Fusion-based quantum computing

Abstract

A method includes receiving a plurality of quantum systems, wherein each quantum system of the plurality of quantum systems includes a plurality of quantum subsystems in an entangled state, and wherein respective quantum systems of the plurality of quantum systems are independent quantum systems that are not entangled with each other. The method further includes performing a plurality of joint measurements on different quantum subsystems from respective quantum systems of the plurality of quantum systems, wherein the joint measurements generate joint measurement result data; and determining, by a decoder, a plurality of syndrome graph values based on the joint measurement result data.

Description

[0001] Cross-references to related applications

[0002] This patent application claims the benefit of U.S. Provisional Patent Application No. 62 / 967,513, filed January 29, 2020, and also claims the benefit of U.S. Provisional Patent Application No. 63 / 140,210, filed January 21, 2021. The disclosures of these two U.S. Provisional Patent Applications are incorporated herein by reference in their entirety for all purposes. Technical Field

[0003] One or more embodiments of the present invention relate generally to quantum computing devices and methods, and more specifically, to fault-tolerant quantum computing devices and methods. Background Technology

[0004] In fault-tolerant quantum computing, quantum error correction is required to prevent the accumulation of errors in qubits that could lead to erroneous computations. One approach to achieving fault tolerance is to use error-correcting codes (such as topological codes) for quantum error correction. More specifically, a set of physical qubits (also referred to as error-correcting codes in this paper) can be generated in entangled states, encoding individual logical qubits that are protected from errors.

[0005] In some quantum computing systems, cluster states (or more generally graph states) of multiple qubits can be used as error-correcting codes. A graph state is a highly entangled multi-qubit state that can be visually represented as a graph with nodes representing qubits and edges representing entanglement between qubits. However, various problems that suppress the generation of entangled states or destroy entanglement once generated have hindered the progress of quantum technologies that rely on the use of highly entangled quantum states.

[0006] Furthermore, in some qubit architectures (such as photonic architectures), generating entangled states of multiple qubits is an inherently probabilistic process with a low success rate.

[0007] Therefore, there is still a need for improved systems and methods for quantum computing that do not rely on large clusters of qubits. Summary of the Invention

[0008] This paper describes embodiments of fault-tolerant systems and methods for quantum computing that do not rely on large cluster states of qubits.

[0009] According to some embodiments, a method may include: receiving a plurality of quantum systems, wherein each of the plurality of quantum systems comprises a plurality of quantum subsystems in an entangled state, and wherein the corresponding quantum systems in the plurality of quantum systems are independent quantum systems that are not entangled with each other; performing a plurality of destructive joint measurements (e.g., fusion operations) on different quantum subsystems from the corresponding quantum systems in the plurality of quantum systems, wherein the destructive joint measurements disrupt the different quantum subsystems and generate joint measurement result data and transfer quantum state information from the different quantum subsystems to other unmeasured quantum subsystems from the plurality of quantum systems; and determining the logical qubit state based on the joint measurement result data. The logical qubit state may be determined in a fault-tolerant manner.

[0010] According to some embodiments, a method may include: receiving a plurality of quantum systems, wherein each of the plurality of quantum systems comprises a plurality of quantum subsystems in an entangled state, and wherein the corresponding quantum systems in the plurality of quantum systems are independent quantum systems that are not entangled with each other; performing a logical qubit gate by performing a plurality of destructive joint measurements (e.g., fusion operations) on different quantum subsystems from the corresponding quantum systems in the plurality of quantum systems, wherein the destructive joint measurements disrupt the different quantum subsystems and generate joint measurement result data and transfer quantum state information from the different quantum subsystems to other unmeasured quantum subsystems from the plurality of quantum systems; and determining the result of the logical qubit gate based on the joint measurement result data. The result of the logical qubit gate may be determined in a fault-tolerant manner.

[0011] According to some embodiments, a quantum computing device may include: a qubit entanglement system that generates a plurality of quantum systems, wherein each of the plurality of quantum systems comprises a plurality of quantum subsystems in an entangled state, and wherein the corresponding quantum systems in the plurality of quantum systems are independent quantum systems that are not entangled with each other; a qubit fusion system that performs a plurality of destructive joint measurements on different quantum subsystems from the corresponding quantum systems in the plurality of quantum systems, wherein the destructive joint measurements destroy the different quantum subsystems and generate joint measurement result data and transmit quantum state information from the different quantum subsystems to other unmeasured quantum subsystems from the plurality of quantum systems; and a classical computing system that determines the logical qubit state based on the joint measurement result data.

[0012] According to some embodiments, a quantum computing device may include: a qubit entanglement system that generates a plurality of quantum systems, wherein each of the plurality of quantum systems comprises a plurality of quantum subsystems in an entangled state, and wherein the corresponding quantum systems in the plurality of quantum systems are independent quantum systems that are not entangled with each other; a qubit fusion system that performs a logical qubit gate by performing a plurality of destructive joint measurements on different quantum subsystems from the corresponding quantum systems in the plurality of quantum systems, wherein the destructive joint measurements destroy the different quantum subsystems and generate joint measurement result data and transmit quantum state information from the different quantum subsystems to other unmeasured quantum subsystems from the plurality of quantum systems; and a classical computing system that determines the result of the logical qubit gate based on the joint measurement result data.

[0013] According to some embodiments, a method includes: receiving a plurality of quantum systems via a qubit fusion system, wherein each of the plurality of quantum systems comprises a plurality of quantum subsystems in an entangled state. The respective quantum systems within the plurality of quantum systems are independent quantum systems that are not entangled with each other. The method further includes: performing multiple joint measurements on different quantum subsystems from the respective quantum systems within the plurality of quantum systems via the qubit fusion system. The joint measurements generate joint measurement result data. The method further includes: determining multiple correction subgraph values ​​based on the joint measurement result data using a decoder.

[0014] According to some embodiments, performing joint measurements includes performing a fusion operation.

[0015] According to some embodiments, performing joint measurements includes performing destructive joint measurements via a type II fusion operation.

[0016] According to some embodiments, performing multiple joint measurements on different quantum subsystems of corresponding quantum systems from multiple quantum systems includes performing multiple joint measurements only on a subset of the multiple quantum subsystems received by the qubit fusion system, thereby producing a subset of unmeasured quantum subsystems.

[0017] According to some embodiments, the method further includes: receiving a plurality of second quantum systems via a qubit fusion system, wherein each quantum system in the plurality of second quantum systems comprises a plurality of second quantum subsystems in an entangled state, and wherein the corresponding quantum systems in the plurality of second quantum systems are independent quantum systems that are not entangled with each other. The method further includes: receiving a subset of unmeasured quantum subsystems, and performing a plurality of second joint measurements between i) the second quantum subsystems from the corresponding second quantum systems in the plurality of second quantum systems and ii) the corresponding quantum subsystems from the subset of unmeasured quantum subsystems via the qubit fusion system. The plurality of second joint measurements generate second joint measurement result data.

[0018] According to some embodiments, a system includes a qubit fusion system comprising a plurality of fusion gates. The qubit fusion system is configured to receive a plurality of quantum systems, wherein each of the plurality of quantum systems comprises a plurality of quantum subsystems in an entangled state, and wherein the respective quantum systems in the plurality of quantum systems are independent quantum systems that are not entangled with each other.

[0019] According to some embodiments, multiple fusion gates are each configured to perform joint measurements on different quantum subsystems of corresponding quantum systems from multiple quantum systems, wherein the joint measurements generate joint measurement result data.

[0020] The system also includes a decoder, which is communicatively coupled to the qubit fusion system and configured to receive joint measurement result data and determine multiple correction subgraph values ​​based on the joint measurement result data.

[0021] According to some embodiments, the fusion gate includes a photonic circuit, and the multiple quantum systems include photons as quantum subsystems, wherein the photonic circuit includes a type II fusion gate.

[0022] According to some embodiments, the joint measurement includes a two-particle projection measurement onto the Belki.

[0023] According to some embodiments, the system further includes a quantum memory coupled to at least one qubit fusion system and receiving and storing a subset of multiple quantum subsystems.

[0024] In some embodiments, the quantum memory is an optical fiber.

[0025] According to some embodiments, a quantum memory is coupled to a qubit fusion system such that joint measurements are performed between i) a quantum subsystem from a corresponding quantum system of a plurality of quantum systems and ii) a corresponding quantum subsystem from a subset of a plurality of quantum subsystems stored in the quantum memory.

[0026] According to some embodiments, the system also includes a quantum bit entanglement system configured to generate multiple quantum systems.

[0027] According to some embodiments, a qubit entanglement system includes a quantum gate array.

[0028] According to some embodiments, a qubit entanglement system includes a photon source system optically connected to an entanglement state generator.

[0029] According to some embodiments, the entangled state generator is configured to receive output photons from a photon source system and convert the output photons into entangled photon states.

[0030] According to some embodiments, a qubit entanglement system includes: a plurality of output waveguides optically coupled to a qubit fusion system and configured to provide entangled photonic states to the input of a fusion gate.

[0031] The following detailed description, together with the accompanying drawings, will provide a better understanding of the nature and advantages of the claimed invention. Attached Figure Description

[0032] Various aspects of the invention will be described by way of example. Non-limiting and non-exhaustive aspects are described with reference to the following drawings, in which, unless otherwise specified, the same reference numerals refer to the same parts throughout the various drawings.

[0033] Figures 1A to 1C This is a schematic diagram illustrating the cluster state of entangled states of physical qubits and the corresponding correction subgraph according to some embodiments.

[0034] Figure 2 A quantum computing system according to one or more embodiments is shown.

[0035] Figure 3 A quantum computing system according to some embodiments is shown.

[0036] Figure 4 Examples of entangled quantum bit systems according to some embodiments are illustrated.

[0037] Figure 5 An example of a qubit fusion system according to some embodiments is shown.

[0038] Figure 6 A possible example of a fusion site according to some embodiments is shown, which is configured to operate with a fusion controller to provide measurements to a decoder for use in fault-tolerant quantum computing.

[0039] Figures 7A to 7C Fusion-based quantum computing schemes for fault-tolerant quantum computing are illustrated according to one or more embodiments.

[0040] Figures 8A to 8B An example of a lattice preparation protocol for fusion-based quantum computing, according to some embodiments, is shown.

[0041] Figures 9A to 9B An example of a lattice preparation protocol for fusion-based quantum computing, according to some embodiments, is shown.

[0042] Figures 10A to 10E A flowchart and an exemplary lattice preparation protocol are shown to illustrate a method for fusion-based quantum computing according to one or more embodiments.

[0043] Figures 11A to 11E A representation of a dual-track encoded optical quantum bit and a photonic circuit for performing unitary operations on the optical quantum bit is shown according to some embodiments.

[0044] Figures 12A to 12B A representation of a dual-track encoded optical quantum bit and a photonic circuit for performing unitary operations on the optical quantum bit is shown according to some embodiments.

[0045] Figure 13 The diagram illustrates a photonic implementation of a beamsplitter according to some embodiments, which can be used to implement one or more diffusers, such as Hadamard gates.

[0046] Figure 14 The following illustrates a photonic implementation of a beamsplitter according to some embodiments, which can be used to implement one or more diffusers, such as Adama gates.

[0047] Figure 15 An example of a Bell state generator circuit that can be used in some dual-track coded photonic embodiments is shown.

[0048] Figure 16 An example of a type II fusion circuit for polarization coding according to some embodiments is shown.

[0049] Figure 17 An example of a Type II fusion circuit for path coding according to some embodiments is shown.

[0050] Figures 18A to 18D The effects of fusion in generated cluster states according to some embodiments are shown.

[0051] Figure 19 An example of a Type II fusion gate that is boosted once in polarization and path coding, according to some embodiments, is shown.

[0052] Figure 20 A table showing variations of the Type II fusion gate for different measurement bases in polarization coding is presented.

[0053] Figure 21 Examples of photonic circuit variations of type II fusion gates for different selections of the measurement basis in path coding are shown according to some embodiments. Detailed Implementation

[0054] Reference will now be made to the embodiments in detail, with examples of embodiments illustrated in the accompanying drawings. Numerous specific details are set forth in the following detailed description to provide a thorough understanding of the various described embodiments. However, it will be apparent to those skilled in the art that the various described embodiments can be practiced without these specific details. In other instances, well-known methods, processes, components, circuits, and networks have not been described in detail to avoid unnecessarily obscuring aspects of the embodiments.

[0055] 1. Introduction to Quantum Computing

[0056] Quantum computing is typically considered within the framework of "circuit-based quantum computing" (CBQC), which involves performing operations (or gates) on physical qubits. Gates can be single-qubit unitary operations (rotations), two-qubit entanglement operations (e.g., CNOT gates), or other multi-qubit gates (e.g., Toffoli gates).

[0057] Measurement-based quantum computing (MBQC) is another approach to realizing quantum computing. In MBQC, computation is performed by first preparing a specific entangled state (often called a cluster state) containing many qubits, and then performing a series of single-qubit measurements on the cluster state to conduct quantum computation. In this approach, the choice of single-qubit measurements is determined by a quantum algorithm running on a quantum computer. In MBQC, fault tolerance can be achieved by carefully designing the cluster state and using its topologically encoded logical qubits, which are protected against any logical errors that might arise from errors on any of the physical qubits that make up the cluster state. In practice, the value of the logical qubit can be determined (i.e., read out) based on the results of single-particle measurements performed on the physical qubits of the cluster state as computation proceeds (also referred to herein as measurement results).

[0058] However, the generation and maintenance of long-range entanglement across cluster states, as well as the subsequent storage of large cluster states, present challenges. For example, for any physical implementation of the MBQC method, a cluster state containing thousands or more mutually entangled qubits must be prepared and then stored for a period of time before performing single-qubit measurements. For instance, to generate a cluster state representing a single logical error correction qubit, each of the set of fundamental physical qubits can be prepared in the |+> state, and controlled phase gate (CZ) states can be applied between the individual physical qubit pairs to generate the overall cluster state. More specifically, a cluster state of highly entangled qubits can be described by an undirected graph G = (V, E), where V and E represent the set of vertices and edges, respectively, and can be generated as follows: 1) Initialize all physical qubits to the |+> state, where, Furthermore, 2) a controlled phase gate (CZ) is applied to each pair of qubits i and j. Therefore, any cluster state physically corresponding to a highly entangled state of a physical qubit can be described as...

[0059]

[0060] Among them, CZ i,j It is a controlled phase gate operator, and V and E are defined as above. Graphically, the cluster state defined by equation (1) can also be represented graphically by vertices V and edges E, where vertex V represents the physical qubits (initialized in the |+> state) and edge E represents the entanglement between them (i.e., applications of various CZ gates). In some cases, such as those involving fault-tolerant MBQC schemes, |Ψ> graph It can be presented in the form of 3D graphics. (And...) Figure 1A and Figure 7C The example shown is similar; this pattern can have a regular structure formed by repeating unit cells and is therefore often called a "lattice." When represented as a 3D lattice, the 2D boundaries of that lattice can be identified. Quantum bits belonging to these boundaries are called "boundary qubits," while all other qubits are called "body qubits."

[0061] In generating |Ψ> graph Then, this large state of the entangled qubits must be maintained for a long enough time to allow for stabilizer measurements, for example, by performing X measurements on all the physical qubits in the bulk of the lattice and Z measurements on the boundary qubits.

[0062] Figure 1AAn example of a fault-tolerant cluster state that can be used in MBQC is shown. This topological cluster state was introduced by Raussendorf et al. and is commonly referred to as the Raussendorf lattice, as described in further detail in Robert Raussendorf, Jim Harrington, and Kovid Goyal. A., “Fault-Tolerant One-Way Quantum Computer, Annals of Physics” (321(9):2242–2270, 2006). The cluster state is in the form of a repeating unit cell (e.g., unit cell 120), in which physical qubits (e.g., physical qubit 116) are arranged on the faces and edges of the unit cell. Entanglement between physical qubits is represented by the edges connecting the physical qubits (e.g., edge 118), where each edge represents an application of a CZ gate, as described above with reference to equation (1). The cluster state shown here is merely one example of many cluster states, and other topological error-correcting codes can be used without departing from the scope of the invention. For example, volumetric codes, such as those disclosed in International Patent Application Publication No. WO / 2019 / 173651, the contents of which are incorporated herein by reference in their entirety for all purposes, can be used. Without departing from the scope of the invention, non-cubic unit cell-based codes described in International Patent Application Publication No. WO / 2019 / 178009, the contents of which are incorporated herein by reference in their entirety for all purposes, can also be used. Furthermore, although the example shown herein is represented in three spatial dimensions, the same structure can also be obtained from other implementations of the code that are not based on purely spatially entangled cluster states, but can include entanglement in 2D space and temporal entanglement, for example, using 2+1D surface code implementations or any other leaf-shaped code. For such cluster state implementations of the code, all the quantum gates required for fault-tolerant quantum computing can be constructed by a series of single-particle measurements on the physical qubits that make up the lattice.

[0063] Return to Figure 1AThe image shows a block of a Lawsendorf lattice. This entangled state can be used to encode one or more logical qubits (i.e., one or more error-correcting qubits) using many entangled physical qubits. A collection of single-particle measurements of multiple physical qubits (e.g., physical qubit 116) can be used to correct errors and perform fault-tolerant computations on the logical qubits using a decoder. Many decoders are available, one example being the disjoint-lookup decoder described in International Patent Application Publication No. WO2019 / 002934A1, the disclosure of which is incorporated herein by reference in its entirety for all purposes. Those skilled in the art will understand that the number of physical qubits required to encode a single logical qubit can vary depending on the precise nature of the physical errors, noise, etc., experienced by the physical qubits, but all schemes to date have required entangled states of thousands of physical qubits to encode a single logical qubit in order to achieve fault tolerance. Generating and maintaining such a large entangled state is a critical challenge for any practical implementation of the MBQC method.

[0064] Figures 1B to 1C This illustrates how the decoding of logical qubits would be performed for cluster states based on Lawsendorfer lattices. For example... Figure 1A It can be seen from this that the geometry of the cluster state is similar to... Figure 1A The geometry of the cubic lattice (cell 120) superimposed on the cluster state is shown in relation to this. Figure 1B The results of single-particle measurements (also superimposed on a cubic lattice) are shown after the states of the individual physical qubits of the cluster state have been measured, with the measurements placed in the previous positions of the measured physical qubits (for clarity, only measurements obtained from these surface qubits are shown).

[0065] In some embodiments, after all qubits have been measured, for example in the x-basis, the measured qubit state can be represented by a digital bit value of 1 or 0, where a 1 bit value corresponds to a +x measurement result and a 0 bit value corresponds to a -x measurement result (or vice versa). There are two types of qubits: qubits located on the edges of a unit cell (e.g., at edge qubit 122) and qubits located on the faces of a unit cell (e.g., at face qubit 124). In some cases, qubit measurements may not be available, or the results of qubit measurements may be invalid. In these cases, no bit value is assigned to the position of the corresponding measured qubit, and the result is referred to herein as erasure, for example, illustrated herein as thick line 126. These known lost measurements can be reconstructed during the decoding process.

[0066] To identify errors in physical qubits, a syndrome graph can be generated from the set of measurement results produced by measurements of the physical qubits. For example, bit values ​​associated with individual edge qubits can be combined to create vertices generated by the intersections of the corresponding edges (e.g., such as...). Figure 1B The vertex 128 shown is associated with the corrector values. A set of corrector values ​​(also referred to as parity checks in this paper) is associated with each vertex of the corrector subgraph, as follows: Figure 1C As shown. More specifically, in Figure 1C The diagram illustrates the calculated parity values ​​for some vertices of a calibration subgraph. In some embodiments, the parity calculation requires determining whether the sum of the edge values ​​generated at a given vertex is even or odd, where the parity result for that vertex is defined as the remainder (mod 2) of the sum divided by 2. If no error occurs in the quantum state or in the qubit measurement, all calibration values ​​should be even (or 0). Conversely, if an error occurs, it will result in some odd (or 1) calibration values. Only half of the bit values ​​from the qubit measurement are associated with the calibration subgraph shown (bits aligned with the edges of the calibration subgraph). There exists another calibration subgraph containing all the bit values ​​associated with the faces of the lattice shown. This leads to an equivalent decoding problem on these bits.

[0067] As mentioned above, the generation and subsequent storage of large cluster states of qubits presents a challenge. However, some embodiments, methods, and systems described herein provide a way to generate a set of classical measurement data (e.g., a set of classical data corresponding to the values ​​of the correction subgraph) that includes the necessary correlations for performing quantum error correction, without first generating large entangled states of qubits in the error-correcting code. For example, embodiments disclosed herein describe systems and methods whereby two-qubit (i.e., joint) measurements (also referred to herein as “fusion measurements” or “fusion gates”) can be performed on a much smaller set of entangled states to generate a set of classical data that includes the long-range correlations necessary for generating and decoding correction subgraphs for a particular selection of cluster states, without actually generating the cluster states. In other words, in some systems and methods described herein, only a relatively small set of entangled states (referred to herein as resource states) was previously generated, and then joint measurements were performed directly on these resource states to generate correction subgraph data, without first generating (and then measuring) large cluster states that form the quantum error-correcting code (e.g., a topological code, such as a Lawsondorf lattice).

[0068] For example, as will be described in further detail below, in the case of linear optical quantum computing using a Lawsondorf lattice code structure, a fusion gate can be applied to a small set of entangled states (e.g., 4-GHz states) to generate calibration subgraph data. These entangled states are not entangled with each other and are therefore not part of a larger Lawsondorf lattice cluster state. Although the qubits from the individual resource states are not entangled with each other before the fusion measurement, the measurement result produced by the fusion measurement generates a calibration subgraph that includes all the necessary correlations for performing quantum error correction. Such a system and method are referred to herein as fusion-based quantum computing (FBQC). Advantageously, the resource states have a size independent of the computation performed or the code distance used, which contrasts sharply with the cluster states in MBQC. This allows the resource states used for FBQC to be generated by a constant number of sequential operations. Therefore, in FBQC, errors in the resource states are limited, which is important for fault tolerance.

[0069] 2. Systems for FBQC

[0070] Figure 2 A quantum computing system according to one or more embodiments is illustrated. The quantum computing system 201 includes a user interface device 204 communicatively coupled to a quantum computing (QC) subsystem 206, which is described below. Figure 3The following describes the user interface device 204 in more detail. User interface device 204 can be any type of user interface device, such as a terminal including a display, keyboard, mouse, touchscreen, etc. Alternatively, the user interface device itself can be a computer, such as a personal computer (PC), laptop computer, tablet computer, etc. In some embodiments, user interface device 204 provides an interface that a user can use to interact with QC subsystem 206 directly or via a local area network, wide area network, or via the Internet. For example, user interface device 204 can run software, such as a text editor, interactive development environment (IDE), command prompt, graphical user interface, etc., allowing the user to program or otherwise interact with the QC subsystem to run one or more quantum algorithms. In other embodiments, QC subsystem 206 can be pre-programmed, and user interface device 204 can simply be an interface through which the user initiates quantum computation, monitors progress, and receives results from QC subsystem 206. QC subsystem 206 may also include classical computing system 208 coupled to one or more quantum computing chips 210. In some examples, the classical computing system 208 and the quantum computing chip 210 can be coupled to other electronic components 212, such as pulsed pump lasers, microwave oscillators, power supplies, networking hardware, etc. In some embodiments requiring cryogenic operation, the quantum computing system 201 can be housed within a cryostat (e.g., cryostat 214). In some embodiments, the quantum computing chip 210 can include one or more constituent chips, such as an integration (direct or heterogeneous) of an electronic chip 216 and an integrated photonic chip 218. Signals can be routed on and off the chip in any number of ways, for example, via optical interconnects 220 and other electronic interconnects 222. Additionally, the computing system 201 can employ quantum computing processes, such as fusion-based quantum computing processes as described further in detail below.

[0071] Figure 3 A block diagram of a QC system 301 according to some embodiments is shown. Such a system can be used in conjunction with the above references. Figure 2 The computing system 201 described is associated with this. Figure 3In the diagram, solid lines represent quantum information channels, and double solid lines represent classical information channels. The QC system 301 includes a qubit entanglement system 303, a qubit fusion system 305, and a classical computing system 307. In some embodiments, the qubit entanglement system 303 may take a set of N physical qubits (also referred to herein as “quantum subsystems”) (e.g., physical qubits 309 (also schematically represented as inputs 311a, 311b, 311c, ..., 311N)) as input, and may generate quantum entanglement between two or more of them to generate entangled resource states 315 (also referred to herein as “quantum systems,” which themselves consist of entangled states of the quantum subsystems). For example, in the case of optical qubits, the qubit entanglement system 303 may be a linear optical system (e.g., an integrated photonic circuit) including waveguides, beam splitters, photon detectors, delay lines, etc. In some examples, the entangled resource state 315 may be a relatively small entangled state of qubits (e.g., a qubit entangled state with between 3 and 30 qubits). In some embodiments, resource states can be selected such that fusion operations applied to certain qubits in these states produce correction subgraph data that includes the correlations required for quantum error correction. Advantageously, Figure 3 The system shown provides fault-tolerant quantum computing using relatively small resource states, without requiring resource states to become entangled with each other to form the typical lattice cluster states required for MBQC.

[0072] In some embodiments, the input qubit 309 may be a collection of quantum systems (also referred to herein as quantum subsystems) and / or particles, and may be formed using any qubit architecture. For example, a quantum system may be a particle, such as an atom, ion, nucleon, and / or photon. In other examples, the quantum system may be other engineered quantum systems, such as flux qubits, phase qubits, or charge qubits (e.g., formed from superconducting Josephson junctions), topological qubits (e.g., Majorana fermions), spin qubits formed from vacancy centers (e.g., nitrogen vacancies in diamond), or qubits otherwise encoded in multiple quantum systems (e.g., Gottesman-Kitaev-Preskill (GKP) encoded qubits, etc.). Furthermore, for clarity of description, the term "qubit" is used herein, but the system may also employ quantum information carriers that encode information in a manner not necessarily associated with binary bits. For example, according to some embodiments, four qubits (i.e., a quantum system in which information can be encoded in more than two quantum states) can be used.

[0073] According to some embodiments, QC system 301 can be a fused quantum computer capable of running one or more quantum algorithms or software programs. For example, a software program (e.g., a set of machine-readable instructions) can be passed to classical computing system 307 (e.g., corresponding to the above). Figure 2 In system 208, the software program represents the quantum algorithm to be run on QC system 301. Classical computing system 307 can be any type of computing device (e.g., a PC, one or more blade servers, etc.), or even a high-performance computing system such as a supercomputer, server farm, etc. Such a system may include one or more processors (not shown) coupled to one or more computer memories (e.g., memory 306). Such a computing system will be referred to herein as a "classical computer". In some examples, the software program may be received by a classical computing module, referred to herein as a fusion pattern generator 313. One function of fusion pattern generator 313 is to generate a set of machine-level instructions from the input software program (which can be generated as high-level code that can be more easily written by a user to program the quantum computer).

[0074] In some embodiments, the fusion mode generator 313 can operate as a compiler for a software program to be run on a quantum computer. The fusion mode generator 313 can be implemented as pure hardware, pure software, or any combination of one or more hardware or software components or modules. In various embodiments, the fusion mode generator 313 can operate at runtime or pre-operate; in either case, machine-level instructions generated by the fusion mode generator 313 can be stored (e.g., in memory 306). In some examples, the compiled machine-level instructions take the form of one or more data frames that instruct the qubit fusion system 305 to perform one or more fusions between certain qubits from individual (i.e., unentangled) resource states 315 during a given clock cycle of the quantum computer. For example, a fusion mode data frame 317 is a set of fusion measurements (e.g., Type II fusion measurements, hereinafter referred to in Figures 18 to 19) that should be applied between certain qubit pairs from different entangled resource states 315 during a certain clock cycle when the program is executed. Figure 21(A more detailed description is provided below.) An example of a group. In some embodiments, several fusion mode data frames 317 may be stored as classical data in memory 306. In some embodiments, the fusion mode data frames 317 may specify whether to apply type II fusion (or any other type of fusion) to a particular fusion gate within the fusion array 321 of the qubit fusion system 305. Additionally, the fusion mode data frames 317 may indicate that type II fusion will be performed in different bases (e.g., XX, XY, ZZ, etc.). As used herein, the terms XX type II fusion, YY type II fusion, XY type II fusion, ZZ type II fusion, etc., refer to a fusion operation that applies a specific two-particle projection measurement (e.g., Bell projection), which, depending on the selected Bell base, projects two qubits onto one of four Bell states. This projection measurement produces two measurement results corresponding to the eigenvalues ​​of a corresponding pair of observables measured in the selected base. For example, XX fusion is a Bell projection that measures the observables XX and ZZ (each observable may have an eigenvalue of +1 or -1, or 0 or 1, depending on the convention used), and XZ fusion is a Bell projection that measures the observables XZ and ZX, and so on. See Figures 18 to below. Figure 21 An example circuit for performing type II fusion for various basis selections in a linear optical system is shown; however, other Bell projection measurements are possible in other qubit architectures without departing from the scope of the invention. Those skilled in the art will understand that in a linear optical system, type II fusion performs probabilistic Bell measurements. Figures 18 to... Figure 21 The probabilistic nature of linear optical fusion was discussed in the context of fusion “success” and “failure” results, and will not be repeated here for clarity.

[0075] The fusion controller circuit 319 of the qubit fusion system 205 can receive data encoded in the fusion mode data frame 317 and, based on this data, can generate configuration signals, such as analog and / or digital electronic signals, to drive the hardware within the fusion array 321. For example, in the case of optical qubits, the fusion gate may include a photon detector coupled to one or more waveguides, beam splitters, interferometers, switches, polarizers, polarization rotators, etc. More generally, the detector can be any detector capable of detecting the quantum state of one or more qubits in resource state 315. Those skilled in the art will understand that many types of detectors can be used depending on the specific qubit architecture employed.

[0076] In some embodiments, applying the fusion mode data frame 317 to the fusion array 321 results in the generation of classical data (generated by the detector of the fusion gate), which is read out and optionally preprocessed, and then sent to the decoder 333. More specifically, the fusion array 321 may include a set of measurement devices that perform joint measurements between certain qubits from two different resource states and generate a set of measurement results associated with the joint measurements. These measurement results may be stored in a measurement result data frame (e.g., data frame 322) and passed back to the classical computing system for further processing.

[0077] In some embodiments, any submodule of the QC system 301 (e.g., controller 323, quantum gate array 325, fusion array 321, fusion controller 319, fusion pattern generator 313, decoder 323, and logic processor 308) may include any number of classical computing components, such as processors (CPU, GPU, TPU), memory (any form of RAM, ROM), hard-coded logic components (classical logic gates, such as AND, OR, XOR, etc.), and / or programmable logic components (e.g., field-programmable gate arrays (FPGAs, etc.)). These modules may also include any number of application-specific integrated circuits (ASICs), microcontrollers (MCUs), systems-on-a-chip (SoCs), and other similar microelectronic devices.

[0078] In some embodiments, the entangled resource state 315 can be any type of entangled resource state that, when a fusion operation is performed, produces a measurement result data frame including the necessary correlations for performing fault-tolerant quantum computing. Although Figure 3 An example of a set of identical resource states is shown, but a system can be employed that generates many different types of resource states and can even dynamically change the type of generated resource states based on the needs of the running quantum algorithm. As described herein, the logical qubit measurement result 327 can be fault-tolerantly recovered from the physical qubit measurement result 322 (e.g., via decoder 333). The logic processor 308 can then process the logic result as part of the program execution. As shown, the logic processor can feed information back to the fusion pattern generator 313 to influence downstream gates and / or measurements, thereby ensuring fault-tolerant computation.

[0079] Figure 4 An example of a qubit entanglement system 401 according to some embodiments is illustrated. According to some embodiments, such a system can be used to generate qubits (e.g., photons) in entangled states (e.g., resource states used in the illustrative examples shown in Figures 7 through 9 below). The qubit entanglement system 401 is an example of a system that can be employed in an FBQC system, such as those described above. Figure 3The illustrated qubit entanglement system 303. Those skilled in the art will understand that any qubit entanglement system can be used without departing from the scope of the invention. Examples of qubit entanglement systems can be found in U.S. Patent Application No. 16 / 621,994 entitled “Generation of entangled qubit states” (published as U.S. Patent Application Publication No. 20200287631), U.S. Patent Application No. 16 / 691,459 entitled “GENERATION OF ENTANGLED PHOTONIC STATE FROM PRIMITIVE RESOURCES” (published as U.S. Patent Application Publication No. XXXXX), and U.S. Patent Application No. 16 / 691,450 entitled “GENERATION OF AN ENTANGLED PHOTONIC STATE FROM PRIMITIVE RESOURCES” (published as U.S. Patent Application Publication No. XXXXX), the disclosures of which are incorporated herein by reference in their entirety for all purposes. For example, in some embodiments, the photon source can directly generate entangled resource states, or even smaller entangled states, instead of generating single photons. These entangled states can undergo additional entanglement operations at the entangled state generator 400 to produce the final resource state to be used for FBQC. Therefore, as used herein, the term "photon source" is intended to encompass at least a source of single photons, a source of multiple photons in entangled states, or more generally, a source of any photon state. Those skilled in the art will understand that the precise form of the resource state generation hardware is not critical and any system can be employed without departing from the scope of the invention.

[0080] In the illustrative photonic architecture, the qubit entanglement system 401 may include a photon source system 405 optically connected to an entanglement state generator 400. Both the photon source system 405 and the entanglement state generator 400 may be coupled to a classical processing system 403, such that the classical processing system 403 can communicate with and / or control (e.g., via classical information channels 430a-b) the photon source system 405 and / or the entanglement state generator 400. The photon source system 405 may include a collection of single-photon sources, which may provide output photon states (e.g., single photons or other photon states such as Bell states, GHZ states, etc.) to the entanglement state generator 400 via interconnecting waveguides 402. The entangled state generator 400 can receive output photon states and convert them into one or more entangled photon states (or, if the source itself outputs entangled photon states, convert them into larger photon states), and then output these entangled photon states into an output waveguide 440. In some embodiments, the output waveguide 440 can be coupled to downstream circuitry that can use the entangled states to perform quantum computing. For example, the entangled states generated by the entangled state generator 400 can be used as a resource for downstream quantum optical circuitry (not shown).

[0081] In some embodiments, the photon source system 405 and the entangled state generator 400 can be coupled with... Figure 3 The illustrated quantum computing systems are used in combination. For example, Figure 3 The illustrated qubit entanglement system 303 may include a photon source system 405 and an entanglement state generator 400, and Figure 4 The classic computer system 403 may include Figure 3 One or more of the various classical computing components illustrated (e.g., classical computing system 307). In this case, entangled photons departing via output waveguide 440 can be fused together by qubit fusion system 305, i.e., they can be input into a detection system that performs a set of joint measurements for use in an FBQC scheme.

[0082] In some embodiments, system 401 may include classical channels 430 (e.g., classical channels 430-a to 430-d) for interconnecting components and providing classical information. It should be noted that classical channels 430-a to 430-d need not all be identical. For example, classical channels 430-a to 430-c may include a bidirectional communication bus carrying one or more reference signals, such as one or more clock signals, one or more control signals, or any other signal carrying classical information (e.g., announcing signals, photon detector readout signals, etc.).

[0083] In some embodiments, the qubit entanglement system 401 includes a classical computer system 403 that communicates with and / or controls the photon source system 405 and / or the entangled state generator 400. For example, in some embodiments, the classical computer system 403 may be used to configure one or more circuits, for example, using a system clock that may be provided to the photon source 405 and the entangled state generator 400, as well as any downstream quantum photonic circuitry used to perform quantum computing. In some embodiments, the quantum photonic circuitry may include optical circuitry, electronic circuitry, or any other type of circuitry. In some embodiments, the classical computer system 403 includes a memory 404, one or more processors 402, a power supply, an input / output (I / O) subsystem, and a communication bus or interconnections of these components. The one or more processors 402 may execute software modules, programs, and / or instructions stored in the memory 404 to perform processing operations.

[0084] In some embodiments, memory 404 stores one or more programs (e.g., instruction sets) and / or data structures. For example, in some embodiments, entangled state generator 400 may attempt to generate entangled states on successive stages and / or on independent instances, any of which may successfully generate entangled states. In some embodiments, memory 404 stores one or more programs for determining whether a corresponding stage is successful and configuring entangled state generator 400 accordingly (e.g., by configuring entangled state generator 400 to switch photons to the output when the stage is successful, or to pass photons to the next stage of entangled state generator 400 if the stage has not yet succeeded). To this end, in some embodiments, memory 404 stores a detection mode that classical computing system 403 can use to determine whether a stage is successful. Additionally, memory 404 may store settings provided to various configurable components (e.g., switches) described herein, which are configured, for example, by setting one or more phase shifts of the components.

[0085] In some embodiments, some or all of the above functions may be implemented using hardware circuitry on the photonic source system 405 and / or the entangled state generator 400. For example, in some embodiments, the photonic source system 405 includes one or more controllers 407-a (e.g., logic controllers) (which may include, for example, a field-programmable gate array (FPGA), an application-specific integrated circuit (ASIC), a "system-on-a-chip" including a classical processor and memory, etc.). In some embodiments, the controller 407-a determines whether the photonic source system 405 is successful (e.g., for a given attempt over a given clock cycle) and outputs a reference signal indicating whether the photonic source system 405 is successful. For example, in some embodiments, the controller 407-a outputs a logic high value to classical channels 430-a and / or classical channels 430-c when the photonic source system 405 is successful, and outputs a logic low value to classical channels 430-a and / or classical channels 430-c when the photonic source system 405 is unsuccessful. In some embodiments, the output of the controller 407-a may be used to configure the hardware in the controller 107-b.

[0086] Similarly, in some embodiments, the entangled state generator 400 includes one or more controllers 407-b (e.g., logic controllers, which may include field-programmable gate arrays (FPGAs), application-specific integrated circuits (ASICs), etc.) that determine whether the corresponding stage of the entangled state generator 400 has been successful, execute the switching logic described above, and output reference signals to classical channels 430-b and / or 430-d to notify other components whether the entangled state generator 400 has been successful.

[0087] In some embodiments, the system clock signal may be provided to the photon source system 405 and the entangled state generator 400 via an external source (not shown) or by the classical computing system 403 via classical channels 430-a and / or 430-b. Examples of clock generators that may be used are described in U.S. Patent No. 10,379,420, the contents of which are incorporated herein by reference in their entirety for all purposes; however, other clock generators may also be used without departing from the scope of the invention. In some embodiments, the system clock signal provided to the photon source system 405 triggers the photon source system 405 to attempt to output one photon per waveguide. In some embodiments, the system clock signal provided to the entangled state generator 400 triggers or gates multiple sets of detectors in the entangled state generator 400 to attempt to detect photons. For example, in some embodiments, triggering a set of detectors in the entangled state generator 400 to attempt to detect photons includes gated that set of detectors.

[0088] It should be noted that in some embodiments, the photon source system 405 and the entangled state generator 400 may have internal clocks. For example, the photon source system 405 may have an internal clock generated and / or used by the controller 407-a, and the entangled state generator 400 may have an internal clock generated and / or used by the controller 407-b. In some embodiments, the internal clocks of the photon source system 405 and / or the entangled state generator 400 are synchronized with an external clock (e.g., the system clock provided by the classical computer system 403) (e.g., via a phase-locked loop). In some embodiments, either internal clock may itself be used as a system clock; for example, the internal clock of the photon source may be distributed to other components in the system and used as a master / system clock.

[0089] In some embodiments, the photon source system 405 includes multiple probabilistic photon sources that can be multiplexed spatially and / or temporally, i.e., so-called multiplexed single-photon sources. In one example of such a source, the source is driven by a pump (e.g., an optical pulse) coupled to an optical resonator that can generate zero, one, or more photons through some nonlinear process (e.g., spontaneous four-wave mixing, second harmonic generation, etc.). As used herein, the term "attempt" is used to refer to the action of driving the photon source with some driving signal (e.g., a pump pulse) that can nondeterministically produce an output photon (i.e., the probability that the photon source will generate one or more photons in response to the driving signal may be less than 1). In some embodiments, a respective photon source may be most likely to produce zero photons in a given attempt (e.g., the probability of producing zero photons in each attempt may be 90%). A second most likely outcome of the attempt may be the production of a single photon (e.g., the probability of producing a single photon in each attempt may be 9%). The third most likely outcome of the attempt is the production of two photons (e.g., the probability of producing two photons on each attempt to produce a single photon could be approximately 1%). In some cases, the probability of producing more than two photons may be less than 1%.

[0090] In some embodiments, the apparent efficiency of a photon source can be increased by using multiple single-photon sources and multiplexing the outputs of multiple photon sources. In some embodiments, the photon source can also generate a classical announcement signal that announces (or declares) successful generation. In some embodiments, this classical signal is obtained from the output of a detector, wherein the photon source system always generates photon states in pairs (e.g., in SPDC), and the detection of a photon signal is used to announce the success of the process. This announcement signal can be provided to a multiplexer and used to properly route successful generation to the multiplexer output port, as described in more detail below.

[0091] The exact type of photon source used is not critical, and any type of source employing any photon generation process can be used, such as spontaneous four-wave mixing (SPFW), spontaneous parametric down-conversion (SPDC), or any other process. Other types of sources that do not necessarily require nonlinear materials can also be used, such as sources employing atomic and / or artificial atomic systems, such as quantum dot sources, color centers in crystals, etc. In some cases, the source can be a photonic cavity or can be coupled to a photonic cavity, as is the case, for example, for artificial atomic systems such as quantum dots coupled to a cavity. Other types of photon sources exist besides SPWM and SPDC, such as optomechanical systems, etc. In some examples, the photon source can emit multiple photons already in an entangled state; in this case, the entanglement generator 400 may not be necessary, or alternatively, entangled states can be used as input and even larger entangled states can be generated.

[0092] In some embodiments, spatial multiplexing of several nondeterministic photon sources (also known as MUX photon sources) can be employed. Many different spatial MUX architectures are possible without departing from the scope of the invention. Temporal MUXs can also be implemented instead of or in combination with spatial multiplexing. MUX schemes employing logarithmic trees, generalized Mach-Zehnder interferometers, multimode interferometers, linked sources, linked sources with dump-pumping schemes, asymmetric polycrystalline single-photon sources, or any other type of MUX architecture can be used. In some embodiments, the photon sources can employ MUX schemes with quantum feedback control, etc. An example of an n×m MUX source is disclosed in U.S. Patent No. 10,677,985, the contents of which are incorporated herein by reference in their entirety for all purposes.

[0093] Figure 5 An example of a quantum bit fusion system 501 according to some embodiments is shown. In some embodiments, the quantum bit fusion system 501 can be integrated into a larger FBQC system (e.g., Figure 3 This is used in the qubit fusion system 305 shown.

[0094] The qubit fusion system 501 includes a fusion controller 519 coupled to a fusion array 521. The fusion controller 519 is configured as described above (refer to the above description). Figure 3The fusion controller circuit 319 operates as described above. The fusion array 521 includes a set of fusion sites, each receiving two or more qubits from different resource states (not shown), and performing one or more fusion operations (e.g., type II fusion) on selected qubits from the two or more resource states. The fusion operations performed on the qubits can be controlled by the fusion controller 519 via classical signals, which are sent from the fusion controller 519 to each fusion site via control channels 503a, 503b, etc. Based on the joint measurements performed at each fusion site, classical measurement results in classical data form are output and then provided to the decoder system, as referenced above. Figure 3 As shown and described. See below for reference. Figure 6 and Figures 18 to Figure 20 Describe an example of a photonic circuit that can be used as a type II fusion gate.

[0095] Figure 6 A possible example of a fusion site 601 according to some embodiments is shown, which is configured to operate in conjunction with a fusion controller 319 to provide measurement results to a decoder for fault-tolerant quantum computing. In this example, the fusion site 601 may be a fusion array 321 ( Figure 3 The elements shown are, and although only one instance is shown for illustrative purposes, the fusion array 321 may include any number of instances of the fusion site 601.

[0096] As described above, the qubit fusion system 305 can receive two or more qubits to be fused (qubit 1 and qubit 2, shown herein in dual-track coding). Qubit 1 is a qubit entangled with one or more other qubits (not shown) as part of a first resource state, while qubit 2 is another qubit entangled with one or more other qubits (not shown) as part of a second resource state. Advantageously, in contrast to MBQC, none of the qubits from the first resource state need to be entangled with any of the qubits from the second (or any other) resource state in order to facilitate fault-tolerant quantum computing. Also advantageously, at the input of the fusion site 601, the set of resource states is not mutually entangled to form a cluster state in the form of a quantum error-correcting code, thus eliminating the need to store and / or maintain large cluster states with long-range entanglement across the entire cluster state. Advantageously, the fusion operation occurring at these fusion sites can be a completely destructive joint measurement of qubit 1 and qubit 2, such that everything remaining after the measurement is classical information representing the measurement results on these detectors (e.g., detectors 603, 605, 607, 609). In this case, the classical information is all that the decoder 333 needs to perform quantum error correction, and no additional quantum information propagates through the system. This contrasts with MBQC systems, which employ fusion sites to fuse resource states into cluster states, which themselves serve as topological codes, and only then generate the required classical information via single-particle measurements of the individual qubits within the large cluster state. In such an MBQC system, not only is it necessary to store and maintain the large cluster state in the system before performing single-particle measurements, but also to apply additional single-particle measurement steps (besides the fusion used to generate the cluster state) to each qubit of the cluster state in order to generate the classical information needed to compute the correction subgraph data required for the decoder to perform quantum error correction.

[0097] Figure 6 An illustrative example of one method for implementing fused sites as part of an optical quantum computer architecture is shown. In this example, qubit 1 and qubit 2 can be dual-track encoded optical qubits. Refer to Figures 11 to... Figure 14 A brief introduction to the dual-track encoding of optical qubits is provided in Section 4 below. Therefore, qubit 1 and qubit 2 can be input on waveguide pairs 621, 623 and waveguide pairs 625, 627, respectively. Interferometers 624 and 628 can be placed in a straight line with the individual qubits, and within one arm of each interferometer 624, 628, programmable phase shifters 630, 632 can optionally be applied to influence the basis for the applied fusion operation, for example, by implementing... Figure 21The specific mode coupling shown implements what is referred to herein as XX, XY, YY, or ZZ fusion. Programmable phase shifters 630, 632 can be coupled to fusion controller 319 via control lines 629 and 631, such that signals from fusion controller 319 can be used to set the basis for which the fusion operation is applied to the qubits. In some embodiments, the basis can be hard-coded within fusion controller 319, or in some embodiments, the basis can be selected based on external input (e.g., instructions provided by fusion mode generator 313). Additional mode couplers (e.g., mode couplers 633 and 632) can be applied after the interferometer, followed by single-photon detectors 603, 605, 607, 609, to provide a readout mechanism for performing joint measurements.

[0098] In some embodiments, fusion can be a probabilistic operation, i.e., it implements a probabilistic Bell measurement, where the measurement sometimes succeeds and sometimes fails, as follows: Figure 20 As described above. In some embodiments, the probability of success of this operation can be increased by using an additional quantum system besides the quantum system in which this operation operates. Embodiments using additional quantum systems are generally referred to as "enhanced" fusion. Figure 6 In the example shown, the fusion site implements a non-enhanced Type II fusion operation on the incoming qubit. Those skilled in the art will understand that any type of fusion operation can be applied (and can be enhanced or not enhanced) without departing from the scope of the invention. Additional examples of Type II fusion circuitry for polarization coding and dual-track path coding are shown and described in Section 5 below. In some embodiments, the fusion controller 319 may also provide control signals to detectors 603, 605, 607, and 609. These control signals may be used, for example, to gate the detectors or to otherwise control the operation of the detectors. Each of detectors 603, 605, 607, and 609 provides a photon detection signal (representing the number of photons detected by the detector, e.g., 0 photons detected, 1 photon detected, 2 photons detected, etc.), and this photon detection signal may be pre-processed at the fusion site 601 to determine a measurement result (e.g., whether fusion was successful) or directly passed to the decoder 333 for further processing.

[0099] 3. Example of FBQC using GHZ resource state

[0100] Figures 7A to 7BAn FBQC scheme for fault-tolerant quantum computing according to one or more embodiments is illustrated. In this example, a topological code known as a Lawsondorf lattice (also known as a leaf-shaped surface code) is used, but any other error-correcting code may be used without departing from the scope of the invention. For example, FBQC may be implemented for various volume codes (e.g., rhombus codes, triangular rhombus codes, etc.), various color codes, or other topological codes may be used without departing from the scope of the invention.

[0101] Figure 7A An example of a Lawsendorfer lattice unit cell 702 is shown. For the case of measurement-based quantum computing, in order to determine the point at the center of the unit cell, referred to herein as P... cell The value of the correction subgraph is measured on the x-basis of the six faces of the unit cell, resulting in the value of the correction subgraph for six M-bases. x Each measurement determines a set of 0 or 1 eigenvalues. These eigenvalues ​​are then combined as follows:

[0102]

[0103] S1, S2, ..., S6 correspond to six sites on the face of the unit cell, and Mx(Si) corresponds to the measurement result (0 or 1) obtained by measuring the corresponding face qubit in the x basis. (S1, S2, and S3 are labeled in Figure 7; S4, S5, and S6 are located on the hidden face of unit cell 702.)

[0104] In FBQC, the goal is to generate a set of classical data corresponding to error correctors of some quantum error-correcting codes through a series of joint measurements on two or more qubits (e.g., positive operator value measurements, also known as POVM). For example, using... Figure 7A The Lawsondorf cell, as an illustrative example, can be used to generate the calibration submap values ​​for this set of measurements in the FBQC method. Figure 7B As shown in the diagram. In this example, the GHZ state is used as the resource state, but those skilled in the art will understand that any suitable resource state can be used without departing from the scope of the invention. In order to... Figure 7A The MBQC scheme shown becomes Figure 7B The FBQC scheme shown is as follows: Figure 7A Each facet qubit is replaced by a separate qubit from a clearly separate (i.e., non-entangled) resource state. For example, Figure 7B Four resource states, R1, R2, and R3 (enclosed by dashed ellipses), are marked in the diagram. Each resource state contributes at least one qubit to the content of the facet qubit S2 of the Lawsondorf unit cell. For example, Figure 7AIn the diagram, the surface qubit S2 is replaced by four qubits, which come from three different resource states: resource state R1 contributes two qubits; resource state R2 contributes the third qubit; and resource state R3 contributes the fourth qubit. During operation, the system will perform two fusions on each surface (e.g., ...). Figure 7B Circles 721 and 722 in the diagram represent the fusion between the contributing qubits of resource states R2 and R1, and R3 and R1, respectively. In the example where the fusion is a type II fusion, all four facet qubits are measured, resulting in four measurement results. The correction subgraph values ​​of the unit cell are obtained through the above equation (2), but now:

[0105] M x (S i )=[F 1,XX (S i )+F 2,XX (S i )]mod 2 (3)

[0106] For the i-th face, F 1,XX (S i ) is a measurement result obtained by performing a joint measurement on the qubit associated with fusion 1 (e.g., indicated by circle 721), where fusion 1 is a type II fusion performed in the XX basis, and where F 2,XX (S i The measurement result is obtained by performing a joint measurement on the qubits associated with fusion 2 (e.g., indicated by circle 722), where fusion 2 is also a type II fusion performed in the XX basis. Similar to the measurements associated with the X observables described above with reference to equation (2), the fusion measurements of the observables XX (and ZZ) take the values ​​of zero or 1 corresponding to the positive or negative eigenvectors of the measured operators (XX and ZZ in this example). Given equation (3), in order to obtain the opposite M... x (S i The various measurements of ) are expected to be performed for the fusion measurement F. 1,XX (S i ) and F 2,XX (S i The correct fusion result of the two. However, if the fusion fails due to some error, making it impossible to recover the operator value, in some embodiments, the face measurement is considered to have failed, resulting in at least one edge being erased in the correction subgraph data. Those skilled in the art will understand that the decoder can be used in conjunction with the above references. Figures 1A to 1CErrors are handled in a similar manner as described. Those skilled in the art will also recognize that, although our description of equation (3) focuses on XX observables, fusion can also produce measurements of ZZ observables, and these results can also be combined according to equation (3) to produce an independent set of calibration subplot data. In some embodiments, these two sets of calibration subplot data are referred to as the original and dual calibration subplots.

[0107] Figure 7C An example of a cluster state consisting of several unit cells of a Lawsondorf lattice is shown. In the MBQC method, it is necessary to generate such an entire cluster state, thus forming an entangled state of many qubits, where the entanglement of this state extends across the lattice from one surface boundary to another. In the MBQC method, it is this large entangled cluster state that serves as the quantum error-correcting code, thus enabling the encoding of logical qubits. Computation is performed by performing single-qubit measurements on the individual qubits of the entangled state to generate measurement results, which are used to generate a correction subgraph fed to the decoder, as referenced above. Figures 1A to 1C As can be seen, increasing computational fault tolerance requires increasing the lattice size, and therefore the size of the entangled states. In one or more embodiments of the FBQC method disclosed herein, such large entangled cluster states are not necessary; instead, smaller resource states are generated, where the size of the resource states is independent of the required fault tolerance. As described in detail above with reference to FIG7, the FBQC method can be constructed from any fault-tolerant lattice by replacing the individual nodes of the lattice with a set of fusions between two or more adjacent resource states. This construction of replacing the individual nodes of the lattice with resource states / fusions is merely one example of obtaining an FBQC scheme, and those skilled in the art will recognize that many different ways of constructing an FBQC scheme from a fault-tolerant lattice can be employed without departing from the scope of the invention.

[0108] Furthermore, as described in more detail below, the process can be performed by generating resource state layers in a given clock cycle and performing fusion within each layer, as illustrated in Figures 8 and 9 below. For example, in Figure 7C In this context, the horizontal direction represents the time in which all or a subset of qubits in any given layer in the xy-plane can be generated / initialized in the same clock cycle. For example, qubits in layer 1 can be generated in clock cycle 1, qubits in layer 2 can be generated in clock cycle 2, qubits in layer 3 can be generated in clock cycle 3, and so on. As will be described in more detail below, a subset of qubits in each layer can be stored / delayed so that they can be used for fusion with qubits from resource states in subsequent layers, and can be used to achieve fault tolerance if necessary.

[0109] In some embodiments, to generate the desired error checksum, a lattice preparation protocol (LPP) can be designed to generate a suitable checksum graph from the fusion of multiple smaller entangled resource states. Figures 8 and 9 illustrate examples of lattice preparation protocols according to some embodiments. For illustrative purposes, resource states are, for example... Figure 8A The resource state 800 shown is the state of resource state 800; however, other resource states may be used without departing from the scope of the invention. Resource state 800 is equivalent to the GHZ state until an Adama gate is applied to a single qubit. For example, the state used in the examples disclosed herein is equivalent to the GHZ state until an H Adama gate is applied. Figure 8A The two terminal qubits in the diagram are 800a-3 and 800a-4. More specifically, the 4-GHz state can be identified as a stable substate with the following stabilizers:<XXXX,ZZII,ZIZI,ZIIZ> . Figure 8A The resource state 800 shown is closely related to this GHZ state, but the stabilizer of state 800 is...<XXZZ,ZZII,ZIXI,ZIIX> (The operators are ordered to correspond to qubits 800a-1, 800a-2, 800a-3, and 800a-4, respectively). Those skilled in the art will understand that when Adama gates are applied to qubits 800a-3 and 800a-4, the 4-GHz state and resource state 800 are equivalent.

[0110] In Figures 8 and 9, the time direction is perpendicular to the page, such that a resource state, having the shape of, for example, resource state 810, represents a set of qubits: qubits 1, 2, and 3 entangled with each other within the same clock cycle, and qubit 4 entangled with, for example, qubits 2 and 3 in the time dimension. Such a resource state can be created, for example, by generating a complete 4-qubit resource state in a single clock cycle and then storing qubit 4 in memory over a fixed time period (e.g., one clock cycle). As used herein, the term "memory" includes any type of memory, such as a quantum memory, a qubit delay line, a shift register for qubits, the qubit itself, etc. In the case of photonic resource states, such qubit memories are equivalent to qubit delays and can therefore be implemented using optical fibers. Figure 8C In the example shown, the delay to qubit 4 is schematically represented by a loop of additional optical path length (e.g., provided by an optical fiber), which is placed collinearly with the existing optical path of the qubit but not present in the optical paths of qubits 1-3. In this example, the length of the optical fiber allows it to achieve a single clock cycle delay of duration T, but other delays are possible, such as 2T, 3T, etc. In terms of physical delay time, such a delay can be in the range of 500ps-500ns, but any delay is possible without departing from the scope of the invention.

[0111] Returning to the FBQC process disclosed herein, Figures 8 and 9 illustrate examples of how FBQC lattice preparation and measurement protocols can be performed layer by layer. Figure 8A A portion of the base layer of the Lawsondorf lattice is shown, which is illustrated as layer 810 (corresponding to...). Figure 7C (A portion of layer 1 is shown). In the example illustrated here, in order to handle something similar to... Figure 8A The layer shown first generates multiple resource states 800 (e.g., in...). Figure 3 In the entangled qubit system 303, resource state 800 is an entangled state comprising four physical qubits (also referred to herein as a quantum subsystem): qubits 800a-1, 800a-2, 800a-3, and 800a-4. In some embodiments, resource state 800 may take the form of a 4-GHz state, wherein the two terminating qubits 800a-4 and 800a-3 have undergone an Adama operation (e.g., for the case of dual-track encoded qubits, by applying a 50:50 beam splitter between the two tracks forming the qubits). In some embodiments, not all qubits in the layer undergo fusion in this clock cycle; instead, the measurement of some qubits generated from certain resource states during this clock cycle can be delayed. For example, the measurement of qubit 820, redundantly encoded qubit 805, or any other qubit can be delayed so that the qubits will be available in the next clock cycle. Such delayed qubits can then be used for fusion with one or more qubits from the resource state, which will only be available for fusion in the next clock cycle.

[0112] In examples employing photonic implementation, qubits from the resource state can then be appropriately routed (via integrated waveguides, optical fibers, or any other suitable photonic routing technique) to a qubit fusion system (e.g., Figure 3 A qubit fusion system 305 is provided to achieve a set of fused measurements that enable quantum error correction, i.e., will result in the collection of measurement results corresponding to selected error correctors. Although this example explicitly uses a Lawsendorf lattice-based topological code, any code can be used without departing from the scope of the invention.

[0113] Figure 8BAn example of a set of GHZ resource states is shown, arranged (i.e., pre-routed) such that qubits to be sent to a given fusion gate are graphically adjacent to each other. For qubits adjacent to each other in this diagram, a corresponding fusion can be performed between multiple pairs of qubits (also referred to herein as corresponding quantum subsystems, where the individual qubit inputs from a pair of qubits are at fusion sites belonging to different corresponding resource states). For example, at site 802, two type II fusion measurements can be applied, once between qubits 822 and 824, and once between qubits 826 and 828. It should be noted that before the fusion is performed, qubits 822 and 824 (or qubits 826 and 828) are not entangled with each other, but are each part of a different resource state. Thus, there is no large entangled cluster state, referred to as a Lawsondorf lattice, before the fusion measurement is performed.

[0114] refer to Figure 9A A portion of the second layer of the basic code structure is shown as layer 910 (corresponding to...) Figure 7C As shown in layer 2). In the FBQC system, in order to handle such... Figure 9B The single-layer FBQC method shown follows the reference above. Figures 8A to 8B The same lines are described above, so the details will not be repeated here.

[0115] Figures 10A to 10E A method for performing FBQC according to one or more embodiments is illustrated in further detail. More specifically, the method described herein includes steps for performing joint measurements for a particular quantum error-correcting code according to some embodiments, wherein different layers of the code may be generated at different time steps (clock cycles) as illustrated above with reference to Figures 8 to 9, and are entangled in a manner that provides a fused measurement to extract the necessary comparator information for performing quantum error correction. As with other examples provided herein, the Lawsendorf lattice is used for illustrative purposes, but other codes may be used without departing from the scope of the invention.

[0116] For example, Figure 10A and Figure 10B The following are respectively shown from Figure 7C The Lawsendorf lattice contains layers 1 and 3, as well as portions of layers 2 and 4 (here referred to as quantum error-correcting (QEC) codes). Figure 10C and Figure 10D Methods for processing these layers in an FBQC system are illustrated, including example resource states that can be used. For illustrative purposes, the description is limited to vertices 1, 2, 3, and 4 of the QEC code, and the example focuses on how resource state generation and measurement can be performed in an FBQC system.

[0117] Back Figure 10AIn step 1001, a first set of resource states is provided during the first clock cycle. Figure 10D An example is shown where, instead of providing a single qubit at vertices 1, 2, 3, 4, 5, etc., where these single qubits are entangled throughout the lattice (as is the case in MBQC systems), two or more qubits are provided, each originating from a different, non-entangled resource state (e.g., respective resource states A, B, C, D, E, F, and G). As used herein, the notation Aij is used to denote the j-th qubit from the A-th resource state of the i-th layer. For example, Figure 10D The A-th resource state of layer 1 is a GHz state, comprising 4 qubits, labeled A11, A12, A13, and A14, as shown in the figure. Similarly, the qubits comprising resource state B, provided as part of layer 1, can be labeled B11, B12, B13, and B14 (but labels not explicitly shown in the figure are used here to avoid confusion). Figure 10D In the diagram, the qubits to be fused to generate the collimator information associated with vertices 1, 2, 3, 4, and 5 are also shown as being surrounded by solid ellipses 1, 2, 3, and 4. As used herein, each of these vertices is associated with hardware used to perform type II fusion at the fusion site, as referenced above. Figures 3 to 6 As stated above.

[0118] In some embodiments, the resource states of any given layer can be generated by a qubit entanglement system (e.g., the above reference). Figure 3 and Figure 4 The described entangled qubit system generates / provides qubit states. However, those skilled in the art will understand that any entangled qubit system can be employed, and a given entangled qubit system can employ many different types of resource state generators, even generating different types of resource states. In this sense, the FBQC system is completely unaware of the choice of resource states and the choice of the architecture of the entangled qubit system, or even the architecture of the qubits themselves, thus giving system designers great flexibility to implement a system that generates the highest threshold for a given primary error / noise source.

[0119] In step 1003, the fusion instruction in classic data form (also referred to herein as the fusion mode) is provided to the fusion site. Return to Reference Figure 3For example, fusion mode data frame 317 is an example of a set of fusion instructions (e.g., a type II fusion measurement in an XX basis) that, when performing quantum applications on an FBQC system, can be applied between qubit pairs from different entangled resource states at the fusion site during a certain clock cycle. Also as described above, in some embodiments, several fusion mode data frames can be stored in memory as classical data. In some embodiments, the fusion mode data frames can specify whether a type II fusion (XX) will be applied to a specific fusion gate within the fusion site (or whether any other type of fusion will be applied). Furthermore, the fusion mode data frames can indicate that type II fusions will be performed in different bases, such as XX, XY, ZZ, etc.

[0120] Back Figure 10D The fusion instructions for layer 1 can include fusion parameters (qubit positions and basis) to fuse two or more qubits from different resource states (also referred to herein as corresponding quantum subsystems, since the qubits reside in or are part of a corresponding individual resource state). For example, for fusion site 1, the fusion instructions can specify fusion parameters to indicate that a type II fusion will occur between qubits A1, B1, and C1 from resource states (similarly, for site 3, between E1, F1, and G1). More specifically, two type II fusions to be performed at fusion site 1 can be specified between A14 and B12 and between C11 and B13. Similar instructions are provided for other fusion sites in this layer. For example, for fusion site 2, the fusion instructions can specify fusion parameters to indicate that a type II fusion will occur between qubits B1, D1, and F1 from resource states. More specifically, two type II fusions to be performed at fusion site 2 can be specified between B14 and D12 and between D13 and F14. However, unlike fusion site 1, where all qubits are measured, fusion site 2 includes qubits that are held in place until the second clock cycle. This is because the fundamental structure of the QEC lattice requires that the quantum state of this qubit be preserved until it is fused to qubits from different layers at different clock cycles. That is, if this were an MBQC scheme, the qubit associated with this vertex would be one entangled with a qubit in another layer, for example, respectively. Figure 10B and Figure 10C The qubits 2 and 6 are shown in the figure.

[0121] Back Figure 10D As shown in the explicit example, the fusion instruction can specify that D14 will not be measured until the next clock cycle, where it will be measured from a later layer (e.g., Figure 10EThe qubit fusion in layer 2) is shown. In the photonic implementation, the optical fiber can realize the qubit delay for the above functions, serving as a reliable quantum memory to store qubits until they are needed for future clock cycles. As used herein, these unmeasured (delayed) qubits are referred to as unmeasured quantum subsystems.

[0122] Moving to fusion point 4, this point is an example of fusion between layers, i.e., fusion between qubits from resource states generated in this clock cycle and qubits from resource states generated in the previous clock cycle but not measured at that time, instead being delayed or equivalently stored until the next clock cycle. For fusion point 4, the fusion instruction can specify fusion parameters to indicate that XX II-type fusion will occur between qubits C1, B0, and B2 from resource states in three different layers. The fusion instruction can also include instructions to delay (not measure) qubits C12 and C13 until the next clock cycle. For example, in this case, the fusion instruction could indicate that in the next time step, C12 will be fused with B04, and C13 will be fused with B21.

[0123] In step 1003, the fusion operation specified by the fusion command is executed, thereby generating classical data in the form of fused measurement results. (See above reference.) Figures 3 to 6 As described in equation (2), the classical data is then passed to the decoder and used to construct the correction subgraph to be used for quantum error correction.

[0124] These examples are illustrative. The choice of error-correcting codes determines a set of qubit pairs fused from certain resource states such that the output of the qubit fusion system is classical data from which a corrector graph can be directly constructed. In some embodiments, classical error-correcting data is generated directly from the qubit fusion system without requiring additional single-particle measurements on any remaining qubits. In some embodiments, joint measurements performed at the qubit fusion system are destructive to the qubits on which joint measurements are performed.

[0125] 4. Introduction to qubits and path coding

[0126] The dynamics of quantum objects (such as photons, electrons, atoms, ions, molecules, nanostructures, etc.) follow the rules of quantum theory. More specifically, in quantum theory, the quantum state of a quantum object (such as a photon) is described by a set of physical properties, the complete set of which is called a mode. In some embodiments, a mode is defined by specifying the values ​​(or distributions of values) of one or more properties of the quantum object. For example, again for a photon, a mode can be defined by the photon's frequency, its position in space (e.g., in which waveguide or superposition of waveguides the photon propagates), its associated propagation direction (e.g., the photon's k-vector in free space), its polarization state (e.g., the direction of the photon's electric and / or magnetic fields (horizontal or vertical)), etc.

[0127] For photons propagating in a waveguide, it is convenient to express the photon's state as one of a set of discrete spatiotemporal modes. For example, the spatial mode k of the photon. i It is determined based on which of the finite set of discrete waveguides the photon can propagate in. Furthermore, the time pattern t... j The time discretization of the system is determined by which of a set of discrete time intervals (referred to herein as "bins") the photon can reside in. In some embodiments, the time discretization of the system can be provided by the timing of the pulsed laser responsible for generating the photon. In the following examples, spatial modes will be used primarily to avoid complicating the description. However, those skilled in the art will understand that the system and method can be applied to any type of mode, such as temporal modes, polarization modes, and any other mode or group of modes used to specify a quantum state. Furthermore, in the following description, embodiments employing photonic waveguides to define the spatial mode of the photon will be described. However, those skilled in the art will understand that any type of mode (e.g., polarization modes, temporal modes, etc.) can be used without departing from the scope of the invention.

[0128] For quantum systems with multiple indistinguishable particles, it is useful to describe the quantum state of the entire many-body system using Fock state form (sometimes called occupancy number representation), rather than describing the quantum state of each individual particle in the system. In the Fock state description, the many-body quantum state is specified by the number of particles present in the various modes of the system. Because a mode is a complete set of properties, this description is sufficient. For example, a multimode, two-particle Fock state |1001> 1,2,3,4Two-particle quantum states are specified, with one photon in mode 1, zero photons in mode 2, zero photons in mode 3, and one photon in mode 4. Again, as mentioned above, the modes can be any set of properties of the quantum object (and can depend on the single-particle ground state used to define the quantum state). In the case of photons, any two modes of the electromagnetic field can be used; for example, the system can be designed to use modes related to degrees of freedom that can be passively manipulated by linear optics. For example, polarization, spatial degrees of freedom, or angular momentum can be used. For example, a two-particle Fock state |1001> 1,2,3,4 The represented four-mode system can be physically realized as four distinct waveguides, two of which (representing mode 1 and mode 4, respectively) have a photon traveling within them. Other examples of states in such many-body quantum systems are four-photon Fokker states representing the individual waveguides containing a single photon. 1,2,3,4 And represent the four-photon Fokker states of waveguides one and two that hold two photons, and waveguides three and four that hold zero photons, respectively |2200> 1,2,3,4 For modes that have zero photons, the term "vacuum mode" is used. For example, for the four-photon Fokker state |2200> 1,2,3,4 Modes 3 and 4 are referred to as “vacuum modes” (also known as “auxiliary modes”) in this paper.

[0129] As used herein, a "qubit" is a physical quantum system with associated quantum states that can be used to encode information. Unlike classical bits, qubits can have states that are, for example, a superposition of logical values ​​of 0 and 1. In some embodiments, qubits are "dual-track encoded," such that the logical value of a qubit is encoded by one of two modes being occupied by exactly one photon (a single photon). For example, consider two spatial modes of a photonic system associated with two different waveguides. In some embodiments, logical 0 and 1 values ​​can be encoded as follows:

[0130] |0> L =|10> 1,2 (1)

[0131] |1> L =|01> 1,2 (2)

[0132] Wherein, the subscript “L” indicates that the right arrow represents a logical value (e.g., a qubit value), and as mentioned above, the symbol |ij> on the right-hand side of equations (1)-(2) above. 1,2 This indicates that there are i photons in the first waveguide and j photons in the second waveguide (e.g., where i and j are integers). In this symbol, the logical value |01> is used. LThe state of a two-qubit array (representing the state of two qubits, where the first qubit is in a "0" logic state and the second qubit is in a "1" logic state) can be expressed as |1001> 1,2,3,4 This is represented using photon occupancy across four different waveguides (i.e., one photon in the first waveguide, zero photons in the second waveguide, zero photons in the third waveguide, and one photon in the fourth waveguide). In some cases, various subscripts are omitted in this invention to avoid unnecessary mathematical confusion.

[0133] 5. Introduction to LOQC

[0134] 5.1 Dual-track optical qubits

[0135] Quantum bits (and operations on them) can be implemented using a variety of physical systems. In some examples described herein, qubits are provided in an integrated photonic system employing waveguides, beamsplitters (or directional couplers), photonic switches, and single-photon detectors, and the modes that can be occupied by photons are spatiotemporal modes corresponding to the presence of photons in the waveguide. Mode couplers (e.g., optical beamsplitters) can be used to couple modes to achieve transformation operations, and measurement operations can be achieved by coupling a single-photon detector to a specific waveguide. Those skilled in the art who have access to this invention will understand that modes defined by any suitable set of degrees of freedom, such as polarization modes, time modes, etc., can be used without departing from the scope of this invention. For example, for modes that differ only in polarization (e.g., horizontal (H) and vertical (V)), the mode coupler can be any optical element with coherently rotating polarization, such as a birefringent material, such as a waveplate. For other systems, such as ion trap systems or neutral atom systems, the mode coupler can be any physical mechanism capable of coupling two modes, such as a pulsed electromagnetic field tuned to couple two internal states of an atom / ion.

[0136] In some embodiments of optical quantum computing systems using dual-track coding, qubits can be implemented using a pair of waveguides. Figure 11ATwo representations (1100, 1100') of a portion of a pair of waveguides 1102, 1104 are shown, which can be used to provide a dual-track encoded optical qubit. At 1100, photon 1106 is in waveguide 1102, and no photon is in waveguide 1104 (also known as the vacuum mode); in some embodiments, this corresponds to the |0> state of the optical qubit. At 1100', photon 1108 is in waveguide 1104, and no photon is in waveguide 1102; in some embodiments, this corresponds to the |1> state of the optical qubit. To prepare an optical qubit in a known state, a photon source (not shown) can be coupled to one end of a waveguide. The photon source can be manipulated to emit single photons into the waveguide to which it is coupled, thereby preparing an optical qubit in a known state. Photons travel through the waveguides, and by periodically manipulating the photon source, a quantum system with qubits can be created in the same pair of waveguides, the logical states of which map to different time modes of the photonic system. Furthermore, by providing multiple pairs of waveguides, quantum systems with qubits can be created, where the logical states of these qubits correspond to different spacetime modes. It should be understood that the waveguides in such a system do not need to have any specific spatial relationship with each other. For example, they can, but do not need to, be arranged in parallel.

[0137] Occupied modes can be created by generating photons using a photon source, which then propagates in the desired waveguide. The photon source can be, for example, a resonator-based source emitting photon pairs, also known as a declared single-photon source. In one example of such a source, the source is driven by a pump (e.g., a light pulse) coupled to an optical resonator system that can generate a pair of photons through a nonlinear optical process (e.g., spontaneous four-wave mixing (SFWM), spontaneous parametric down-conversion (SPDC), second harmonic generation, etc.). Many different types of photon sources can be employed. Examples of photon pair sources can include a microring-based spontaneous four-wave mixing (SPFW) declared photon source (HPS). However, the exact type of photon source used is not critical, and any type of source employing any process, such as SPFW, SPDC, or any other process, can be used. Other types of sources that do not necessarily require nonlinear materials can also be used, such as sources employing atomic and / or artificial atomic systems, such as quantum dot sources, color centers in crystals, etc. In some cases, the source may or may not be a photonic cavity, or it may or may not be coupled to a photonic cavity, as is the case for artificial atom systems, such as quantum dots coupled to a cavity. Other types of photonic sources also exist, such as optomechanical systems, in addition to SPWM and SPDC.

[0138] In this context, the operation of the photon source can be deterministic or nondeterministic (sometimes referred to as "stochastic"), such that a given pump pulse may or may not produce photon pairs. In some embodiments, coherent spatial and / or temporal multiplexing of several nondeterministic sources (referred to herein as "active" multiplexing) can be used to allow the probability of a mode being occupied during a given period to approach 1. Those skilled in the art will understand that many different active multiplexing architectures incorporating spatial and / or temporal multiplexing are possible. For example, active multiplexing schemes employing logarithmic trees, generalized Mach-Zehnder interferometers, multimode interferometers, linked sources, linked sources with dump pump schemes, asymmetric polycrystalline single-photon sources, or any other type of active multiplexing architecture can be used. In some embodiments, the photon source may employ an active multiplexing scheme with quantum feedback control, etc.

[0139] Measurement operations can be implemented by coupling a waveguide to a single-photon detector that generates a classical signal (e.g., a digital logic signal) indicating that a photon has been detected. Any type of photodetector sensitive to single photons can be used. In some embodiments, the detection of a photon (e.g., at the output of the waveguide) indicates an occupied mode, while the absence of a detected photon indicates an unoccupied mode. In some embodiments, the measurement operation is performed in a specific basis (e.g., a basis defined by a Pauli matrix and referred to as X, Y, or Z), and mode coupling as described below can be applied to transform the qubit to the specific basis.

[0140] The embodiments described below relate to the physical implementation of unitary transformation operations of modes in a coupled quantum system, which can be understood as transforming the quantum states of the system. For example, if the initial state of the quantum system (before mode coupling) is a state in which one mode is occupied by probability 1 and the other mode is not occupied by probability 1 (e.g., state |10> in Fokker notation, where the numbers indicate the occupancy of each state), then mode coupling can result in a state in which both modes have a non-zero probability of being occupied, for example, state a1|10>+a2|01>, where |a1| 2 +|a2| 2 =1. In some embodiments, this operation can be achieved by using a beam splitter to couple the modes together and using a variable phase shifter to apply a phase shift to one or more modes. Amplitudes a1 and a2 depend on the reflectivity (or transmittance) of the beam splitter and any phase shift introduced.

[0141] Figure 11BA schematic diagram 1110 (also known as a circuit diagram or circuit symbol) for coupling two modes is shown. The modes are drawn as horizontal lines 1112, 1114, and the mode coupler 1116 is indicated by vertical lines terminating at nodes (solid dots) to identify the coupled modes. In the more specific language of linear quantum optics, Figure 11B The mode coupler 1116 shown represents a 50 / 50 beam splitter that implements the transfer matrix:

[0142]

[0143] Here, T defines a linear mapping of the photon generation operator across the two modes. (In some contexts, the transition matrix T can be understood as implementing a first-order fictitious Hadamard transformation.) By convention, if the system includes more than two modes, the first column of the transition matrix corresponds to the generation operator on the top mode (referred to as mode 1 in this paper, denoted by horizontal line 1112), and the second column corresponds to the generation operator on the second mode (referred to as mode 2 in this paper, denoted by horizontal line 1114), and so on. More specifically, the mapping can be written as:

[0144]

[0145] Wherein, the subscript on the generator operator indicates the mode being operated on, the subscript input and output identify the form of the generator operator before and after the beam splitter, respectively, and wherein:

[0146]

[0147] For example, Figure 11B The application of the pattern coupler shown results in the following mapping:

[0148]

[0149]

[0150] Therefore, the function of the mode coupler described in equation (4) is to transform the input states |10>, |01>, and |11> into:

[0151]

[0152] Figure 11CA physical implementation of mode coupling according to some embodiments is shown, which achieves the transfer matrix T of equation (4) for two photonic modes. In this example, mode coupling is achieved using a waveguide beamsplitter 1120 (sometimes also called a directional coupler or mode coupler). The waveguide beamsplitter 1120 can be implemented by bringing two waveguides 1122, 1124 close enough that the evanescent field of one waveguide can be coupled to the other. Different couplings between modes can be obtained by adjusting the spacing d between waveguides 1122, 1124 and / or the length l of the coupling region. Thus, the waveguide beamsplitter 1120 can be configured to have a desired transmittance. For example, the beamsplitter can be designed to have a transmittance equal to 0.5 (i.e., a 50 / 50 beamsplitter for implementing the specific form of the transfer matrix T described above). If other transfer matrices are desired, the reflectivity (or transmittance) can be designed to be greater than 0.6, greater than 0.7, greater than 0.8, or greater than 0.9 without departing from the scope of the invention.

[0153] Besides mode coupling, some monotropic transformations can involve phase shifts applied to one or more modes. In some photonic implementations, variable phase shifters can be implemented in integrated circuits, thereby providing control over the relative phases of photonic states diffused across multiple modes. An example of a transfer matrix defining such a phase shift is given by the following equation (used to apply +i and -i phase shifts to the second mode, respectively):

[0154]

[0155]

[0156] For silicon-based silicon dioxide materials, some embodiments use thermo-optic switches to implement variable phase shifters. Thermo-optic switches utilize resistive elements fabricated on the chip surface, which, via a thermo-optic effect, can provide a change in refractive index n by raising the waveguide temperature by an amount on the order of 10⁻⁵ K. Those skilled in the art, who have access to this disclosure, will understand that any effect that changes the refractive index of a portion of the waveguide can be used to generate a variable, electrically tunable phase shift. For example, some embodiments use beam splitters based on any material that supports the electro-optic effect, any material being so-called x² and x³ materials (e.g., lithium niobite, BBO, KTP, BTO, PZT, etc.), or even doped semiconductors (e.g., silicon, germanium, etc.).

[0157] 5.2 Photonic Mode Coupler: Beam Splitter

[0158] By combining a directional coupler and a variable phase shifter in a Mach-Zehnder interferometer (MZI) configuration 1130, a beam splitter with variable transmittance and arbitrary phase relationships between output modes can also be realized, for example, as... Figure 11DAs shown. By changing the phase imparted by phase shifters 1136a, 1136b and 1136c, as well as the length and proximity of coupling regions 1134a and 1134b, complete control over the relative phase and amplitude of the two modes 1132a and 1132b in dual-track encoding can be achieved. Figure 11E A slightly simplified example of the MZI 1140 is shown, which allows for variable transmittance between modes 1132a and 1132b by changing the phase imparted by the phase shifter 1137. Figure 11D and Figure 11E This is an example of how a mode coupler can be implemented in a physical device, but any type of mode coupler / beam splitter can be used without departing from the scope of the invention.

[0159] In some embodiments, beam splitters and phase shifters can be combined to implement various transfer matrices. For example, Figure 12A With similar Figure 11A A schematic representation of a mode coupler 1200 implementing the following transition matrix is ​​shown:

[0160]

[0161] Therefore, the mode coupler 1200 applies the following mapping:

[0162]

[0163] The transition matrix T of equation (10) r The phase shift in the second mode is related to the transition matrix T of equation (4). This is in Figure 12A The closed node 1207, coupled to the first mode (line 1212), and the open node 1208, coupled to the second mode (line 1214), are schematically illustrated via mode coupler 1216. More specifically, T r =sTs, and as Figure 12A As shown on the right-hand side, the mode coupler 1216 can be implemented using a mode coupler 1216 (as described above) with front and rear phase shifts (represented by hollow squares 1218a, 1218b). Therefore, the transition matrix T r It can be by Figure 12B The physical beam splitter shown is used to achieve this, where the hollow triangle represents +i phase shifters.

[0164] 5.3 Exemplary Photon Diffusing Circuit

[0165] Networks of mode couplers and phase shifters can be used to achieve coupling between more than two modes. For example, Figure 13A four-mode coupling scheme is illustrated, which implements a "diffuser" or "mode information erasure" transformation for the four modes. That is, it acquires photons in any input mode and delocalizes the photons between each of the four output modes, such that the probability of a photon being detected is equal in any of the four output modes. (The well-known Hadamard transform is an example of a diffuser transform.) Figure 11A Similar to the diagram, horizontal lines 1312-1315 correspond to modes, and mode coupling is indicated by vertical line 1316, which has nodes (points) identifying the coupled modes. In this case, four modes are coupled. Circuit symbol 1302 is an equivalent representation of circuit diagram 1304, which is a first-order mode-coupled network. More generally, where higher-order mode coupling can be implemented as a first-order mode-coupled network, a circuit symbol similar to symbol 1302 (with an appropriate number of modes) can be used.

[0166] Figure 14 Examples of implementations according to some embodiments are illustrated. Figure 13 An example optical device 1400 schematically illustrates a four-mode diffusion transformation. The optical device 1400 includes components formed in a first material layer (composed of…). Figure 14 The first set of optical waveguides 1401 and 1403 (represented by solid lines in the image) and the second material layer (formed on a different and separate material layer from the first material layer) are shown in the image. Figure 14 The second set of optical waveguides, 1405 and 1407 (represented by dashed lines in the image), are shown. The second material layer and the first material layer are located at different heights on the substrate. Those skilled in the art will understand that, for example, if appropriate low-loss waveguide crossings are employed, Figure 14 The interferometer shown can be implemented in a single layer.

[0167] At least one optical waveguide 1401, 1403 in the first group of optical waveguides is coupled to optical waveguides 1405, 1407 in the second group of optical waveguides using any type of suitable optical coupler. For example, Figure 14 The optical device shown includes four optical couplers 1418, 1420, 1422, and 1424. Each optical coupler may have a coupling region in which the two waveguides propagate in parallel. Although in Figure 14The two waveguides are illustrated as offset from each other in the coupling region, but the two waveguides can be positioned directly above and below each other in the coupling region without offset. In some embodiments, one or more of the optical couplers 1418, 1420, 1422, and 1424 are configured to have a coupling efficiency of approximately 50% between the two waveguides (e.g., coupling efficiency between 49% and 51%, coupling efficiency between 49.9% and 50.1%, coupling efficiency between 49.99% and 50.01%, and 50%, etc.). For example, the lengths of the two waveguides, the refractive indices of the two waveguides, the widths and heights of the two waveguides, the refractive index of the material between the two waveguides, and the distance between the two waveguides are selected to provide a 50% coupling efficiency between the two waveguides. This allows the optical coupler to operate like a 50 / 50 beam splitter.

[0168] in addition, Figure 14 The illustrated optical device may include two interlayer optical couplers 1414 and 1416. Optical coupler 1414 allows light propagating in a waveguide on a first material layer to be transmitted to a waveguide on a second material layer, and optical coupler 1416 allows light propagating in a waveguide on a second material layer to be transmitted to a waveguide on a first material layer. Optical couplers 1414 and 1416 allow optical waveguides located in at least two different layers to be used in a multi-channel optical coupler, which in turn enables the realization of a compact multi-channel optical coupler.

[0169] also, Figure 14 The optical device shown includes an uncoupled waveguide crossover region 1426. In some implementations, two waveguides (1403 and 1405 in this example) cross each other, and there is no parallel coupling region at the crossover in the uncoupled waveguide crossover region 1426 (e.g., the waveguides could be two straight waveguides that cross each other at an angle of approximately 90 degrees).

[0170] Those skilled in the art will understand that the foregoing examples are illustrative, and that photonic circuits using beam splitters and / or phase shifters can be used to implement many different transfer matrices, including those for real and imaginary Hadamard transforms, discrete Fourier transforms, etc., of any order. One class of photonic circuits (referred to herein as “diffusers” or “mode information erasure (MIE)” circuits) has the property that if the input is a single photon located in an input mode, the circuit delocalizes the photon between each of several output modes, such that the photon has an equal probability of being detected in any output mode. Examples of diffuser or MIE circuits include circuits that implement Hadamard transfer matrices. (It should be understood that diffuser or MIE circuits can receive inputs of single photons not located in an input mode, and in this case, the behavior of the circuit depends on the specific transfer matrix implemented.) In other cases, photonic circuits can implement other transfer matrices, including those that provide unequal probabilities of detecting photons in different output modes for a single photon in an input mode.

[0171] 5.4 Example Photonic Bell State Generator Circuit

[0172] A Bell pair is a pair of qubits in any type of maximally entangled state (called a Bell state). Examples of Bell states (also called Bell ground states) for dual-track encoded qubits include:

[0173]

[0174]

[0175]

[0176]

[0177] In a computational basis (e.g., a logic basis) with two states, a Greenberger-Horne-Zeilinger state is a quantum superposition of all qubits in the first state and all qubits in the second state. Using the above logic basis, a general M-qubit GHZ state can be written as:

[0178]

[0179] In some embodiments, entangled states of multiple optical qubits can be generated by coupling modes of two (or more) qubits and measuring other modes. For example, Figure 15A circuit diagram of a Bell state generator 1500 that can be used in some dual-track encoded photonic embodiments is shown. In this example, modes 1532(1)-1532(4) are initially occupied by photons (indicated by wavy lines); modes 1532(5)-1532(8) are initially vacuum modes. (Those skilled in the art will understand that other combinations of occupied and unoccupied modes can be used).

[0180] First-order mode coupling is performed on occupied and unoccupied mode pairs as shown by mode couplers 1531(1)-1531(4) (e.g., implementing the transition matrix T of equation (4)). Subsequently, mode information erasure coupling is performed on the four modes (modes 1532(5)-1532(8)) as shown by mode coupler 1537 (e.g., implementing the transition matrix T of equation (4)). Figure 13 (The four-mode diffusion transformation is shown). Modes 1532(5)-1532(8) act as “announcement” modes, which are measured and used to determine whether a Bell state has been successfully generated on the other four modes 1532(1)-1532(4). For example, detectors 1538(1)-1538(4) can be coupled to modes 1532(5)-1532(8) after a second-order mode coupler 1537. Each detector 1538(1)-1538(4) can output classical data signals (e.g., voltage levels on conductors) indicating whether it has detected photons (or the number of photons detected). These outputs can be coupled to classical decision logic circuit 1540, which determines, based on the classical output data, whether a Bell state exists on the other four modes 1532(1)-1532(4). For example, the decision logic circuit 1540 can be configured such that a Bell state (also known as the "success" of the Bell state generator) is confirmed only if a single photon is detected by exactly one of the detectors 1538(1)-1538(4). Modes 1532(1)-1532(4) can be mapped to the logic states of two qubits (qubit 1 and qubit 2), as follows Figure 15 Instructions. Specifically, in this example, the logical state of qubit 1 is based on the occupation of modes 1532(1) and 1532(2), and the logical state of qubit 2 is based on the occupation of modes 1532(3) and 1532(4). It should be noted that the operation of the Bell state generator 1500 can be nondeterministic; that is, inputting four photons as shown in the figure does not guarantee the generation of Bell states in modes 1532(1)-1532(4). In one implementation, the success probability is 4 / 32.

[0181] In some embodiments, it is desirable to form resource states of multiple entangled qubits (typically three or more qubits, but a Bell state can be understood as a resource state of two qubits). One technique for forming larger entangled systems is by using a "fusion" gate. A fusion gate receives two input qubits, each typically part of an entangled system. The fusion gate performs a "fusion" operation on the input qubits, producing one ("Type I fusion") or zero ("Type II fusion") output qubits in such a way that the initial two entangled systems are fused into a single entangled system. The fusion gate is a concrete example of a general class of two-particle projection measurements, which can be used to generate entanglement between qubits and are particularly well-suited for photonic architectures. Examples of Type I and Type II fusion gates will now be described.

[0182] 6. Examples of fused gate photonic circuits

[0183] Figures 16 to 21 Examples of photonic circuit implementations of fusion gates or fusion circuits for optical qubits, which can be used according to some embodiments employing type II fusion, are shown. It should be understood that these example embodiments are illustrative and not limiting. More generally, as used herein, the term "fusion gate" refers to a device capable of implementing two-particle projection measurements (e.g., Bell projection), which can measure two operators, such as operators XX, ZZ, XX, ZY, etc., based on a chosen Bell basis. In polarization coding, a type II fusion circuit (or gate) takes two input modes, mixes them at a polarization beam splitter (PBS), and then rotates each of them by 45° before measuring them in the computational basis. Figure 16 An example is shown. In path coding, the Type II fusion circuit uses four modes, swaps the second and fourth modes, applies a 50:50 beam splitter between two pairs of adjacent modes, and then detects all modes. Figure 17 An example is shown.

[0184] By utilizing the so-called "redundant coding" of qubits, fusion gates can be used to construct large entangled states. This is because a single qubit is represented by multiple photons, i.e.,

[0185]

[0186] This allows logical qubits to be encoded in n individual qubits. This is achieved by measuring adjacent qubits in the X basis.

[0187] This encoding (graphically represented as n qubits with no edges between them, as shown in Figure 18(b))) has the following advantages: Pauli measurements on redundant qubits do not split the cluster, but rather remove photons measured from the redundant encoding and combine adjacent qubits into a single qubit that inherits the combination of the input qubits, potentially adding phase. Another advantage of this type of fusion is its robustness to loss. Two modes are measured, therefore it is impossible to obtain a detection mode that declares success when a photon is lost. Finally, Type II fusion does not require distinguishing between different photon counts because both detectors need to click to declare a successful fusion, and this only occurs when the photon count at each detector is 1.

[0188] When a single photon is detected at each detector in the polarization coding, fusion succeeds with a 50% probability. In this case, the gate effectively performs Bell state measurements on the qubits sent through it, thus projecting the logical qubit pairs into maximally entangled states. When the gate fails (as announced by zero or two photons at a detector), it performs measurements on the individual photons in the computational basis, thereby removing them from the redundant coding without destroying the logical qubits. Figures 18A to 18D The effect of fusion on generated clusters is described in the text, where, Figure 18A and Figure 18B The measurement of a qubit in a linear cluster in the X basis is shown to combine that qubit with its neighbors into a single logical qubit, and Figure 18C and Figure 18D The effects of successful and unsuccessful gate fusions on the cluster structure are shown. It can be seen that successful fusions allow for the construction of two-dimensional clusters.

[0189] The correspondence between the detection mode and the Kraus operator implemented by the gate in that state can be retrieved. In this case, since both qubits are detected, these qubits are projection operators:

[0190]

[0191]

[0192]

[0193]

[0194] The first two rows correspond to the "success" result, which projects the two qubits into a Bell state, and the last two rows correspond to the "failure" result, in which case the two qubits are projected into a product state.

[0195] In some embodiments, the success probability of type II fusion can be increased by using an auxiliary Bell pair or a single-photon pair. Using a single auxiliary Bell pair or two single-photon pairs allows the success probability to be increased to 75%.

[0196] One technique for enhancing fusion gates stems from the understanding that, when successful, it is equivalent to a Bell state measurement of the input qubit. Therefore, increasing the success probability of a fusion gate corresponds to increasing the success probability of the Bell state measurement it performs. Grice (using Bell pairs) and Ewert, and van Loock (https: / / arxiv.org / pdf / 1403.4841.pdf) (using single photons) have developed two different techniques to improve the probability of distinguishing Bell states.

[0197] The former shows that an assisted Bell pair allows for a 75% success probability, and theoretically, the process can be iterated using increasingly complex interferometers and large entangled states to achieve arbitrary success probabilities. However, the complexity of the circuit and the necessary size of the entangled states may make this impractical.

[0198] The second technique utilizes four single photons (input in pairs with opposite polarizations in two modes) to increase the success rate to 75%. It has also been shown, numerically, that the process can be iterated a second time to achieve a probability of 78.125%, but it has not been shown that the success rate can be arbitrarily increased as with other schemes.

[0199] Figure 19 This demonstrates a Type II fusion gate enhanced once using both polarization and path coding techniques. Both circuits have a success rate of 75%.

[0200] The following describes the detection mode for announcing the successful fusion of the two types of circuits.

[0201] When Bell states are used to enhance fusion, the logic behind the "successful" detection mode is best understood by considering two pairs of detectors: one pair corresponds to the input photon modes (polarization modes 1 and 2, the top 4 modes of path coding) and the other corresponds to the Bell pair input modes (polarization modes 3 and 4, the bottom 4 modes of path coding). These pairs are referred to as the "master" pair and the "auxiliary" pair, respectively. Then, successful fusion is declared whenever: (a) a total of 4 photons are detected; and (b) fewer than 4 photons are detected in each pair of detectors.

[0202] When four single photons are used as auxiliary resources, the gate is declared successful whenever the following occurs: (a) a total of six photons are detected; and (b) fewer than four photons are detected at each detector.

[0203] When the gate succeeds, the two input qubits are projected onto one of the four Bell pairs, since these qubits are distinguishable from each other due to the use of auxiliary resources. The specific projection depends on the detection mode obtained as described above.

[0204] If the auxiliary components are absent or only some of them are present (in the case of four single-photon auxiliary components), two enhanced type II fusion circuits, designed to use one Bell pair and four single-photon auxiliary components respectively, can be used to perform type II fusion with variable success probabilities. This is particularly useful because it allows for flexible fusion execution using the same circuitry, depending on available resources. If the auxiliary components are present, they can be fed into the gates to increase the probability of successful fusion. However, if the auxiliary components are absent, the gates can still be used to attempt fusion with a lower but non-zero probability of success.

[0205] For a fusion gate enhanced by a Bell pair, the only case that needs to be considered is the absence of an auxiliary detector. In this case, the logic of the declared successful detection mode can be understood by reconsidering the detectors in the aforementioned pair. Fusion is still successful in the following cases: (a) detecting two photons at different detectors; and (b) detecting one photon in the "main" detector pair and one photon in the "auxiliary" detector pair.

[0206] With the circuitry using four single-photon enhancements, multiple modifications are possible, allowing for the removal of all or part of the auxiliary components. This is analogous to an enhanced Bell state generator based on the same principle.

[0207] First, consider the case where there are no auxiliary materials at all. As expected, fusion succeeds with a 50% probability, which is the success rate of unenhanced fusion. In this case, fusion succeeds as long as two photons are detected at any two different detectors.

[0208] For the enhanced BSG, the presence of an odd number of aids proves to be detrimental to the gate's success probability: if there is 1 photon, the gate succeeds only 32.5% of the time, while if there are 3 photons, the success probability is 50%, similar to the unenhanced case.

[0209] If only two of the four auxiliary items exist, there are two possible effects.

[0210] If they are input in different modes in polarization coding, i.e., input in different adjacent auxiliary modes in path coding, the success probability drops to 25%.

[0211] However, if the two aids are input with the same polarization pattern, i.e., in the same adjacent pattern pair in the path coding, the success probability increases to 62.5%. In this case, the declared successful pattern can be understood again by grouping the detectors into two pairs (a pair in the circuit branch of the input aid (Group 1) and a pair in the other branch (Group 2)). This distinction is particularly clear in the polarization coding diagram. Considering these groups, fusion succeeds when: (a) a total of 4 photons are detected; (b) fewer than 4 photons are detected at each detector in Group 1; and (c) fewer than 2 photons are detected at each detector in Group 2.

[0212] In these examples, the fusion gate works by projecting the input qubits into a maximally entangled state upon success. The basis encoding this state can be altered by introducing a local rotation of the input qubits before they enter the gate (i.e., before they are mixed at the PBS in polarization coding). Changing the polarization rotation of a photon before it interferes at the PBS results in the photon's state being projected into a different subspace, leading to different fusion operations on the cluster states. In path coding, this corresponds to applying a local beam splitter or a combination of beam splitters and phase shifts, which correspond to the desired rotation between the mode pairs constituting the qubits (adjacent pairs in the above figure).

[0213] This can be useful for implementing different types of cluster operations in both success and failure scenarios, and it is particularly useful for optimizing the construction of large cluster states from small entangled states.

[0214] Figure 20 A table showing the effects of some rotational variations of a type II fusion gate for fusing two small entangled states is presented. A diagram of the gate in polarization encoding, the effective projection performed, and the final effect on the cluster state are shown.

[0215] Figure 21 The diagram further illustrates rotations to different ground states, showing examples of photonic circuits using a type II fusion gate implementation with path coding. Fusion gates for ZX fusion, XX fusion, ZZ fusion, and XZ fusion are shown. In various cases, combinations of beam splitters and phase shifters (e.g., as described above) can be used.

[0216] 7. Additional Examples

[0217] Those skilled in the art will understand that the embodiments described herein are illustrative and not restrictive, and many modifications and variations are possible. The measurements performed and the states in which they operate can be selected to allow for redundancy in the measurement results, which introduces fault tolerance. For example, the code can be directly input along with the measurement, or correlations can be generated within the measurement, directly addressing the destructive and entanglement-destructive properties of the measurement in a fault-tolerant manner. This can be handled as part of classical decoding; for example, a failed fusion operation can be treated as code erasure.

[0218] Referring to the accompanying drawings, components that may include memory may include non-transient machine-readable media. As used herein, the terms "machine-readable media" and "computer-readable media" refer to any storage medium involved in providing data that enables a machine to operate in a particular manner. In the embodiments provided above, various machine-readable media may be involved in providing instructions / code to a processor and / or one or more other devices for execution. Additionally or alternatively, machine-readable media may be used to store and / or carry such instructions / code. In many implementations, computer-readable media are physical and / or tangible storage media. Such media can take many forms, including but not limited to non-volatile media, volatile media, and transmission media. Common forms of computer-readable media include, for example, magnetic and / or optical media, punched cards, paper tape, any other physical media with a perforated pattern, RAM, programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), FLASH-EPROM, any other memory chip or cartridge, a carrier wave as described below, or any other medium from which a computer can read instructions and / or code.

[0219] The methods, systems, and devices discussed herein are examples. Various processes or components may be appropriately omitted, substituted, or added in various embodiments. For example, features described with respect to certain embodiments may be combined in various other embodiments. Different aspects and elements of embodiments may be combined in a similar manner. The various components of the accompanying drawings provided herein can be embodied in hardware and / or software. Moreover, technology is evolving, and therefore many elements are not intended to limit the scope of the invention to those specific examples.

[0220] Primarily for general reasons, referring to such signals as bits, information, values, elements, symbols, characters, variables, terms, numbers, etc., has proven convenient in some cases. However, it should be understood that all these or similar terms are associated with appropriate physical quantities and are merely convenient notations. Unless otherwise specifically stated, as is apparent from the foregoing discussion, it should be understood that throughout this invention, discussions using terms such as “processing,” “calculating,” “determining,” “identifying,” “ascertaining,” “associating,” “measuring,” “executing,” etc., refer to the actions or processes of a particular device (e.g., a dedicated computer or similar dedicated electronic computing device). Therefore, in the context of this invention, a dedicated computer or similar dedicated electronic computing device is capable of manipulating or transforming signals that generally represent physical electronic quantities, electrical quantities, or magnetic quantities within the memory, registers, or other information storage devices, transmission devices, or display devices of the dedicated computer or similar dedicated electronic computing device.

[0221] Those skilled in the art will understand that any of a variety of different techniques and methods can be used to represent the information and signals used to transmit the messages described herein. For example, data, instructions, commands, information, signals, bits, symbols, and chips that may be mentioned throughout the foregoing description can be represented by voltage, current, electromagnetic waves, magnetic fields or magnetic particles, light fields or optical particles, or any combination thereof.

[0222] As used herein, the terms “and,” “or,” and “and / or” can have a variety of meanings, which are also contemplated to depend at least in part on the context in which they are used. Generally, “or,” when used with a list of related terms (e.g., A, B, or C), is intended to mean A, B, and C (used herein in an inclusive sense) and A, B, or C (used herein in an exclusive sense). Additionally, the term “one or more,” as used herein, can be used to describe any feature, structure, or characteristic in the singular form, or can be used to describe some combination of features, structures, or characteristics. However, it should be noted that this is merely an illustrative example, and the claimed subject matter is not limited to this example. Furthermore, the term “at least one of…” when used with a list of related terms (e.g., A, B, or C) can be interpreted as meaning any combination of A, B, and / or C, such as A, B, C, AB, AC, BC, AA, AAB, ABC, AABBCCC, etc.

[0223] Throughout this invention, references to “an example,” “example,” “some examples,” or “exemplary implementation” mean that a particular feature, structure, or characteristic described in conjunction with a feature and / or example may be included in at least one feature and / or example of the claimed subject matter. Therefore, the phrases “in an example,” “example,” “in some examples,” “in some implementations,” or other similar phrases appearing throughout this invention do not necessarily all refer to the same feature, example, and / or limitation. Furthermore, a particular feature, structure, or characteristic may be combined in one or more examples and / or features.

[0224] In some implementations, the operation or processing may involve the physical manipulation of a physical quantity. Typically, though not strictly necessary, such a quantity may take the form of an electrical or magnetic signal that can be stored, transferred, combined, compared, or otherwise manipulated. For general reasons, referring to such signals as bits, data, values, elements, symbols, characters, items, numbers, etc., has proven convenient in some cases. However, it should be understood that all these or similar terms are associated with the appropriate physical quantity and are merely convenient notations. Unless otherwise specifically stated, as will be apparent from the discussion herein, it should be understood that throughout this invention, discussions using terms such as “processing,” “calculation,” “determination,” etc., refer to the actions or processes of a particular device (e.g., a dedicated computer, dedicated computing device, or similar dedicated electronic computing device). Thus, in the context of this invention, a dedicated computer or similar dedicated electronic computing device is capable of manipulating or transforming signals that are generally represented as physical electronic or magnetic quantities within the memory, registers, or other information storage, transmission, or display devices of the dedicated computer or similar dedicated electronic computing device.

[0225] Numerous specific details have been set forth in the foregoing detailed description to provide a thorough understanding of the claimed subject matter. However, those skilled in the art will understand that the claimed subject matter can be practiced without these specific details. In other instances, methods and apparatus that would be understood by a person of ordinary skill have not been described in detail to avoid obscuring the claimed subject matter. Therefore, it is contemplated that the claimed subject matter is not limited to the specific examples disclosed, but rather that it may also include all aspects falling within the scope of the appended claims and their equivalents.

[0226] For implementations involving firmware and / or software, the methods can be implemented using modules (e.g., procedures, functions, etc.) that perform the functions described herein. Any machine-readable medium that tangibly implements the instructions can be used to implement the methods described herein. For example, software code can be stored in memory and executed by a processor unit. Memory can be implemented within or outside the processor unit. As used herein, the term "memory" refers to any type of long-term, short-term, volatile, non-volatile, or other memory, and is not limited to any particular type of memory or any particular quantity of memory, or the type of medium on which memory is stored.

[0227] If implemented in firmware and / or software, functionality can be stored as one or more instructions or code on a computer-readable storage medium. Examples include computer-readable media encoding data structures and computer-readable media encoding computer programs. Computer-readable media include physical computer storage media. Storage media can be any available medium accessible to a computer. By way of example and not limitation, such computer-readable media can include RAM, ROM, EEPROM, optical disc read-only memory (CD-ROM) or other optical disc storage, disk storage, semiconductor storage, or other storage devices, or any other medium that can be used to store desired program code in the form of instructions or data structures and that can be accessed by a computer; as used herein, disks and optical discs include compact optical discs (CDs), laser optical discs, optical discs, digital versatile optical discs (DVDs), floppy disks, and Blu-ray discs, wherein disks typically reproduce data magnetically, while optical discs reproduce data optically using lasers. Combinations of the above should also be included within the scope of computer-readable media.

[0228] In addition to being stored on a computer-readable storage medium, instructions and / or data may be provided as signals on a transmission medium included in the communication device. For example, the communication device may include a transceiver having signals indicating instructions and data. The instructions and data are configured to cause one or more processors to perform the functions outlined in the claims. That is, the communication device includes a transmission medium having signals indicating information for performing the disclosed functions. At a first time, the transmission medium included in the communication device may include a first portion of the information for performing the disclosed functions, while at a second time, the transmission medium included in the communication device may include a second portion of the information for performing the disclosed functions.

[0229] All patent applications, patents, and print publications cited herein are incorporated herein by reference in their entirety, except for any definitions, subject matter disclaimers, or denials, and unless the incorporated material is inconsistent with the express disclosure herein, in which case the language of this invention shall prevail.

Claims

1. A method for determining calibration subgraph values ​​for quantum computing using a quantum system, the method comprising: Multiple quantum systems are received through a qubit fusion system, wherein each of the multiple quantum systems comprises multiple quantum subsystems in an entangled state, and wherein the corresponding quantum systems in the multiple quantum systems are independent quantum systems that are not entangled with each other. The qubit fusion system performs multiple joint measurements on different quantum subsystems from corresponding quantum systems among the plurality of quantum systems, wherein the joint measurements are destructive to the input quantum subsystems and generate joint measurement result data; and The decoder determines multiple correction subgraph values ​​based on the joint measurement result data.

2. The method according to claim 1, wherein, Performing the joint measurement includes performing a Type II fusion operation.

3. The method according to claim 1, wherein, Performing the multiple joint measurements on different quantum subsystems from the respective quantum systems in the plurality of quantum systems includes performing the multiple joint measurements only on a subset of the plurality of quantum subsystems received by the qubit fusion system, thereby producing a subset of unmeasured quantum subsystems.

4. The method according to claim 3, further comprising: The quantum bit fusion system receives multiple second quantum systems, wherein each of the multiple second quantum systems comprises multiple second quantum subsystems in an entangled state, and wherein the corresponding quantum systems in the multiple second quantum systems are independent quantum systems that are not entangled with each other. Receive a subset of the unmeasured quantum subsystem; and The qubit fusion system performs multiple second joint measurements between i) a second quantum subsystem from a corresponding second quantum system in one of the plurality of second quantum systems and ii) a corresponding quantum subsystem from a subset of the unmeasured quantum subsystems, wherein the plurality of second joint measurements generate second joint measurement result data.

5. The method according to claim 1, wherein each of the plurality of quantum systems comprises 3 to 30 qubits.

6. A system for determining calibration subgraph values ​​for quantum computing using a quantum system, comprising: A qubit fusion system including multiple fusion gates, wherein the qubit fusion system is configured to receive multiple quantum systems, wherein each of the multiple quantum systems includes multiple quantum subsystems in an entangled state, and wherein the corresponding quantum systems in the multiple quantum systems are independent quantum systems that are not entangled with each other. Each of the plurality of fusion gates is configured to perform a joint measurement on different quantum subsystems from corresponding quantum systems in the plurality of quantum systems, wherein the joint measurement is destructive to the input quantum subsystem and generates joint measurement result data; and A decoder, communicatively coupled to the qubit fusion system, is configured to receive the joint measurement result data and determine multiple correction subgraph values ​​based on the joint measurement result data.

7. The system according to claim 6, wherein, The fusion gate includes a photonic circuit, and the plurality of quantum systems include photons as quantum subsystems, wherein the photonic circuit includes a type II fusion gate.

8. The system according to claim 6, wherein, The joint measurement includes a two-particle projection measurement onto the Belki.

9. The system according to claim 6, further comprising: A quantum memory coupled to at least one of the said qubit fusion systems and receiving and storing a subset of the plurality of quantum subsystems.

10. The system according to claim 9, wherein, The quantum memory is an optical fiber.

11. The system according to claim 9, wherein, The quantum memory is coupled to the qubit fusion system such that the joint measurement is performed between i) a quantum subsystem from a corresponding quantum system of one of the plurality of quantum systems and ii) a corresponding quantum subsystem from a subset of the plurality of quantum subsystems stored in the quantum memory.

12. The system according to claim 6, further comprising: A qubit entanglement system configured to generate the plurality of quantum systems.

13. The system according to claim 12, wherein, The entangled qubit system includes a quantum gate array.

14. The system according to claim 13, wherein, The qubit entanglement system includes: a photon source system optically connected to the entanglement state generator.

15. The system according to claim 14, wherein, The entangled state generator is configured to receive output photons from the photon source system and convert the output photons into entangled photon states.

16. The system according to claim 15, wherein, The entangled quantum bit system includes a plurality of output waveguides optically coupled to the quantum bit fusion system and configured to provide the entangled photonic state to the input of the fusion gate.

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