near the cavities. As previously described, the trapping may involve using blue and red lasers to trap the quantum emitters at the binding locations. With reference to Figures 13A-13C, one or more of the quantum emitters (1206_1-1206_n) may include atoms, such as atom 102 of Figure 1. The atoms may be positioned at the binding locations (1204_1-1204_n) by trapping the atoms near the cavities (1202_1-1202_n).

[0188] According to some embodiments, the plurality of quantum emitters include quantum dots, and the positioning includes at least one of lithographically placing the quantum dots near a cavity or lithographically placing a cavity near the self-assembled 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) with optical and / or electronic properties that exhibit 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 FIGS. 13A-13C, one or more of the quantum emitters (1206_1-1206_n) may include a quantum dot. The quantum dots can be positioned at the binding locations 1204_1 to 1204_n using lithographic 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 quantum bits are generated using a quantum emitter coupled to a cavity. For example, the quantum emitter coupled to the cavity may be configured to generate or release one or more photons. By way of non-limiting example, source unit 401 in Figures 4A and 4B and photon generator 812 in Figures 8 and 9B are examples of such uses of a quantum emitter coupled to a cavity. Such a quantum emitter coupled to a cavity may be provided, for example, in photon generator 1230 of Figures 13A-13C.

[0190] According to some embodiments of the present 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 electronic or nuclear configurations of an ion or neutral atom, or the electronic or nuclear configurations of a defect or quantum dot in a material substrate.

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

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

[0193] According to some embodiments, the quantum emitter comprises an atom. According to some embodiments, the atom is neutral. Neutral refers to an atom with 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 with an overall charge, such as an atom with an unequal number of protons and electrons. According to some embodiments, the quantum emitter comprises at least one of a rubidium atom or a cesium atom, as previously described. The rubidium or cesium atom can be neutral or ionic. According to some embodiments, the quantum emitter comprises at least one of a strontium, erbium, ytterbium, calcium, barium, beryllium, or magnesium atom, as previously described.

[0194] According to some embodiments, the entanglement gate is one of a controlled Z gate (CZ gate), a controlled NOT gate (CNOT gate), a square root of a SWAP gate, or a virtual SWAP gate (iSWAP gate). A controlled Z gate (CZ gate) refers to a quantum gate operable on two qubits, whose combined quantum state experiences a conditional phase shift (e.g., a pi phase shift as described above). For example, one or more of the entanglement gates 1216_1 through 1216_n may function as any one of a CZ gate, a CNOT gate, a square root of a SWAP gate, or an iSWAP gate. For example, the entanglement gate 1216_1 may be a controlled Z gate (CZ) gate.

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

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

[0197] In step 1264, the process involves initializing the state of a 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 a component, group of components (e.g., optical elements), or circuitry to initialize the quantum emitter qubit associated with each of the multiple quantum emitters. Control may include exposing the quantum emitter (in which the quantum emitter qubit is stored or to which the quantum emitter qubit belongs) to a laser and / or controlling a photon pulse generator and / or a magnetic field generator to apply a magnetic field to the quantum emitter. For example, photon pulse generator 151 and / or magnet 141 in FIG. 1 may be controlled in this manner.

[0198] In step 1266, the process involves transmitting the optical quantum bit toward multiple quantum emitters in at least one first instance of transmission to create an entanglement gate between the optical quantum bit and the quantum emitter quantum bit to entangle the quantum emitter quantum bit. For example, the transmission in the at least one first instance of transmission may involve controlling a component, group of components (e.g., optical elements), or circuit to transmit the optical quantum bit toward the multiple quantum emitters in the first instance. For example, the control may include one or more of: controlling a photon generator or photon source unit to provide photons belonging to the optical quantum bit; and controlling one or more of a switch, a beam splitter, and a waveguide to direct and convey the provided photons to quantum emitters that have been initialized to be in a desired state for the entanglement gate to effect entanglement between the optical quantum bit and the quantum emitter quantum bit.

[0199] In step 1268, the process involves, after at least one of the first instance transmissions, transmitting the optical quantum bit toward multiple quantum emitters in at least one second instance transmission to map the quantum emitter quantum bits to the optical quantum bits to generate a SWAP gate between the optical quantum bit and the quantum emitter quantum bit. For example, the transmission in the at least one second instance transmission may involve controlling a component, group of components (e.g., optical elements), or circuitry to transmit the optical quantum bit toward multiple quantum emitters at a second time (after the first instance). The controlling may include, for example, one or more of: controlling a photon generator or photon source unit to provide one or more photons belonging to one or more optical quantum bits; and controlling one or more of a switch, a beam splitter, and a waveguide to direct and convey the one or more provided photons to the quantum emitter.

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

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

[0202] According to other embodiments relating to generating photon graph states, there is provided 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 1260 shown in Figure 13D. The same examples provided 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 photonic graph states, there is provided a layout of an integrated circuit device or circuit comprising layout portions, each layout portion defined to pattern a respective feature from a combination of features of system 1200 in Figures 13A-13C, entanglement 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 photonic graph states. By way of example, the layout of the integrated circuit device or circuit includes a cavity layout portion defined to pattern a plurality of cavities, a coupling location layout portion defined to pattern a plurality of coupling locations for positioning a plurality of quantum emitters, and a controller layout portion defined to pattern a circuit or at least one processor.

[0204] In some embodiments of the present disclosure, the layout of the integrated circuit device or circuit further includes a photon generator layout portion defined to pattern a photon generator or a channel carrying photons provided 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 in the other cavity. In some embodiments of the present disclosure, the circuit layout portion may be defined to pattern one or more of a waveguide carrying one or more photons or lasers, and one or more linear optical elements that direct or transport one or more photons, control the flow of one or more photons, manipulate the state of one or more photons, and / or perform various functions related to performing quantum computations.

[0205] In some embodiments of the present disclosure, the controller layout portion is defined to pattern a controller that controls (e.g., directs or switches between different waveguides) the flow of input and output photons between the photon generator and the entanglement gate or SWAP gate, and the controller may include one or more processors to perform the control, as well as memory, circuit components, or circuits.

[0206] It will be appreciated that if lithographically deposited quantum emitters (e.g., quantum dots) are used, the binding location layout portion can be defined to also pattern the quantum emitters. The same examples discussed above for each process or system feature of the embodiments relating to generating photon graph states are also applicable to the corresponding feature of the present embodiment.

[0207] Some embodiments involve generating photonic graph states for quantum computation. Quantum computation may refer to computation performed through the utilization or application of one or more quantum state properties, such as superposition, entanglement, and interference. As previously discussed, a graph state represents relationships between groups of qubits, and qubits are the basic units of quantum information. A photonic graph state refers to a graph state that represents relationships between groups of optical qubits. As previously discussed, an optical qubit refers to the basic unit of quantum information stored in (or belonging to) one or more photons or electromagnetic fields. For example, a graph state (or multiple graph states) generated from a sequence of input optical qubits may represent relationships between qubits stored in (or belonging to) output photons.

[0208] Generating a photon graph state for quantum computing refers to generating and / or providing a plurality of photons that can be used in a computation through the use or application of one or more quantum state properties. The plurality of photons may have a group of associated optical qubits, and the relationship between the group of associated optical qubits may be represented using a graph state. For example, generating a photon graph state for quantum computing may include determining operational parameters and instructions for generating the photon graph state. Consistent with some embodiments relating to generating a photon graph state for quantum computing, as described below, the photon graph state may be generated, for example, by entangling one or more optical qubits in succession. In such examples, the photon graph state may be a type of multi-qubit state that may 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, e.g., entanglement, between the pairs.

[0209] Some embodiments involve coupling a quantum emitter to a cavity. A cavity, as described above, refers to a structure, enclosure, or container that can function as a resonator, which is a component that establishes or supports an electromagnetic mode. 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 an electromagnetic mode. For example, a quantum emitter may include a stationary quantum system with an anharmonic spectrum configured to couple to an electromagnetic mode. Coupling a quantum emitter to a cavity refers to enabling an interaction between the quantum emitter and the cavity. For example, allowing the dipole field of the quantum emitter to overlap with the electromagnetic mode of the cavity allows an interaction between the quantum emitter's qubit and the cavity. When a quantum emitter is coupled to a cavity (also referred to as a cavity-coupled quantum emitter) at its associated coupling location, the quantum emitter is coupled to the electromagnetic mode of the cavity. Thus, a cavity-coupled quantum emitter can be configured to either release or emit photons when excited (e.g., function as a photon generator) or to interact with photons passing through the cavity (e.g., function as an entanglement gate to entangle photons).

[0210] As non-limiting examples, Figures 4A and 4B show source unit 401 (including source unit atom 402 as a quantum emitter) implemented as a photon generator, 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 (including entanglement unit atom 502 as a quantum emitter) implemented as an entanglement gate, 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, the coupling may involve positioning the quantum emitter within an internal cavity field of the cavity. As previously mentioned, positioning the quantum emitter refers to placing or locating the quantum emitter to allow interaction between the quantum emitter and the cavity. For example, positioning the quantum emitter within an area configured to allow coupling between the quantum emitter and the cavity, which area may also be referred to as a binding location or binding site. As previously mentioned, quantum emitter positioning may include, for example, one or more of: positioning the quantum emitter to be located at a binding location or binding site (e.g., positioning or locating the quantum emitter at a binding location or binding site), positioning the quantum emitter within an internal cavity field of the cavity, trapping the quantum emitter near the cavity, lithographically placing a quantum dot near the cavity, or lithographically placing a cavity near a self-assembled quantum dot. Trapping a quantum emitter near a cavity refers to creating a trap that maintains the quantum emitter within a binding 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 binding position. Figure 14A shows a non-limiting example of a binding position 1420.

[0212] According to some embodiments, a quantum emitter is a stationary qubit that can interact with photons. A stationary qubit may refer to a material quantum system that can be used to store and process quantum information. For example, a stationary qubit may refer to a qubit that (i) reliably stores quantum information on nanosecond or longer timescales, (ii) reliably performs calculations and / or operations, including operations that can transfer or convert information to flying qubits (e.g., non-stationary qubits or photons), (iii) can be reliably measured or read out, and / or (iv) can be operated to be highly entangled (or meets these conditions). Examples of stationary qubits may include qubits stored in or residing in quantum emitters. For example, qubits stored in or residing in rubidium or cesium atoms may serve as a stationary qubit source. For example, Rydberg atoms may also serve as a stationary qubit source. The use of Rydberg atoms can provide advantageous properties 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. Rydberg atoms can refer to excited atoms with one or more electrons that have a large principal quantum number n.

[0213] For example, the quantum emitter may include a superconducting qubit. As previously mentioned, a superconducting qubit refers to a qubit that is stored in or resides in 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 an example, the quantum emitter may include a quantum dot. A quantum emitter including a quantum dot may refer to a quantum emitter having a substrate (e.g., a solid-state substrate such as a semiconductor particle) with optical and / or electronic properties that exhibit quantum mechanical principles, as described above. For example, a quantum dot may be a nanoparticle with optical and electronic properties different from those of its bulk component. In the presence of high-energy photons (e.g., UV light), electrons in the quantum dot may be excited to a higher energy state and emit one or more photons upon transitioning to the ground state. For example, quantum dots 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, quantum dots may self-assemble from indium arsenide in a gallium arsenide substrate. For example, quantum dots may refer to atomic defects in a solid-state substrate, such as nitrogen-vacancy centers in diamond.

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

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

[0217] As previously mentioned, an optical quantum bit refers to a basic unit of quantum information stored in (or residing in) one or more photons or electromagnetic fields. Forming an optical quantum bit using a dirty photon or forming a first optical quantum bit using a first dirty photon refers to establishing or providing a dirty photon or a first dirty photon as a source of the optical quantum bit or the first optical quantum bit, which is then stored in or residing in the dirty photon or the first dirty photon or its associated electromagnetic field. For example, establishing or providing a dirty photon or a 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, the linear optical element may include one or more of a channel (e.g., a waveguide), a reflector (e.g., a mirror), a beam splitter, a lens, a phase shifter, or another linear optical device that can manipulate the properties or motion of photons.

[0218] Generating a dirty photon, or generating a first dirty photon, refers to providing, releasing, or emitting a photon that may be distinguishable from another photon, e.g., a photon that has been provided, released, or emitted or is destined for that photon. 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. Single photons generated according to some embodiments of the present disclosure are perfectly suitable for optical qubit entanglement using quantum emitters coupled to cavities as described herein, even if the photon exhibits irregularities (e.g., in its temporal profile) that make the photons easily distinguishable.

[0219] The single-photon-securing photon source units described herein are non-limiting examples of such photon generators that can optionally provide dirty photons. As a non-limiting example, FIGS. 4A and 4B show an emitted photon 406, which may be a dirty photon, and a temporally consecutive series of output photons 412 generated by a source unit 401 (including a source unit atom 402 as a quantum emitter). In another non-limiting example, FIGS. 8-9B also show rubidium ( 874A and 4B show a single photon, which may be a dirty photon, generated and output by Rb) atom 820. Referring to source unit 401 in FIGS. 4A and 4B, source unit 401 includes a cavity, such as optical cavity 103 in FIG. 1, and atom 402 (e.g., a quantum emitter). After initialization pulse 403 initializes the state of atom 402 to state 111 (FIG. 1), generation pulse 404 may result in transitions 121A and 122A in FIG. 2A, causing atom 402 to emit photon 406. Repeating this process generates a temporally continuous series of output photons 412 in FIG. 4B. According to some embodiments related to generating photon graph states for quantum computing, generation pulse 404 need not be precisely controlled, e.g., in terms of its pulse time and / or shape, and thus the output photon may be dirty. The output photon has a temporal profile that exhibits irregularities and may therefore be distinguishable.

[0220] Optical quantum computing refers to computation performed through the use or application of one or more quantum state properties of one or more photons. Traditional optical quantum computing, which uses linear optical elements to generate photon graph states, relies on the use of indistinguishable photons (also called clean photons) because the indistinguishable photons do not exhibit any irregularities (e.g., in their temporal profiles). Some of the operations involved in traditional optical quantum computing require the use of destructive interference between multiple photons, which relies on multiple photons being indistinguishable from one another. For example, if the photons used in traditional optical quantum computing are distinguishable, this may result in a decrease in the fidelity of the generated photon graph state and an increase in computational errors.

[0221] In contrast, optical quantum computing can be performed using photon entanglement through cavity-enhanced quantum emitter-photon interactions (e.g., using a quantum emitter coupled to a cavity, also referred to as a cavity-coupled quantum emitter) to use the dirty photons in quantum computing operations. This is because entangling photons through cavity-enhanced quantum emitter-photon interactions uses a cavity-coupled quantum emitter as a mediator to entangle the photons. The cavity-coupled quantum emitter mediates the interaction between photons to generate a photon graph state. Mediating refers to facilitating, enabling, or otherwise promoting the interaction. The interaction may transfer, convey, 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 to achieve the interaction between the incident photons. Thus, optical quantum computing using some embodiments of generating photon graph states for quantum computing described herein does not require the use of indistinguishable photons (also referred to as clean photons), which would otherwise be the case for probabilistic entanglement using linear optics. This means, for example, that the input photon pulse (e.g., generation pulse 404 in FIG. 4A ) used to generate photons for use in quantum computing does not need to be precisely timed and shaped, and may result in the generation of dirty photons with temporal profiles that are not precisely controlled or tuned, as discussed above. 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 second dirty photons having a second temporal profile, and some embodiments involve using the second dirty photons to form a second optical quantum bit. For example, the second dirty photons may be generated and used to form a second optical quantum bit in a manner similar to the way the first dirty photons are generated and used to form the first optical quantum bit described above. The examples described above regarding generating and using first dirty photons to form a first optical quantum bit are also applicable to the second dirty photons.

[0223] Some embodiments involve using a quantum emitter coupled to a cavity to entangle a first optical quantum bit with a second optical quantum bit to form an entangled optical quantum bit pair. An entangled optical quantum bit pair refers to related states of a pair of optical quantum bits, as described above. For example, the states of a pair of optical quantum bits may be related to each other, such that their states cannot be described independently of each other. Such entanglement may, for example, correlate a measurement of the state of one optical quantum bit with a measurement of the state of the other optical quantum bit, generating a correlation between the measurements of their states, whereby mutual information can be stored or processed using the correlation. A quantum emitter coupled to a cavity (or a cavity-coupled quantum emitter) may be used to function as an entanglement gate, as described above. The necessary gate refers to a component or group of components or control sequence configured to entangle the quantum bits. Thus, the cavity-coupled quantum emitter may interact with the first and second optical qubits, for example, in a sequential manner, such that the first and second optical qubits become entangled with the cavity-coupled quantum emitter and, therefore, with each other.

[0224] As non-limiting examples, FIGS. 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 FIGS. 8 and 9C show a rubidium ( 87 Rb) atom 820 is shown.

[0225] Some embodiments involve using pairs of entangled optical qubits for quantum computing. Performing quantum computing may refer to applying an operation to optical qubits, where applying an operation relies on exploiting or applying one or more quantum state properties such as superposition, entanglement, and interference. Entangled optical qubits may be transported through or directed by linear optical elements and / or quantum emitters, thereby enabling the transport and / or manipulation of information encoded therein.

[0226] Some embodiments involve generating third dirty photons having a third temporal profile different from the first and second temporal profiles and using the third dirty photons to form a third optical quantum bit. For example, the third dirty photons can be generated and used to form a third optical quantum bit in a manner similar to the generation and use of the first or second dirty photons to form a first or second optical quantum bit, as described above. The examples described above regarding generating and using the first or second dirty photons to form a first or second optical quantum bit are also applicable to the third dirty photons. The temporal profile, as described above, refers to the temporal envelope of the propagating photon field. Examples of temporal profiles include an exponentially decreasing or increasing profile with a specific decay time and initial time, a constant profile with a specific initial time and final time, or a Gaussian profile with a specific mean time and time variation. Thus, a third temporal profile of a third dirty photon that differs from the first and second temporal profiles of the first and second dirty photons refers to a field of the third dirty photon that has a profile that behaves or changes differently over time than the fields of the first and second dirty photons.

[0227] Some embodiments involve using a quantum emitter coupled to a cavity to entangle a third optical quantum bit with either the first or second optical quantum bit to form three entangled optical quantum bits. For example, as described above, the cavity-coupled quantum emitter may interact with the third optical quantum bit and the first or second optical quantum bit, e.g., in a sequential manner, such that the third optical quantum bit and the first or second optical quantum bit become entangled with the cavity-coupled quantum emitter and, therefore, with each other. The examples described above with respect to entangling a first optical quantum bit with a second optical quantum bit are also applicable to entanglement of a third dirty photon with the first or second optical quantum bit.

[0228] Some embodiments involve using three entangled optical qubits for quantum computing. For example, as described above with reference to using pairs of entangled optical qubits for quantum computing, the three entangled optical qubits may be conveyed through or directed by linear optical elements and / or quantum emitters, thereby enabling the transport and / or manipulation of information encoded therein.

[0229] Some embodiments involve using a cavity coupled to the quantum emitter to entangle a plurality of additional photons to generate a photon graph. The additional photons refer to photons other than the first dirty photon, the second dirty photon, and / or the third dirty photon described above. For example, the additional photons may be generated and used to form additional optical quantum bits in a manner similar to the generation and use of the first dirty photon (or the second or third dirty photon) to form the first optical quantum bit (or the second or third optical quantum bit) described above. The examples described above with respect to generating and using a first dirty photon (or a second or third dirty photon) to form a first optical quantum bit (or a second or third optical quantum bit) are also applicable to additional photons. Entangling multiple additional photons using a cavity coupled to a quantum emitter refers to using a cavity coupled quantum emitter (or a cavity coupled quantum emitter) to function as an entanglement gate, as described above with respect to forming a pair of entangled optical quantum bits involving a first optical quantum bit with a second optical quantum bit. When each photon is entangled with a cavity-coupled quantum emitter, the cavity-coupled quantum emitter generates a photon graph of entangled photons that includes the additional photon and the first and second dirty photons. If a third dirty photon is also entangled using the cavity-coupled quantum emitter, the entangled photons include the third photon. This photon graph of entangled photons can then be used, for example, in quantum computing. The examples discussed above regarding involving a first optical quantum bit with a second optical quantum bit, or entanglement of a third optical quantum bit with the first or second optical quantum bit, are also applicable to entanglement of multiple additional photons.

[0230] 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-contiguous series of entangled photons 512, and FIG. 6 shows repeating the entanglement process using the entanglement unit 501, according to some embodiments. As a result of step 602 repeating the loop of steps 603-606, the entanglement unit atom (such as atom 502) can become entangled with a plurality of photon states, thereby generating a photon graph with 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 similar to the first dirty photon, the second dirty photon described above, or the third dirty photon described below. For example, the additional dirty photons may be generated and used in a manner similar to the first or second dirty photons to form additional optical quantum bits. A quantum emitter coupled to the cavity may then be used to entangle the formed additional optical quantum bit with the first and / or second optical quantum bit or any other optical quantum bit to form multiple entangled optical quantum bits. The multiple entangled optical quantum bits may then be used for quantum computing. The examples and discussion provided herein with respect to the first, second, or third dirty photon are also applicable to dirty additional photons.

[0232] In some embodiments, the first dirty photon is generated by extracting it from an interfering laser pulse using a quantum emitter coupled to the cavity. A laser pulse refers to a light pulse, e.g., a time-confined pulse of laser light containing a specific average number of photons. An interfering laser pulse refers to a laser pulse having a wavelength of laser light that is phase in space and time. A quantum emitter coupled to the cavity (also referred to as a cavity-coupled quantum emitter) can then be used to extract the photon from the interfering laser pulse. The extracted photon can be considered a first dirty photon generated by extracting it from the interfering laser pulse using a quantum emitter coupled to the cavity. The cavity-coupled quantum emitter used for the extraction can be a different quantum emitter than the quantum emitter coupled to the cavity to entangle the first optical quantum bit with the second optical quantum bit. Thus, the extraction cavity-coupled quantum emitter can 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 the extraction of photons from coherent laser pulses based on quantum emitters coupled to a cavity. The photon extraction is based on the single-photon Raman interaction (SPRINT) mechanism described in Bechler O. et al., "A passive photon-atom qubit swap operation," Nature Physics 14, 996-1000 (2018), Rosenblum S. et al., "Extraction of a single photon from an optical pulse," Nature Photon 10, 19-22 (2016), and Shomroni, I. et al., "All-optical routing of single photons by a one-atom switch controlled by a single photon," Science 345.6199, 903-906 (2014), the entire contents of which, as well as the contents relating 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 FIG. 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 to waveguide 1433a via cavity 1434 (e.g., a microresonator). The arrangement of quantum emitter 1432, cavity 1434, and waveguide 1433a is such that light or photons transported within waveguide 1433a are evanescently coupled into cavity 1434 beside waveguide 1433a. Here, evanescent coupling refers to the ability to interact or be transferred by the evanescent field surrounding the waveguide.

[0234] As shown in FIG. 15A, an interfering laser pulse containing multiple photons 1436a, 1436b, and 1436c is introduced into waveguide 1433a. Then, as shown in FIG. 15B, a first photon 1436a of the interfering laser pulse in waveguide 1433a originating from a certain direction interacts with quantum emitter 1432 via cavity 1434 through evanescent coupling 1435 of cavity 1434. This interaction, due to destructive interference in transmission, causes the first photon 1436a of the interfering laser pulse originating from that direction to be deterministically reflected, as shown by reflected photon 1439a in FIG. 15C. This interaction between first photon 1436a and quantum emitter 1432 is similar to mapping a quantum emitter qubit to an optical qubit, as described above with reference to SWAP gate 201 from FIG. 2E. The interaction results in a Raman transfer of the quantum emitter 1432 from one ground state to another, making the quantum emitter 1432 transparent to subsequent photons 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 FIG. 15C , the subsequent 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 the waveguide 1433a. The reflected photon 1439a can then serve as the first dirty photon generated by extraction from the interfering laser pulse using the quantum emitter 1432 coupled to the cavity 1434. Therefore, the SPRINT mechanism-based cavity-coupled quantum emitter can be used to extract dirty photons from the interfering laser pulse. The extracted dirty photon from the SPRINT mechanism is the first photon of the interfering laser pulse that interacts with the cavity-coupled quantum emitter first and is therefore reflected back so that it is output in the direction from which the extracted dirty photon originally came. Subsequent photons of the interfering laser pulse are only transmitted, so that the first photon of the interfering laser pulse that interacts with the cavity-coupled quantum emitter is extracted as a reflected photon, while the remaining photons of the interfering laser pulse are transported unaffected.

[0235] In some embodiments, the second dirty photon is generated by extraction from the interfering laser pulse using a quantum emitter coupled to the cavity. For example, the second dirty photon can be generated by extraction from the interfering laser pulse in a manner similar to how the first dirty photon was generated by extraction from the interfering laser pulse described above. The first and second dirty photons can be generated, for example, by extraction from the interfering laser pulse using a quantum emitter coupled to the cavity. The examples described above regarding generating the first dirty photon are also applicable to generating the second dirty photon. Similarly, in some embodiments, the third dirty photon and / or additional photons can be generated by extraction from the interfering 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, as described above, refers to a quantum emitter whose physical state or properties change (at least temporarily) over time. For example, a quantum emitter may fluctuate because its resonant frequency changes over time due to stray magnetic or electric fields. 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 single-photon-securing photon source unit (e.g., source unit 401 in FIG. 4A ) or photon generator (e.g., quantum emitter 820 coupled to cavity resonator 818 in FIG. 9B ) described herein, such that the fluctuating quantum emitter can provide a photon upon excitation.

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

[0238] In some embodiments, the spectrum of the first dirty photon and the second dirty photon is within the interaction bandwidth of a quantum emitter coupled to the cavity. Spectrum refers to a range of wavelengths of electromagnetic radiation. The spectrum of the first dirty photon and the second dirty photon refers to a range of wavelengths of electromagnetic radiation associated with the first dirty photon and the second dirty photon. The interaction bandwidth of a quantum emitter coupled to the cavity refers to a range of frequencies capable of interacting with a quantum emitter coupled to the cavity. For example, the interaction bandwidth of a quantum emitter may be the absorption spectrum of the quantum emitter, and electromagnetic fields are likely to interact with the quantum emitter at frequencies that fall within the interaction bandwidth. Similarly, in some embodiments, the spectrum of the third dirty photon and / or additional photons may be within the interaction bandwidth of a quantum emitter coupled to the cavity.

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

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

[0241] In some embodiments, at least one of the first dirty photon and the second dirty photon is obtained from an optical delay line. As mentioned above, an optical delay line refers to a component or group of components arranged to introduce a time delay for one or more photon pulses. 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 in free space, fiber, and / or on-chip waveguides. In an example, the optical delay line may be configured to synchronize the timing of obtaining at least one of the first and second dirty photons. For example, the optical delay line may be configured to transport at least one of the first and second dirty photons such that the first and second dirty photons are provided to a quantum emitter coupled to the cavity in a sequential manner, and the first and second dirty photons become entangled with the quantum emitter coupled to the cavity one by one. Additionally, the optical switch that selectively entangles the optical delay line may be provided with at least one processor or circuitry that may be configured to control the optical switch to lengthen the travel path of at least one of the first and second dirty photons. In another example, when one or more photons are generated, the photons 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 create a time delay in one or both pulses carried by the optical delay line. The time delay may alter the temporal coherence of the photons, resulting in pulses with different temporal profiles and therefore outputting one or more dirty photons.

[0242] In some embodiments, the first dirty photon and the second dirty photon are portions of a graph, the graph including optical qubits lacking a quantum emitter qubit. A graph refers to a graph state that represents entanglement relationships between groups of qubits, where a qubit is, as previously described, the basic unit of quantum information. This may mean that the graph is a photon graph, and the first dirty photon and the second dirty photon originate not from a quantum emitter but from another source that does not involve a quantum emitter. In some embodiments, the first dirty photon and the second dirty photon are portions of a graph, the graph including an optical qubit and a quantum emitter qubit. 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 generates photons using a quantum emitter.

[0243] As a non-limiting example, Figure 14A illustrates a preferred system 1400 or device according to some embodiments relating to generating photonic graph states for quantum computing. The system 1400 in Figure 14A includes a cavity 1404, a quantum emitter 1402 coupleable to the cavity 1404, photon generators 1416a, 1416b configured to generate dirty photons, and a circuit 1418 configured to perform a quantum computing method according to embodiments relating to generating photonic graph states for quantum computing described herein.

[0244] 14A shows two separate photon generators 1416a, 1416b, it is understood that a single photon generator may generate the first dirty photon 1406a and the second dirty photon 1406b. In some examples according to some embodiments relating to generating photon graph states for quantum computing, the photon generators 1416a, 1416b may include a quantum emitter coupled to a cavity (e.g., quantum emitter 1432 coupled to cavity 1434 in FIGS. 15A-15C), and the photon generators 1416a, 1416b may be configured to generate the first dirty photon 1406a and / or the second dirty photon 1406b by extracting them from an interfering laser pulse using the quantum emitter coupled to the cavity (e.g., quantum emitter 1432 coupled to cavity 1434 in FIGS. 15A-15C), as described above. In some examples, as previously described, the quantum emitters in photon generators 1416a, 1416b may be atomic or fluctuation quantum emitters.

[0245] In an example, circuit 1418 may be configured to control photon generators 1416a, 1416b to generate first dirty photons 1406a having a first temporal profile and second dirty photons 1406b having a second temporal profile, and circuit 1418 may be configured to use first dirty photons 1406a to form a first optical quantum bit and second dirty photons 1406b to form a second optical quantum bit.

[0246] System 1400 in FIG. 14A includes waveguides 1412a, 1412b configured to carry one or more photons or lasers. Waveguides 1412a, 1412b in FIG. 14A may serve the same purposes as waveguides 816, 910, 930 in FIGS. 8-9C, for example. Circuit 1418 may include one or more linear optical elements configured to perform various functions related to directing or transporting one or more photons, controlling the flow of one or more photons, manipulating the state of one or more photons, and / or performing quantum computation. For example, circuit 1418 may be configured to use one or more linear optical elements to couple quantum emitter 1402 to cavity 1404, use quantum emitter 1402 coupled to cavity 1404 to entangle a first optical qubit with a second optical qubit to form entangled optical qubit pair 1408, and use entangled optical qubit pair 1408 for quantum computation. In some embodiments of the present disclosure related to generating photon graph states for quantum computation, a controller 1414 may be provided to control (e.g., direct or switch between different waveguides) the flow of input and output photons between the photon generator and the entanglement gate. For example, the controller 1414 may include one or more processors. Memory, circuit components, or circuits may also be provided for controlling.

[0247] The circuit 1418 may, for example, receive the first dirty photon 1406 a and the second dirty photon 1406 b from the photon generators 1416 a, 1416 b and output the first dirty photon 1406 a and the second dirty photon 1406 b so that they may be transported in the waveguides 1412 a, 1412 b as consecutive photons. In an example, the circuit 1418 may also include an optical delay line configured to transport at least one of the first dirty photon 1406 a and the second dirty photon 1406 b, as described above for some embodiments related to generating photon graph states for quantum computation. The first dirty photon 1406a and the second dirty photon 1406b may then interact with the quantum emitter 1402 through the cavity 1404 due to 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 described above with reference to Figures 15A-15C. Such interaction between the quantum emitter 1402 and the first dirty photon 1406a and the second dirty photon 1406b may then result in entanglement of the first optical qubit with the second optical qubit, as described above with respect to some embodiments relating to generating photon graph states for quantum computation.

[0248] As a non-limiting example, FIG. 14B illustrates an exemplary process 1450 according to some embodiments related to generating photon graph states for quantum computation. Because example process steps are described throughout this disclosure, such examples will not be repeated or will be briefly summarized in connection with FIG. 14B . In some embodiments of the present disclosure, the exemplary process 1450 is performed by at least one processor or circuitry, e.g., in the control system 1031 and / or optical chip 1015 of FIG. 10 , or the circuitry 1418 and / or 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 in a non-transitory computer-readable medium or computer-readable medium. In some embodiments, some aspects of the process 1450 may be implemented as hardware (e.g., dedicated circuitry). In some embodiments, the process 1450 may be implemented as hardware or a combination of software and hardware.

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

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

[0251] In step 1454, the process involves generating first dirty photons having a first temporal profile and using the first dirty photons to form a first optical quantum bit in step 1456. In step 1458, the process involves generating second dirty photons having a second temporal profile and using the second dirty photons to form a second optical quantum bit in step 1460. As mentioned above, Figure 14A shows an example of first dirty photons 1406a and second dirty photons 1406b used to form the first and second optical quantum bits.

[0252] At 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 an entangled optical qubit pair. At step 1464, the process involves using the entangled optical qubit pair for quantum computation. Figure 14A shows an exemplary pair 1408 of entangled optical qubits, as described above.

[0253] As mentioned above, conventional quantum computing relies on linear optics to generate graphs, requiring the photons used therein to be nearly indistinguishable (“clean”) so that destructive interference can be achieved. In such conventional quantum computing, any distinguishability between photons results in reduced graph fidelity or errors. Quantum computing with distinguishable (“dirty”) photons is possible using nonlinear elements, for example, using interactions between photons and quantum emitters coupled to a cavity. The embodiments described herein relating to generating photonic graph states for quantum computing provide examples of such optical quantum computing that can use “dirty” (distinguishable) photons.

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

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

[0256] According to other embodiments relating to generating photonic graph states for quantum computing, there is provided 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 1450 shown in Figure 14B. The same examples provided above for each process or system feature of the embodiments relating to generating photonic graph states for quantum computing are also applicable to the corresponding features of these embodiments.

[0257] According to yet another embodiment relating to generating photonic graph states for quantum computing, an integrated circuit device or circuit layout is provided that includes layout portions, each layout portion defined to pattern a feature from a combination of features of the system 1400 in FIG. 14A or the photon generator 1416a in FIGS. 15A-15C. By way of example, the modified circuit device or circuit layout includes a cavity layout portion defined to pattern a cavity, a coupling location layout portion defined to pattern a coupling location that couples a quantum emitter to the cavity, a photon generator layout portion defined to pattern a photon generator or a channel that carries photons provided by the photon generator to the cavity, 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 location that couples another quantum emitter to the another cavity. In some embodiments of the present disclosure, the circuit layout portion may be defined to pattern one or more of: a waveguide that carries one or more photons or lasers; and one or more linear optical elements that perform various functions related to directing or transporting one or more photons, controlling the flow of one or more photons, manipulating the state of one or more photons, and / or performing quantum computations.

[0258] In some embodiments of the present disclosure, the layout of the integrated circuit device or circuit further comprises a controller layout portion defined to pattern a controller that controls (e.g., directs or switches between different waveguides) the flow of input and output photons between the photon generator and the entanglement gate, and the controller may comprise one or more processors to perform the control, and memory, circuit components, or circuitry.

[0259] It will be appreciated that if lithographically deposited quantum emitters (e.g., quantum dots) are used, the binding location layout portion can be defined to also pattern the quantum emitters. The same examples described above for each process or system feature of the embodiments relating to generating photonic graph states for quantum computing are also applicable to the corresponding features of the present embodiment.

[0260] Some embodiments of the present disclosure involve initializing the state of a resonator-coupled quantum emitter. A quantum emitter may include any component configured to couple to an electromagnetic mode, a resonator may include any component that establishes an electromagnetic mode, and a resonator-coupled quantum emitter may include a quantum emitter capable of interacting with a 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 particular 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 a starting tuning state system for the resonator-coupled quantum emitter. The initialized resonator-coupled quantum emitter may be one of multiple initialized resonator-coupled quantum emitters. Initialization of multiple resonator-coupled quantum emitters may occur simultaneously or sequentially.

[0261] 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 the present disclosure, initialization may cause the state of the resonator-coupled quantum emitter to be an equal superposition of two basis states. The basis state may be the lowest energy rest state, and the energy of the basis state may be referred to as zero-point energy. Superposition may refer to being in multiple states simultaneously, for example, until a measurement is made. Superposition may refer to, for example, a sum (or superposition) of two or more quantum states, and equal superposition may refer to having the two or more quantum states with equal probability.

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

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

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

[0266] As a non-limiting example, a quantum emitter can 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 can be a stationary quantum bit capable of interacting with photons. For example, a quantum emitter can include a quantum system having one or more of the following configurations: 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 configuration of a superconducting circuit including one or more Josephson junctions. For example, a quantum emitter can be any one or more of a superconducting quantum bit, a quantum dot, an atom, a neutral atom, an ion, a rubidium atom, a cesium atom, a strontium, erbium, ytterbium, calcium, barium, beryllium, or magnesium atom (in either neutral or ionic form). For example, a quantum emitter can include a superconducting quantum bit. For example, a quantum emitter can include a quantum dot. For example, a quantum emitter can include an atom. The atom (e.g., a rubidium atom or a cesium atom) can be neutral. Alternatively, the atoms may be ions. Similarly, when strontium, erbium, ytterbium, calcium, barium, beryllium, or magnesium atoms are employed, the atoms may be in neutral or ionic form.

[0267] Some embodiments of the present disclosure involve receiving at least two photon graph states, each of which includes at least two photons, and selecting at least one photon from each graph state. A graph state represents a relationship between a group of qubits, where a qubit is a basic unit of quantum information, and a photon graph state refers to a graph state applied to photons, 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 a photon graph state described above, which is a quantum state representing a composite quantum system (e.g., a quantum state associated with one or more photon degrees of freedom). A composite quantum system may include multiple quantum subsystems, each subsystem may be represented by a node or vertex of the graph. For example, each photon graph state may have vertices representing photon states, where each vertex corresponds to a single-photon qubit. For example, a single-photon qubit may describe the path of a single photon, the polarization of a single photon, the time bin 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 superpositions of photon number states.

[0268] The 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 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 in 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, a switch such as switches 1735, 1737 shown in Figure 11D may be used to direct at least two photons in a channel (or waveguide) and / or separate at least two photons into individual single photons. Additionally or alternatively, a single photon generator (e.g., a photon source unit described herein), a resonator-coupled quantum emitter configured to generate photons as described herein, and / or an optical cavity-coupled atom configured for use as a photon generator as shown in Figures 8-9B may be used to provide at least one photon or make at least one photon available for selection.

[0270] At least one photon from each photon graph state is then selected for feeding through an entanglement gate, as described below, so that selected photons from at least two photon graph states may become entangled with one another, ultimately entangling the at least two graph states. For example, the entangled photon states may form or generate a larger cluster of entangled photons. The feeding through the entanglement gate may be, for example, sequential.

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

[0272] As a non-limiting example, an embodiment relating to entangling a photon graph or those shown in Figures 11A through 11D involves receiving at least two photon graph states, each of the at least two photon graph states including at least two photons, and selecting at least one photon from each graph state.

[0273] Some embodiments of the present disclosure involve feeding selected photons through an entanglement gate via a resonator-coupled quantum emitter. For example, feeding through an entanglement gate via a resonator-coupled quantum emitter may involve feeding selected photons sequentially, i.e., one at a time, through a waveguide, where each selected photon interacts with the resonator-coupled quantum emitter via the resonator, causing the photon states of the selected photons to become entangled with the state of the resonator-coupled quantum emitter and, therefore, with each other.

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

[0275] As non-limiting examples, Figures 11C or 11D show 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 (87 Rb) atom 820 is shown.

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

[0277] 11D illustrates the sequential feeding of photons through an entanglement gate. In this example, photons 1743, 1745 from two graph states 1742, 1744 are sequentially fed into channel 1736 (e.g., a waveguide) to form or generate cluster 1748 of entangled photons. Photon 1743 is selected from photon graph state 1742, and photon 1745 is selected from photon graph state 1744. These selected photons 1743, 1745 are sequentially fed 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., cluster 1748 of entangled photons). The formed or generated cluster of entangled photon states can then be used in performing quantum computing operations.

[0278] 5B and 6 also show an exemplary cluster in the form of a time-sequential cluster state of n entangled photon states, where the time-sequential series of single photons 412 generated by the single photon source unit 401 in FIG. 4B are fed one by one through the entanglement unit 501 (e.g., steps 602 to 606 are repeated n times in step 608) to generate a time-sequential series of entangled photons 512.

[0279] As a non-limiting example, an embodiment relating to entangling a photon graph or those shown in Figures 11A through 11D involves continuously feeding selected photons through an entanglement gate via a resonator-coupled quantum emitter (e.g., via the exemplary quantum emitter 1731 coupled to the exemplary resonator 1733 shown in Figure 11C or 11D).

[0280] Some embodiments of the present disclosure involve disentangling a resonator-coupled quantum emitter from one or more selected photons. Disentangling refers to releasing something from entanglement (e.g., removing an entangled state). Disentangling a resonator-coupled quantum emitter from one or more selected photons refers to releasing the resonator-coupled quantum emitter from such photon-quantum emitter entanglement, where the state of the quantum emitter is entangled with the state of one or more selected photons (photon states). For example, disentangling 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, and the resonator-coupled quantum emitter is disentangled from the last photon with which it interacted, and the resonator-coupled quantum emitter is disentangled from that photon and any other photons with which it previously interacted.

[0282] As previously mentioned, mapping the state of the resonator-coupled quantum emitter to the state of the additional photon refers to transferring the state of the resonator-coupled quantum emitter qubit to the additional optical qubit. For example, mapping the state of the resonator-coupled quantum emitter to the state of the additional photon may be the result of performing a SWAP gate operation on the quantum emitter qubit and the additional optical qubit, where the SWAP gate operation results in transferring the state of the resonator-coupled quantum emitter to the additional photon and transferring the state of the additional photon to the resonator-coupled quantum emitter. In other words, the mapping may be achieved by applying a SWAP gate to the quantum emitter and the additional photon. As previously mentioned, providing an additional photon at a frequency corresponding to the frequency of a particular transition of the resonator-coupled quantum emitter may map the state of the resonator-coupled quantum emitter to the additional photon while leaving the resonator-coupled quantum emitter disentangled from the selected photon. This is because the state of the resonator-coupled quantum emitter has been swapped with the state of the additional photon.

[0283] Step 610 of Figure 6 illustrates an example of entanglement that involves performing a measurement on an entangled unit atom, in other words, detecting the state of the entangled unit atom (which is an example of a resonator-coupled quantum emitter, such as atom 502). For example, the measurement may be measurement 200, shown schematically in Figure 2E. Measurement 200 is performed to quantum disentangle the entangled unit atom from its photon-entangled state, leaving a time-contiguous cluster state of n photon states in the entangled state, which is output for use by a qubit in a quantum computation.

[0284] 2E shows an example of disentanglement involving atom-to-photon mapping 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 an incoming photon is swapped with the state of an atom (which is an example of a resonator-coupled quantum emitter, such as atom 502).

[0285] 11A-11D involve so disentangling a resonator-coupled quantum emitter (e.g., exemplary quantum emitter 1731 coupled to exemplary resonator 1733) from a selected photon. For example, disentangling 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 the additional photon, as described above.

[0286] 11A illustrates a quantum computing method 1710 according to an embodiment relating to entangling a photon graph to form or generate a cluster of entangled photons. The quantum computing method 1710 illustrated in FIG. 11A includes steps of initializing a 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, feeding the selected photons through an entanglement gate via the resonator-coupled quantum emitter 1717, and disentangling the resonator-coupled quantum emitter from the selected photons 1719. The feeding of the selected photons through the entanglement gate may be sequential. For example, disentanglement may include at least one of detecting the state of the resonator-coupled quantum emitter in step 1721 and / or mapping the state of the resonator-coupled quantum emitter to the state of the additional photon in step 1722, as shown in FIG. 11B.

[0287] The same examples given above for each step of the embodiment relating to entangling photon graphs are also applicable to the embodiment 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, the 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 a resonator of a different shape and / or configuration 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 interaction between the quantum emitter and photons transported in the waveguide. For example, the resonator may have an electromagnetic mode that overlaps with the dipole field of the quantum emitter and / or has an internal cavity field in which the quantum emitter may be placed or positioned.

[0290] A switch refers to a component or group of components configured to make or break a connection in a circuit. Switches can be, for example, a component or group of components that can make or break a connection with a channel (waveguide) through which a photon, one or more pulses of photons, a laser, or any electromagnetic beam can be carried.

[0291] The at least one processor may include any physical device or group of devices having electrical circuitry that performs logical operations on an input or multiple inputs. The quantum computing system may also include a memory that stores instructions executed by the at least one processor.

[0292] A circuit may include one or more functional units (or one or more layout portions), each configured to perform one or more process steps. The one or more functional units (or one or more layout portions) may be arranged (e.g., positioned and connected to each other or to other functional units or other layout portions) such that the circuit can perform some or all of the steps of a method or process. For example, a circuit may perform some or all of the steps of a method or process according to some embodiments of the present 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 methods described herein.

[0294] 11C illustrates an example quantum computing system 1730 according to an embodiment relating to entangling a photon graph to form or generate clusters of entangled photons. The quantum computing system 1730 may relate to the quantum computing method 1710 shown in FIGS. 11A and 11B. For example, the quantum computing system 1730 may be configured to perform the quantum computing method 1710. 11C includes a resonator-coupled quantum emitter (e.g., exemplary quantum emitter 1731 coupled to exemplary resonator 1733 shown in FIG. 11C), a plurality of switches 1735, 1737, and at least one processor (or controller 1739 shown in FIG. 11C) configured to control the plurality of switches 1735, 1737 to initialize a state of resonator-coupled quantum emitter 1731, receive at least two photon graph states, each of the at least two photon graph states including at least two photons, select at least one photon from each graph state, feed the selected photons through an entanglement gate via resonator-coupled quantum emitter 1731, and unentangle the resonator-coupled quantum emitter 1731 from the selected photons. The feeding of the selected photons through the entanglement gate may be continuous. Disentangling may involve at least one of detecting the state of the cavity coupled quantum emitter 1731 or mapping the state of the cavity coupled quantum emitter 1731 to the state of the additional photon.

[0295] The quantum computing system 1730 in FIG. 11C may also include a plurality of channels 1736 (e.g., waveguides) for carrying lasers (or pulses), or resonator-coupled quantum emitters 1731, at least two photons, and / or a magnetic field applicator (e.g., a magnetic field generator or solenoid) for initializing the states of additional photons. The quantum emitter 1731 can be coupled to a resonator, which can be a ring-shaped whispering gallery mode cavity 1733 as shown in FIG. 11C. It is understood that another resonator of a different shape and / or configuration can be coupled to the quantum emitter 1731 to achieve the same effect as long as the other resonator can be coupled to the quantum emitter as described above.

[0296] The plurality of switches includes switches such as switches 1735, 1737 shown in FIG. 11D, and the switches can be used to direct at least two photons into a channel (or waveguide) and / or direct at least two photons when separating at least two photons into individual single photons.

[0297] FIG. 11D shows an example of an embodiment related to entangling a photon graph, and the quantum computing system 1730 shown in FIG. 11C is used to entangle photon graphs 1742, 1744 to form or generate a cluster 1748 of entangled photons. 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) through an entangling gate (e.g., a resonator-coupled quantum emitter such as the exemplary resonator 1733 and exemplary quantum emitter 1731 shown in FIG. 11C or FIG. 11D), whereby the selected photons 1743, 1745 interact with the resonator-coupled quantum emitters 1733, 1731 to become entangled, and finally, when all the photons from photon graph states 1742, 1744 pass through the entangling gate, a cluster 1748 of entangled photons is formed or generated. And the cluster 1748 of entangled photons can be used when performing operations of quantum computing.

[0298] The same examples given above for each step of the embodiment relating to entangling photon graphs 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-transitory computer-readable medium (or computer-readable medium or computer program) containing instructions that, when executed by at least one processor (or device), cause the at least one processor (or device) to perform a method or process in accordance with some embodiments of the present disclosure.

[0300] For example, a non-transitory computer-readable medium (or computer-readable medium or computer program) may include instructions that, when executed by at least one processor (or device), cause the at least one processor (or device) to perform a 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 the at least one processor (or device) to perform a quantum computing method 1710 shown in FIG. 11A or 11B.

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

[0302] According to other embodiments relating to entangling photon graphs to form or generate clusters of entangled photons, there is 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 11B. The same examples given above for each step of the embodiments relating to entanglement of photon graphs 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 is an integrated circuit device or circuit layout comprising layout portions, each layout portion defined to pattern a respective feature from a combination of features of quantum computing system 1730 shown in Figure 11C or 11D. For example, there is a resonator-coupled quantum emitter layout portion defined to pattern at least one coupling location for positioning one or more resonators and resonator-coupled quantum emitters (e.g., exemplary resonator 1733 and exemplary quantum emitter 1731 in Figure 11C or 11D), a switch layout portion defined to pattern a plurality of switches 1735, 1737, and a number of steps including: initializing a state of resonator-coupled quantum emitter 1731; receiving at least two photon graph states, each of the at least two photon graph states being a combination of at least two resonator-coupled quantum emitters; and a controller layout portion defined to pattern at least one processor (or controller 1739 in FIG. 11C or FIG. 11D ) configured to control a plurality of switches 1735, 1737 to include photons from each graph state, select at least one photon from each graph state, feed the selected photon through an entanglement gate via a resonator coupled quantum emitter 1731, and disentangle the resonator coupled quantum emitter 1731 from the selected photon. The feeding of the selected photons through the entanglement gate may be continuous. Disentangling 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 a channel layout portion defined to pattern multiple channels 1736 (e.g., waveguides) that carry the laser (or pulses), or a magnetic field applicator (e.g., a magnetic field generator or solenoid) that initializes the state of the resonator-coupled quantum emitter 1731, at least two photons, and / or additional photons.

[0304] It will be appreciated that if lithographically placed quantum emitters (e.g., quantum dots) are used, the resonator-coupled quantum emitter layout portion can be defined to pattern one or more resonators and resonator-coupled quantum emitters (e.g., quantum dots). The same examples provided above for each step of the embodiment relating to entangling photon graphs are also applicable to the corresponding features of this embodiment.

[0305] According to yet another embodiment relating to entanglement of photon graphs to form or generate clusters of entangled photons, there is a method of controlling or initializing a quantum computing system 1730 shown in Figure 11C, which method includes corresponding method steps of the quantum computing method 1710 shown in Figure 11A or Figure 11B. According to yet another embodiment relating to entanglement of photon graphs to form or generate clusters of entangled photons, there is a signal or data carrier signal carrying 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 given above for each step of the embodiments relating to entanglement of photon graphs are also applicable to corresponding features of these embodiments.

[0306] The embodiments described herein relating to entangling photon graphs can use quantum emitter-photon entanglement gates to entangle photon graphs. For example, the quantum computing system 1730 shown in FIG. 11C or FIG. 11D or the quantum computing method 1710 shown in FIG. 11A or FIG. 11B can be used to form or generate clusters of photon states (e.g., the cluster 1748 of entangled photons shown in FIG. 11D). Such quantum emitter-photon entanglement gates, such as atom-photon controlled Z (CZ) gates, can be used to entangle photon graphs to form larger clusters of entangled photon states. Such methods of entangling photon graphs can result in clusters of dirty (distinguishable) photons, where dirty photons are distinguishable from other photons. For example, as described above, dirty photons can include propagating photons of mixed states, e.g., with respect to multiple space-time modes, e.g., multiple temporal profiles. However, it will be appreciated that the use of such quantum emitter-photon entanglement gates (e.g., resonator-coupled quantum emitters) in performing quantum logic gate operations means that quantum computing operations can be performed using such clusters of dirty (distinguishable) photons even if the photons exhibit irregularities that make them distinguishable.

[0307] Some embodiments of the present disclosure involve a cavity-coupled quantum emitter having at least four levels arranged in an N configuration, with the N configuration including a first ground state, a second ground state, a first excited state, and a second excited state. Excited state and ground state are relative terms in that an excited state is one having a higher energy level than the ground state. For example, the ground state may refer to the lowest energy rest state, and the energy of the ground state may be referred to as zero-point energy. An excited state refers to any quantum state having a higher energy than the ground state. Excitation refers to an increase in energy levels above a chosen starting point, which is usually the ground state but can sometimes be an already excited state. Spontaneous or stimulated emission of a quantum of energy (such as a photon or phonon) can occur shortly after a system (e.g., a quantum emitter or atom) is driven to an excited state and returns the system to a state with lower energy, e.g., a lower excited state or ground state. The N configuration refers to an arrangement that can be represented by the shape of the letter "N." The at least four levels arranged in an N configuration refer to each of the at least four levels represented by endpoints or vertices of the "N" shape and transitions connecting lower levels to higher levels represented by edges of the "N" shape. For example, the at least four levels may refer to at least four energy levels of a resonator-coupled quantum emitter, where each energy level corresponds 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 may 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 FIGS. 16A through 16D (e.g., exemplary resonators 1833, 1863 and exemplary quantum emitter 1831 shown in FIGS. 16B through 16D), by controlling or setting the frequencies associated with the first ground state, second ground state, first excited state, second excited state, and transitions between two of those states of the resonator-coupled quantum emitter, the resonator-coupled quantum emitter can be configured to perform various types of operations. 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 to perform a SWAP gate operation or a controlled-Z (CZ) gate operation. A controlled magnetic field having a specific frequency and amplitude can, for example, enable control or manipulation of the energy levels associated with those states, such that specific types of photons can be generated, released, or emitted from the resonator-coupled quantum emitter.

[0309] As mentioned above, a quantum emitter may include any component configured to couple to an electromagnetic mode, a resonator may include any component that establishes an electromagnetic mode, and a resonator-coupled quantum emitter may include a quantum emitter capable of interacting with a 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. A resonator may include, for example, a cavity, a photonic cavity, an optical cavity, a whispering gallery mode cavity, a Fabry-Perot cavity, or a ring (shaped) cavity. As mentioned above, a resonator-coupled quantum emitter may include a quantum emitter whose dipole field overlaps with the electromagnetic mode of the resonator, for example, a quantum emitter or atom positioned within the internal cavity field of the resonator. As a non-limiting example, Figures 16B through 16D show an example of an exemplary resonator 1833, 1863 and an exemplary quantum emitter 1831 disposed within the internal cavity field of the resonator.

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

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

[0312] As non-limiting examples, 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 the present disclosure involve initializing the state of a resonator-coupled quantum emitter. The state of a resonator-coupled quantum emitter, as described above, refers to a state or configuration of the quantum emitter. For example, the state of a resonator-coupled quantum emitter can be an electronic state, a nuclear state, or a combination thereof. Initializing the state of a resonator-coupled quantum emitter can refer to setting a baseline state for the resonator-coupled quantum emitter. For example, initialization can include establishing a starting adjustment state system for the resonator-coupled quantum emitter. The starting adjustment state system can refer, for example, to the resonator-coupled quantum emitter being in a particular state or superposition of states from its N configurations of a first ground state, a second ground state, a first excited state, and a second excited state.

[0314] In some embodiments of the present disclosure, initializing the state of the resonator-coupled quantum emitter includes preparing the resonator-coupled quantum emitter in a superposition of a first ground state and a second ground state. Superposition may refer to 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. For example, initializing the state of the resonator-coupled quantum emitter, setting a baseline state, establishing a starting tuning 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 an appropriate superposition of modes such that a desired state associated with the appropriate superposition of modes is mapped onto the resonator-coupled quantum emitter when the resonator-coupled quantum emitter interacts with the pulse.

[0315] In some examples, the superposition state is an equal superposition of a first basis state and a second basis state. An equal superposition may refer to having two or more quantum states that have equal probability.

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

number

[0317] Some embodiments of the present disclosure involve tuning the frequency of a transition between two states. A transition refers to a change in energy levels, e.g., from one state to another. The frequency of a transition refers to the energy difference between the energy levels of the two states. A transition can occur when one or more photons having a frequency corresponding to the transition frequency interact with a resonator-coupled quantum emitter. Tuning the frequency of a transition refers to fine-tuning, adjusting, and / or setting the frequency of the transition. For example, tuning the frequency of a transition between two states can involve one or more of using a magnetic field and / or a laser. For example, tuning the frequency of a transition can occur by light shifting using a laser and / or by Zeeman shifting using a magnetic field.

[0318] Some embodiments of the present disclosure involve one or more of 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 the second ground state and the first excited state. In an example, tuning the frequencies of the first, second, and third transitions begins before initialization. Tuning one or more of the frequencies of the transitions can be caused by optical shifting using a laser. Optical shifting can refer to ac Stark shift, which is a perturbation effect that shifts atomic energy levels in a laser field. Tuning one or more of the frequencies of the transitions can be caused by application of a magnetic field. For example, tuning one or more of the frequencies of the transitions can be caused by application of a Zeeman shift using a magnetic field.

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

[0320] As a non-limiting example, FIG. 16B shows transitions 1841, 1842, 1843, and FIG. 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 tuning of the frequencies of the transitions.

[0321] Some embodiments of the present disclosure involve providing multiple photons at a frequency corresponding to the frequency of the second transition, thereby entangling the multiple photons with the resonator-coupled quantum emitter. For example, providing the multiple photons includes sequentially providing multiple single photons. The sequential providing may involve providing the multiple photons one by one through the waveguide such that each photon interacts with the resonator-coupled quantum emitter through the resonator, thereby entangling the multiple photons one by one with the resonator-coupled quantum emitter. The second transition is between a second ground state and a second excited state. In an example, the resonator-coupled quantum emitter may be primed / initialized in a superposition of the first ground state and the second ground state, and when a photon at a frequency corresponding to the frequency of the second transition is provided to the waveguide, the photon interacts with the resonator-coupled quantum emitter through the resonator (due to the evanescent field surrounding the waveguide). The interaction produces a second transition from the cavity-coupled quantum emitter's second ground state to a second excited state. The cavity-coupled quantum emitter then transitions back to its second ground state, liberating or emitting an output photon. This sequence of events results in a pi phase shift in the emitted photon provided the cavity-coupled quantum emitter is in its second ground state. Thus, the emitted photon may become entangled with the cavity-coupled quantum emitter.

[0322] As a non-limiting 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-limiting example, Figure 3 shows an incident photon 301 in mode 3 (optical mode 3 associated with the transition 123 between the second ground state 133 and the second excited state 114), which gives rise to transition 123A and then transition 123B, thereby emitting an output photon 302 entangled with the atom 102 (an example of a cavity 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, e.g., 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 a controlled Z gate (CZ gate), a controlled NOT gate (CNOT gate), a square root of a SWAP gate, or a virtual SWAP gate (iSWAP gate). A resonator-coupled quantum emitter may be configured to function as any one or more of these gates.

[0324] As non-limiting examples, FIG. 3 shows a controlled Z-gate implementation, FIGS. 5A and 5B show an entanglement unit 501 (including entanglement unit atoms 502) implemented as an entanglement gate, and FIGS. 8 and 9C show rubidium ( 87 Rb) atom 820 is shown.

[0325] Non-limiting examples of waveguides into which photons can be delivered include quantum waveguide 930 in Figures 9A-9C or waveguides 1838, 1868 in Figures 16B-16D. Photons can be delivered continuously.

[0326] Some embodiments of the present disclosure involve providing a photon at a frequency corresponding to the frequency of at least one of the first transition or the third transition, thereby mapping the state of the resonator-coupled quantum emitter to the photon. As previously discussed, mapping the state of the resonator-coupled quantum emitter to the photon refers to transferring the state of the resonator-coupled quantum emitter qubit to the photon qubit. For example, mapping the state of the resonator-coupled quantum emitter to the photon may be the result of performing a SWAP gate operation on the quantum emitter qubit and the photon qubit, where the SWAP gate operation results in the state of the resonator-coupled quantum emitter being transferred to the photon and the state of the photon being transferred to the resonator-coupled quantum emitter. In other words, the mapping may be achieved by applying a SWAP gate to the quantum emitter and the photon.

[0327] As previously mentioned, by supplying a photon at a frequency corresponding to the frequency of a particular transition of the resonator-coupled quantum emitter, one can map the state of the resonator-coupled quantum emitter to the photon, while simultaneously leaving the resonator-coupled quantum emitter disentangled from the previously interacting photons that were entangled with each other, because the state of the resonator-coupled quantum emitter has been swapped with the state of the supplied photon.

[0328] By providing photons at a frequency corresponding to a frequency associated with a particular transition of the resonator-coupled quantum emitter, the state of the provided photons can be transferred to the resonator-coupled quantum emitter, thereby initializing the resonator-coupled quantum emitter to an initial state, such as a first ground state or a second ground state. The first transition is between the first ground state and a first excited state, and the third transition is between the second ground state and the first excited state. Thus, for example, by providing photons at a frequency corresponding to a frequency associated with at least one of the first transition or the third transition, 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. In an example, a resonator-coupled quantum emitter may be prepared / initialized in a superposition of a first ground state and a second ground state, and when a photon at a frequency corresponding to the superposition of the frequency for the first transition and the frequency for the third transition is provided to the waveguide, the photon interacts with the resonator-coupled quantum emitter through the resonator (due to the evanescent field around the waveguide), causing the photon's superposition state to be swapped with the superposition state of the resonator-coupled quantum emitter.

[0329] 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-limiting example, FIG. 2E shows a SWAP gate 201 in which an incident photon 202 in a superposition of optical modes 1 and 2 (optical modes 1 and 2 associated with transitions 121 and 122, respectively) produces transition 121A, then transition 122A in FIG. 2A, and transition 122B, then transition 121B in FIG. 2B. An exiting photon 204 is then left in the state of atom 102, and atom 102 is left in the state of the incident photon 202.

[0330] 16A illustrates a quantum computing method 1810 according to an embodiment for an N-configuration resonator-coupled quantum emitter. The quantum computing method 1810 illustrated in FIG. 16A includes a step 1811 of initializing a state of 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; a step 1813 of adjusting a frequency for a first transition between the first ground state and the first excited state; and a step 1814 of adjusting a frequency for a second transition between the second ground state and the second excited state. 15, step 1817 of tuning a frequency for a third transition between the second ground state and the first excited state, step 1818 of providing a plurality of photons at a frequency corresponding to the frequency for the second transition, thereby entanglement of the plurality of photons in the resonator coupled quantum emitter, and step 1819 of providing photons at a frequency corresponding to the frequency for at least one of the first transition or the third transition, thereby mapping states of the resonator coupled quantum emitter to the photons. In an example, in step 1818, the plurality of photons may be provided continuously.

[0331] The same examples described above for each step of the embodiment relating to the N-configuration resonator-coupled quantum emitter are also applicable to the embodiment shown in FIG. 16A . For example, initializing the state of the resonator-coupled quantum emitter may include preparing the resonator-coupled quantum emitter in a superposition of a first ground state and a second ground state. In an example, tuning the frequencies of the first transition, the second transition, and the third transition may occur before initialization. In an example, tuning one or more of the frequencies of the transitions occurs by light shifting using a laser or by applying a magnetic field. In an example, providing a plurality of photons may include sequentially providing a plurality of single photons. Providing photons at a frequency corresponding to the frequency of at least one of the first transition or the third transition may further initialize the resonator-coupled quantum emitter to correspond to at least one of the first ground state or the second ground state.

[0332] Some embodiments of the present disclosure involve a quantum computing system including 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 may be configured as described above. The resonator may be a ring-shaped whispering gallery mode cavity. Alternatively or additionally, the resonator may include a resonator of a different shape and / or configuration 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 interaction between the quantum emitter and photons transported in the waveguide. For example, the resonator may have an electromagnetic mode that overlaps with the dipole field of the quantum emitter and / or has an internal cavity field in which the quantum emitter may be placed or positioned.

[0333] The at least one processor may include any physical device or group of devices having electrical circuitry that performs logical operations on an input or multiple inputs. The quantum computing system may also include a memory that stores instructions executed by the at least one processor.

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

[0335] 16B illustrates a quantum computing system 1830 according to some embodiments relating to a resonator-coupled quantum emitter in an N-configuration. The quantum computing system 1830 may relate to the quantum computing method 1810 shown in FIG. 16A. For example, the quantum computing system 1830 may be configured to perform the quantum computing method 1810. The quantum computing system illustrated in FIG. 16B includes a resonator-coupled quantum emitter having at least four levels arranged in an N-configuration 1801 (e.g., the exemplary quantum emitter 1831 coupled to the exemplary resonator 1833 shown in FIGS. 16B-16D ), the N-configuration 1801 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, e.g., the quantum computing method 1810.

[0336] The quantum computing system 1830 in FIG. 16B may also include multiple channels (e.g., waveguides 1836, 1838) that carry lasers (or pulses) or a magnetic field applicator (e.g., a magnetic field generator or solenoid) that initializes the state of the resonator-coupled quantum emitter 1831. The waveguide 1836 may perform the same function as the utility waveguide 910 in FIGS. 9A through 9C, and the waveguide 1838 may perform the same function as the quantum waveguide 930 in FIGS. 9A through 9C. The quantum emitter 1831 may be coupled to a resonator, which may be a ring-shaped whispering gallery mode cavity 1833, as shown in FIGS. 16B through 16D. The quantum emitter 1831 may be coupled to two resonators 1833, 1863, as shown in FIG. 16D. It will be appreciated that another resonator of a different shape and / or configuration can be coupled to quantum emitter 1831 to achieve the same effect, provided that the other resonator is capable of coupling to the quantum emitter as described above.

[0337] 16C illustrates a quantum computing system 1850 according to some embodiments for an N-configuration of resonator-coupled quantum emitters. 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 initialize the resonator-coupled quantum emitters and / or tune the frequencies of the transitions. Laser source 1851 may provide a laser that shifts light (e.g., ac Stark shifts) and thereby tunes at least one of the frequencies of the transitions. Magnetic field generator 1853 may provide a magnetic field and provide application of a magnetic field that tunes at least one of the frequencies of the transitions.

[0338] 16D illustrates a quantum computing system 1860 according to some embodiments with an N-configuration of resonator-coupled quantum emitters. Compared to quantum computing system 1830 or quantum computing system 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 waveguide 1838, 1868 that couples photons carried therein to the associated resonator 1833, 1863 via an evanescent field established around the waveguide 1838, 1868. It will also be understood that multiple upper waveguides 1836 may be provided, with each resonator having its own utility waveguide.

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

[0340] Some embodiments of the present disclosure involve a non-transitory computer-readable medium (or computer-readable medium or computer program) containing instructions that, when executed by at least one processor (or device), cause the at least one processor (or device) to perform a method or process in accordance with some embodiments of the present disclosure.

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

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

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

[0344] Further embodiments relating to N-configuration resonator-coupled quantum emitters include integrated circuit device or circuit layouts having layout portions, each layout portion defined to pattern a respective feature from a combination of features of the quantum computing systems 1830, 1850, 1860 shown in Figures 16B through 16D. For example, some embodiments may include an integrated circuit device or circuit layout having a resonator-coupled quantum emitter layout portion defined to pattern at least one coupling location for positioning one or more resonators and 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 defined to pattern a circuit (e.g., at least one processor or circuit 1839 in Figures 16B through 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 associated with one coupling location that positions one resonator-coupled quantum emitter (e.g., exemplary resonators 1833, 1863 and exemplary quantum emitter 1831 in FIG. 16D ). It will be understood that if lithographically deposited quantum emitters (e.g., quantum dots) are used, 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 the embodiments relating to N-configuration resonator-coupled quantum emitters or those shown in FIGS. 16A through 16D are also applicable to the corresponding features of this embodiment.

[0346] The layout of the integrated circuit device or circuit may also include a channel layout portion defined to pattern multiple channels (e.g., waveguides 1836, 1838) that carry lasers (or pulses) or magnetic field applicators (e.g., magnetic field generators or solenoids) that initialize the state of the resonator-coupled quantum emitter 1831.

[0347] The layout of the integrated circuit device or circuit may also include a laser or magnetic field layout portion defined to pattern 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 initialize and / or tune the frequency of the transition of the resonator-coupled quantum emitter.

[0348] According to yet another embodiment relating to an N-configuration resonator coupled quantum emitter, there is provided a method of controlling a quantum computing system 1830, 1850, 1860 as shown in Figures 16B through 16D, which method includes corresponding method steps of quantum computing method 1810 as shown in Figure 16A. According to yet another embodiment relating to an N-configuration resonator coupled quantum emitter, there may be provided a signal or data carrier signal carrying multiple entangled photons for resonator coupled quantum emitter 1831 as shown in Figures 16B through 16D, or quantum computing method 1810 as shown in Figure 16A. The same examples given above for each step of the embodiments relating to an N-configuration resonator coupled quantum emitter or those shown in Figures 16A through 16D are also applicable to corresponding features of these embodiments.

[0349] Quantum computing may leverage entanglement between entangled states to perform certain quantum computing operations and / or algorithms. In most conventional optical quantum computing systems, output from a source of entangled states, sometimes referred to as a resource state generator (RSG), is obtained via a probabilistic scheme. This means that performing quantum computing using or generating this type of output involves taking into account feedforward measurements (also referred to as messengers) with unpredictable or inconsistent inputs. Some embodiments described herein can output an entangled state (e.g., a photon graph state or multiple entangled photons) in a deterministic manner, i.e., can output a predictable or consistent entangled state via a deterministic scheme. This eliminates the n...

Claims

1. 1. A quantum computing system, comprising: a plurality of photonic cavities; a plurality of binding locations for quantum emitter positioning, each binding location associated with a different one of the plurality of photonic cavities, and a quantum emitter associated with each binding location configured to mediate interactions between successive incoming optical qubits to generate a graph state; a photon generator configured to provide photons to the plurality of photonic cavities, the photonic cavities configured to couple optical quantum bits to the quantum emitters; a plurality of photon output channels downstream of the plurality of cavities for outputting the graph states; A quantum computing system comprising:

2. 10. The system of claim 1 , wherein the quantum emitter comprises a stationary qubit capable of interacting with photons.

3. 10. The system of claim 1 , wherein the quantum emitter comprises a superconducting qubit.

4. The system of claim 1 , wherein the quantum emitter comprises a quantum dot.

5. The system of claim 1 , wherein the quantum emitter comprises an atom.

6. The system of claim 5 , wherein the atoms are neutral.

7. The system of claim 5 , wherein the atoms are ions.

8. The system of claim 5 , wherein the quantum emitter comprises rubidium atoms.

9. The system of claim 5 , wherein the quantum emitter comprises cesium atoms.

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

11. The system of claim 1 , wherein the photon generator comprises at least one additional photon cavity.

12. 12. The system of claim 11 , wherein the photon generator includes at least one additional quantum emitter and at least one additional binding location for quantum emitter positioning, each additional binding location associated with a different one of the at least one additional photon cavity.

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

14. 13. The system of claim 12, wherein the at least one additional quantum emitter comprises a superconducting qubit.

15. The system of claim 12 , wherein the at least one additional quantum emitter comprises a quantum dot.

16. The system of claim 12 , wherein the at least one additional quantum emitter comprises an atom.

17. 17. The system of claim 16, wherein the at least one additional quantum emitter comprises rubidium atoms.

18. 17. The system of 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. 1. A quantum computation method for generating a graph state, the method comprising: coupling a quantum emitter at each of a plurality of binding locations, such that each of the plurality of quantum emitters is associated with a different binding location, each binding location being associated with a different photonic cavity of the plurality of photonic cavities, the quantum emitter associated with each binding location being configured to mediate interactions between successive incoming optical qubits to generate a graph state; providing photons to the plurality of photonic cavities, the photonic cavities configured to couple optical quantum bits to the quantum emitters; outputting the graph state via a plurality of photon output channels downstream of the plurality of cavities; A quantum computing method comprising:

20. 1. A non-transitory computer-readable storage medium comprising instructions that, when executed by at least one processor, cause the at least one processor to perform a quantum computing method, the quantum computing method comprising: coupling a quantum emitter at each of a plurality of binding locations, such that each of the plurality of quantum emitters is associated with a different binding location, each binding location being associated with a different photonic cavity of the plurality of photonic cavities, the quantum emitter associated with each binding location being configured to mediate interactions between successive incoming optical qubits to generate a graph state; providing photons to the plurality of photonic cavities, the photonic cavities configured to couple optical quantum bits to the quantum emitters; outputting the graph state via a plurality of photon output channels downstream of the plurality of cavities; A non-transitory computer readable storage medium comprising:

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