A decoding method and device for topological quantum error correction based on a coherent Ising machine

Abstract

The application provides a quantum error correction decoding method and device, the method comprising: firstly, measuring error syndromes of a surface code in a quantum computer using the surface code to perform topological quantum error correction; then, converting a decoding problem into a problem of solving a Hamiltonian ground state, and solving the Hamiltonian ground state by using a coherent Ising machine system; and finally, determining quantum bits with errors according to the Hamiltonian ground state. The topological quantum error correction decoding method based on the coherent Ising machine can obtain a solution with higher precision than a classical computer, and is especially suitable for topological quantum error correction decoding of multiple bits. The method introduces the coherent Ising machine system into quantum error correction, improves the operation complexity of a quantum decoding algorithm, and has scalability and potential acceleration advantages.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of quantum computing, and particularly relates to a decoding method and device for topological quantum error correction based on a coherent Ising machine. BACKGROUND

[0002] Quantum computers show potential to outperform classical computers in certain specific tasks, however, quantum bits are inevitably affected by noise during operation and thus errors occur. Quantum error correction techniques are crucial to eliminate these errors. The process of quantum error correction is as follows: first, encode quantum information on multiple quantum bits through quantum error-correcting codes (such as Shor code, Steane code or surface code), then detect errors by measuring specific ancillary bit stabilizer operators, then determine the location and type of errors through quantum decoding, and finally apply a series of quantum operations to correct these errors, thereby protecting quantum information from noise and decoherence, ensuring the accuracy and reliability of quantum computing.

[0003] Among them, the process of quantum decoding is particularly critical. This process needs to accurately detect and locate errors from the measurement results of stabilizers, and needs to have both accuracy and high efficiency, involving complex algorithms, which are often hindered by computational limitations.

[0004] In the field of quantum information, the Minimum Weight Perfect Matching (MWPM) technique is commonly used for quantum error correction decoding. This method is particularly suitable for processing surface codes (Surface codes) and other topological quantum error correction codes. The following are the general steps of MWPM algorithm for quantum error correction decoding:

[0005] 1. Error model and error identification

[0006] First, the error model that the quantum system may encounter needs to be defined, such as bit flip (X error), phase flip (Z error) or their combination. By measuring the stabilizer operators, it is identified whether there is an error in the region, and the error syndrome on the quantum bits is identified, the location of the error syndrome provides important clues about the location of the error.

[0007] 2. Constructing a graph model

[0008] Based on the measured error syndromes, a graph model is constructed, in which the vertices represent error syndromes, and the edges represent possible error paths. Specifically, each two vertices can be connected by an edge, which represents a possible error path, i.e. a series of errors that can lead to the association between two error syndromes. The weight of the edge should be inversely proportional to the probability of the occurrence of the error path. In the simplest case, it is assumed that the probability of error occurring at each position is uniform, and then the weight is proportional to the length of the error path. The specific calculation of the weight is usually based on the error model. For example, in a system with uniform error rate, the edge weight is proportional to the number of physical qubits on the path.

[0009] 3. Minimum weight perfect matching solution

[0010] The MWPM algorithm is applied to find the edge set with the minimum total weight in the constructed graph, which represents the error pattern that is most likely to cause the observed error syndromes. According to the result of the MWPM solution, the most likely error path is found, i.e. the way in which errors are most likely to occur given the set of error syndromes, and then the corresponding quantum gate can be applied to correct the errors.

[0011] The surface code efficient decoder based on the MWPM algorithm was proposed in 2001 and has been carefully optimized over the past 20 years, but its computational complexity is relatively high, and as the number of encoded qubits increases, the problem of finding the minimum weight perfect matching becomes more complex, which can lead to a longer calculation time and more computing resources required for the decoding process. In addition, the MWPM decoding algorithm lacks scalability, and as the size of the quantum system increases, the problem of finding the minimum weight perfect matching can become infeasible. Therefore, there is an urgent need to find a quantum decoding method with higher decoding speed, accuracy and scalability. SUMMARY

[0012] To solve the above problems, the present application provides a quantum error correction decoding method and device.

[0013] According to the first aspect, a quantum error correction decoding method is provided, comprising the following steps:

[0014] S1, in a quantum computer using surface code to perform topological quantum error correction, measuring the error syndromes of the surface code.

[0015] S2, using a coherent Ising machine system, solving the ground state of a Hamiltonian, wherein the Hamiltonian is:

[0016]

[0017] wherein W ij and V i are coefficients related to error syndromes, and c is a constant related to error syndromes. Defined as:

[0018]

[0019] in, ,in Indicates the first Whether an error has occurred on each quantum bit; Represents auxiliary binary variables and , For the number of working bits, The number of auxiliary binary variables.

[0020] S3. Determine the qubit that has erred based on the ground state of the Hamiltonian.

[0021] In some embodiments, after determining the erroneous qubit, the method further includes: feeding the erroneous qubit back to the quantum computer for error correction.

[0022] In some embodiments, solving for the ground state of the Hamiltonian using a coherent Ising machine system specifically includes:

[0023] Based on the Hamiltonian, initialize the coherent Ising machine and initiate the coherent Ising machine system evolution process.

[0024] During the evolution of the coherent Ising machine system, the phase and intensity of the optical field within the coherent Ising machine system are measured multiple times. Based on the measurement results, the parameters of the coherent Ising machine system are adjusted in real time, and finally a collective oscillation mode is obtained. The quantum spin state in this mode corresponds to the ground state of the Hamiltonian.

[0025] In some embodiments, the coherent Ising machine system includes:

[0026] 1) Optical parametric oscillator network for simulating spin interactions in the Ising model.

[0027] 2) Phase-sensitive amplifier, used to amplify signals of a specific phase.

[0028] 3) Field-programmable gate array (FPGA) for controlling optical parametric oscillator networks.

[0029] 4) Phase / intensity measuring device, used to measure the phase and intensity of the optical field inside the cavity.

[0030] 5) Optical modulators are used to change the phase difference between beams, thereby simulating the interaction strength between different spin states.

[0031] 6) Beam splitter, used to generate interference effects and simulate the connection relationship between spins in the Ising model.

[0032] 7) optical fiber, used as a transmission medium for optical signals.

[0033] According to a second aspect, the present application provides a decoding device for topological quantum error correction, characterized in that comprising:

[0034] An acquisition module is configured to measure an error syndrome of a surface code in a quantum computer using the surface code to perform topological quantum error correction.

[0035] A solving module is configured to solve a ground state of a Hamiltonian using a coherent Ising machine system, the Hamiltonian being:

[0036]

[0037] wherein W ij and V i are coefficients related to the error syndrome, and c is a constant related to the error syndrome, defined as:

[0038]

[0039] wherein, wherein represents whether an error occurs on the i th qubit; represents an auxiliary binary variable and , is the number of working bits, is the number of auxiliary binary variables.

[0040] An output module is configured to determine the quantum bit in which an error occurs according to the ground state of the Hamiltonian.

[0041] In some embodiments, the output module is further configured to, after determining the quantum bit in which an error occurs, feed back the quantum bit in which an error occurs to the quantum computer for error correction.

[0042] In some embodiments, the solving module is specifically configured to:

[0043] According to the Hamiltonian, initialize the coherent Ising machine, and start the coherent Ising machine system evolution process.

[0044] During the coherent Ising machine system evolution process, the phase and intensity of the light field in the coherent Ising machine system are measured multiple times, and the parameters of the coherent Ising machine system are adjusted in real time according to the measurement results, and finally a collective oscillation mode is obtained, and the quantum spin state under this mode corresponds to the ground state of the Hamiltonian.

[0045] In some embodiments, the coherent Ising machine system comprises:

[0046] 1) Optical parametric oscillator network, used to simulate the spin interaction in the Ising model.

[0047] 2) Phase-sensitive amplifier, used to amplify signals of a specific phase.

[0048] 3) Field programmable gate array, used to control the optical parametric oscillator network.

[0049] 4) Phase / intensity measurer, used to measure the phase and intensity of the optical field in the cavity.

[0050] 5) Optical modulator, used to change the phase difference between the light beams, thereby simulating the interaction strength between different spin states.

[0051] 6) Beam splitter, used to produce interference effects to simulate the connection between spins in the Ising model.

[0052] 7) Optical fiber, used as a transmission medium for optical signals.

[0053] The topological quantum error correction decoding method based on the coherent Ising machine provided by the present application can obtain a solution with higher precision than a classical computer, and is particularly suitable for multi-bit topological quantum error correction decoding. The method introduces a coherent Ising machine system into quantum error correction, improves the operation complexity of the quantum decoding algorithm, and makes the algorithm complexity have a polynomial improvement scaling or constant factor advantage. These small differences can have a great difference in the running time of multi-bit decoding tasks, so that the method has scalability and potential acceleration advantage, that is, as the number of quantum bits increases, the advantage of the method becomes more and more obvious. BRIEF DESCRIPTION OF DRAWINGS

[0054] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings needed in the embodiment description are briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and those skilled in the art can obtain other drawings according to these drawings without creating any creative labor.

[0055] Figure 1 A decoding process of topological quantum error correction provided by an embodiment of the present application is shown;

[0056] Figure 2 A decoding method flowchart of topological quantum error correction provided by the present application is shown;

[0057] Figure 3 A coherent Ising machine system structure provided by an embodiment of the present application is shown;

[0058] Figure 4 A decoding device structure of topological quantum error correction provided by the present application is shown. DETAILED DESCRIPTION

[0059] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions in the embodiments of this application will be described below with reference to the accompanying drawings.

[0060] This invention proposes a novel method for quantum decoding using a coherent Ising machine, and based on this method, conceives a highly efficient and scalable quantum decoder, providing a completely new approach to achieving high efficiency in quantum decoding. The core of this invention lies in transforming the error correction challenge of stabilizer codes into an optimization problem of the Ising model, namely a quadratic unconstrained binary optimization (QUBO) problem, and solving it using a coherent Ising machine.

[0061] The principle and usage of the quantum decoding method provided by this invention are explained in detail below with reference to an embodiment. This embodiment focuses on the decoding of surface codes.

[0062] The specific process of mapping the surface code decoding problem to the Ising Hamiltonian optimization problem is as follows:

[0063] Taking the Pauli X error as an example (the Pauli Z error can be handled in the same way by introducing spin), let b v For the X-type stabilizer B v The syndrome, whose value can be determined based on B v Whether a Pauli X error was detected is set; for example, -1 is used when an error was detected, and 1 is used when no error was detected.

[0064] Errors on a qubit are represented by spins. If an error occurs on a qubit, the corresponding spin σ will flip from +1 to -1.

[0065] Therefore, the Ising Hamiltonian used for error correction is defined as:

[0066] (1)

[0067] Where, N v It is the number of X-type stabilizers; N d It is the number of working bits; σ i It is the i-th spin variable, used to represent the error on the qubit; J and h are hyperparameters; δ V Represents the vertex of a cell in the surface code.

[0068] This Ising Hamiltonian consists of interaction terms with 4 spins. and outdoor items composition. Here, the interaction term requires that the error must satisfy a given syndrome, J is a hyperparameter for this constraint. The field term is used to limit the number of errors to a minimum, which can be controlled by the hyperparameter Thus, the state of the global energy minimum configuration corresponds to the error that is most likely to satisfy the syndrome condition in the limit of large J.

[0069] Thus, the decoding problem of the surface code is successfully converted to the problem of solving the ground state of the Ising Hamiltonian, but this Ising Hamiltonian has 4 spins, and solving its ground state is a four-body interaction ground state problem, which is difficult to directly use the coherent Ising machine to solve. Therefore, it is necessary to simplify through variable substitution, map this four-body interaction ground state problem to a QUBO problem, and add a penalty term to the constraint by providing a hyperparameter, so that the problem is simplified to be able to use the coherent Ising machine to solve.

[0070] Let the binary variable Then equation (1) is transformed into:

[0071] (2)

[0072] It can be seen that equation (2) still contains The highest 4-order interaction, by introducing Auxiliary binary variables (0≤k< ), the order of equation (2) is reduced to obtain:

[0073] (3)

[0074] Equation (3) contains only The highest 2-order interaction. Next, introduce the penalty term:

[0075] (4)

[0076] Where, is the penalty term parameter.

[0077] Combine equation (3) with the penalty term to obtain:

[0078] (5)

[0079] In order to be able to use the coherent Ising machine system to solve, equation (5) is arranged into the form of the Ising model to obtain:

[0080] (6)

[0081] Where, is defined as:

[0082] (7)

[0083] Combining equation (7), comparing equation (5) with equation (6), it can be found that the second-order interaction term of the first term in equation (6), i.e. corresponds to all the second-order interaction terms of in equation (5), W ij represents the coefficient of these second-order interaction terms, the value of which is related to b v , J, h and , and the calculation method is different in different second-order interaction terms, which can be obtained in equation (5). Similarly, the first-order term of the second term in equation (6), i.e. corresponds to all the first-order terms of in equation (5), V i represents the coefficient of these first-order terms, the value of which is related to b v , J, h and , and the calculation method is different in different first-order terms, which can be obtained in equation (5). The third term in equation (6), i.e. the constant term c, corresponds to the sum of all constant terms in equation (5), the value of which is related to b v , J and h, and the specific calculation method can be obtained in equation (5).

[0084] The above is the specific process of mapping the decoding problem of the surface code to the Ising Hamiltonian optimization problem provided by the present application. Next, based on the above results, combined with the accompanying drawings, the decoding method of the topological quantum error correction provided by the present application will be specifically introduced.

[0085] The general process diagram of the decoding method of the topological quantum error correction provided by the present application is shown in Figure 1 . Figure 1 The left half part represents the surface code measurement result obtained from the topological quantum computer, wherein the area where the error is detected is represented by a black square, the area where the error is not detected is represented by a white square, and the hollow white circle at the four corners of the square represents a qubit. Figure 1 The right half part represents the coherent Ising machine system used by the embodiment of the present application. In general, the decoding method of the topological quantum error correction provided by the present application is to input the error syndrome obtained by the surface code into the coherent Ising machine system as a parameter, so that the coherent Ising machine system calculates the qubit error that best fits the error syndrome measurement result, thereby completing the decoding.

[0086] The flow chart of the decoding method of the topological quantum error correction provided by the present application is shown in Figure 2 , which comprises the following steps:

[0087] S1, in a quantum computer using a surface code to perform topological quantum error correction, measuring the error syndrome of the surface code.

[0088] Before performing this step, the error model that the quantum system can encounter needs to be determined, such as bit flip (X error), phase flip (Z error) or their combination. Each stabilizer operator can only identify one type of error, for example, X-type stabilizer can only identify whether X error exists.

[0089] In this step, the measurement result of each stabilizer operator can be obtained by measuring the ancillary bits in the surface code, as the error syndrome. The measurement result indicates whether the error represented by the stabilizer operator exists in the region where the stabilizer operator is located, that is, the error syndrome of the region.

[0090] The measurement result (that is, the error syndrome) can be represented by a numerical value, for example, -1 when an error is detected, and 1 when no error is detected. The measurement result can also be represented by an image, for example, Figure 1 The left half of the figure shows a surface code error syndrome measurement result, where the region where an error is detected is represented by a black square, the region where no error is detected is represented by a white square, and the hollow white circle in the corner of the square represents a qubit.

[0091] S2, using a coherent Ising machine system, solving the ground state of the Hamiltonian, the Hamiltonian is:

[0092]

[0093] where W ij and V i are coefficients related to the error syndrome, and c is a constant related to the error syndrome, defined as:

[0094]

[0095] where, where represents whether an error occurs on the th qubit; represents an ancillary binary variable and , is the number of working bits, is the number of ancillary binary variables.

[0096] The source of the Hamiltonian has been explained in detail in the previous section, and will not be repeated here.

[0097] In some embodiments, the implementation of this step specifically includes:

[0098] S21, initializing the coherent Ising machine according to the Hamiltonian, and starting the coherent Ising machine system evolution process.

[0099] The initialization of the coherent Ising machine includes inputting the parameters in equation (5) into the programmable coherent Ising machine system, the parameters including the specific error syndrome b v .

[0100] S22, during the evolution of the coherent Ising machine system, the phase and intensity of the light field in the coherent Ising machine system are measured multiple times, the parameters of the coherent Ising machine system are adjusted in real time according to the measurement results, and finally a collective oscillation mode is obtained, and the quantum spin state in the mode corresponds to the ground state of the Hamiltonian.

[0101] This step can effectively improve the efficiency and accuracy of the solution by repeatedly measuring and feeding back the modulation process in the coherent Ising machine cavity and adjusting the parameters of the coherent Ising machine system in real time.

[0102] S3, according to the ground state of the Hamiltonian, the quantum bit that occurs error is determined.

[0103] The ground state of the Hamiltonian corresponds to the spin state of y i in equation (6), which can be obtained by inversely deducing the formula during programming to determine the state of the quantum bit and thus determine the quantum bit that occurs error.

[0104] In some embodiments, after determining the quantum bit that occurs error, the quantum bit that occurs error can be fed back to the quantum computer, and the quantum computer can apply corresponding operations to the bit that occurs error according to the decoding result to correct the error.

[0105] The complete process of repeating the method can complete the quantum error correction in time sequence.

[0106] The above is the protein structure alignment method based on the coherent Ising machine provided by the application, and the coherent Ising machine system used in the method will be briefly introduced below.

[0107] The coherent Ising machine system uses a doubly resonant optical parametric oscillator (DOPO) to realize artificial spin, and a phase sensitive amplifier (PSA) is placed in the optical cavity to realize the enhancement of light signals with specific phases. The PSA is an optical amplifier based on optical parametric amplification, which can effectively amplify the 0 and π phase components relative to the pump phase. Therefore, the DOPO only uses 0 or π phase above the oscillation threshold; therefore, the discrete phase state can be used to represent the Ising spin state. The interaction between DOPO pulses is realized by using a measurement feedback technique, which repeatedly measures and feeds back the modulation process in the cavity multiple times, while increasing the pump amplitude from 0, and finally obtains a "strongest" collective oscillation mode much higher than the threshold, which corresponds to the best solution of the given Ising problem.

[0108] A schematic diagram of the coherent Ising machine system is shown in Figure 3 , which includes:

[0109] (1) An optical parametric oscillator network for simulating the spin interaction in the Ising model.

[0110] (2) A phase-sensitive amplifier for amplifying signals of a specific phase.

[0111] (3) A field-programmable gate array (FPGA) for controlling the optical parametric oscillator network.

[0112] The FPGA can be programmed to configure its internal circuit, which can be used to adjust the parameters of the coherent Ising machine system in real time according to the measurement results during the evolution of the coherent Ising machine system.

[0113] (4) A phase / intensity measurer for measuring the phase and intensity of the optical field in the cavity.

[0114] (5) An optical modulator for changing the phase difference between the light beams, thereby simulating the interaction strength between different spin states.

[0115] (6) A beam splitter for generating interference effects to simulate the connection between spins in the Ising model.

[0116] (7) Optical fibers used as transmission media for optical signals.

[0117] As can be seen from the above, compared with the prior art, the topological quantum error correction decoding method provided by the present application has the following beneficial effects:

[0118] 1. The present application introduces a coherent Ising machine system into quantum error correction decoding, uses a control module, photons and linear optical elements to complete the decoding process, and provides a new way to achieve high efficiency of quantum decoding.

[0119] 2. The quantum error correction decoding method provided by the present application has scalability, and is particularly suitable for multi-bit topological quantum error correction decoding, and as the number of quantum bits increases, i.e. the scale of the number of nodes increases, the advantages of the method become more and more obvious.

[0120] 3. The quantum error correction decoding method provided by the present application can obtain a more accurate approximate solution than a classical computer.

[0121] 4. The quantum error correction decoding method provided by this invention has potential speedup advantages. The potential advantages of the Ising machine largely extend beyond the realm of complexity theory. Compared with existing heuristic algorithms running on conventional processors, the Ising machine has a polynomial-level scaling or constant factor advantage. That is, the Ising machine is generally expected to have exponentially extended runtime to achieve near-optimal solutions, regardless of its underlying algorithm or actual hardware implementation, but the exponent may be smaller than that of conventional solvers, or the constant factor before the exponent can be smaller. Small differences in the exponent can have a large difference in the runtime of large problems, and the fast clock speeds of various physical implementations can lead to improvements in the constant factor, potentially resulting in significant practical speedups compared to conventional solutions.

[0122] The present invention also provides a topological quantum error correction decoding device 400, the schematic diagram of which is shown below. Figure 4 As shown, it includes:

[0123] The acquisition module 401 is configured to obtain the measurement results of each stable suboperator as an error syndrome by measuring the auxiliary bits in the surface code in a quantum computer that performs topological quantum error correction using surface codes.

[0124] Solver module 402 is configured to use a coherent Ising machine system to solve for the ground state of the Hamiltonian, wherein the Hamiltonian is:

[0125]

[0126] Among them, W ij and V i Here, c is a coefficient related to the error syndrome, and c is a constant related to the error syndrome. Defined as:

[0127]

[0128] in, ,in Indicates the first Whether an error has occurred on each quantum bit; Represents auxiliary binary variables and , For the number of working bits, The number of auxiliary binary variables.

[0129] Output module 403 is configured to determine the erroneous qubit based on the ground state of the Hamiltonian.

[0130] It should be noted that the above device can perform the aforementioned quantum error correction and decoding method. For the functions of each module, please refer to the aforementioned description of the method, which will not be repeated here.

[0131] In the description of the embodiments of the present application, the words "exemplary", "for example", or "e.g." are used to mean "an example of" or "an example, only". Any embodiment or design solution described as "exemplary", "for example" or "e.g." in the embodiments of the present application should not be construed as preferred or superior over other embodiments or design solutions. In fact, the use of the words "exemplary", "for example" or "e.g." is intended to present related concepts in a specific manner.

[0132] In the description of the embodiments of the present application, the term "and / or" is merely a description of the association relationship of the associated objects, which means that there can be three relationships, for example, A and / or B, which can represent the three cases of A alone, B alone, and A and B simultaneously. In addition, unless otherwise specified, the term "a plurality of" means two or more.

[0133] In addition, the terms "first", "second" are only for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the indicated technical features. Therefore, the features defined with "first", "second" can explicitly or implicitly include one or more of the features. The terms "include", "contain", "have" and their variants mean "include but not limited to", unless otherwise specifically emphasized.

[0134] The above specific embodiments further illustrate the purpose, technical solutions and beneficial effects of the present application. It should be understood that the above description is only a specific embodiment of the present application and is not intended to limit the protection scope of the present application. Any modification, equivalent replacement, improvement, etc. made on the basis of the technical solutions of the present application should be included in the protection scope of the present application.

Claims

1. A method of decoding topological quantum error correction, characterized in that, The method comprises the following steps: In a quantum computer using a surface code to perform topological quantum error correction, an error syndrome of the surface code is measured; a ground state of a Hamiltonian is solved using a coherent Ising machine system, the Hamiltonian being: where W ij and V i are coefficients related to the error syndrome, c is a constant related to the error syndrome, defined as: where, where represents whether an error occurs on the i th qubit; represents an auxiliary binary variable and , is the number of working bits, is the number of auxiliary binary variables; According to the ground state of the Hamiltonian, determine the quantum bit that occurs error; The method for solving the ground state of the Hamiltonian comprises the following steps: According to the Hamiltonian, initialize the coherent Ising machine, and start the evolution process of the coherent Ising machine system; During the evolution process of the coherent Ising machine system, the phase and intensity of the light field in the coherent Ising machine system are measured multiple times, and the parameters of the coherent Ising machine system are adjusted in real time according to the measurement results, and finally the collective oscillation mode is obtained, and the quantum spin state in this mode corresponds to the ground state of the Hamiltonian.

2. The method of claim 1, wherein, After determining the quantum bit that occurs error, the method further comprises: feeding back the quantum bit that occurs error to the quantum computer for error correction.

3. The method of claim 1, wherein, The coherent Ising machine system comprises: An optical parametric oscillator network for simulating spin interactions in the Ising model; A phase-sensitive amplifier for amplifying signals of a specific phase; A field programmable gate array for controlling the optical parametric oscillator network; A phase / intensity measurer for measuring the phase and intensity of the light field in the cavity; An optical modulator for changing the phase difference between light beams to simulate the interaction strength between different spin states; A beam splitter for generating interference effects to simulate the connection relationship between spins in the Ising model; An optical fiber serving as a transmission medium for optical signals.

4. A decoding device for topological quantum error correction, characterized in that, The method comprises the following steps: An acquisition module configured to measure error syndromes of a surface code in a quantum computer that performs topological quantum error correction using the surface code; A solving module configured to solve the ground state of a Hamiltonian using a coherent Ising machine system, the Hamiltonian being: where W ij and V i are coefficients related to error syndrome, c is a constant related to error syndrome, is defined as: wherein, wherein represents whether an error occurred on the th qubit; represents an ancilla binary variable and , is the number of working bits, is the number of ancilla binary variables; An output module configured to determine a quantum bit that occurs error according to the ground state of the Hamiltonian; The solving module is specifically configured to: According to the Hamiltonian, initialize the coherent Ising machine, and start the evolution process of the coherent Ising machine system; During the evolution process of the coherent Ising machine system, the phase and intensity of the light field in the coherent Ising machine system are measured multiple times, and the parameters of the coherent Ising machine system are adjusted in real time according to the measurement results, and finally the collective oscillation mode is obtained, and the quantum spin state in this mode corresponds to the ground state of the Hamiltonian.

5. The apparatus of claim 4, wherein, The output module is further configured to: after determining the quantum bit that occurs error, feed back the quantum bit that occurs error to the quantum computer for error correction.

6. The apparatus of claim 4, wherein, The coherent Ising machine system comprises: An optical parametric oscillator network for simulating spin interactions in the Ising model; A phase-sensitive amplifier for amplifying signals of a specific phase; A field programmable gate array for controlling the optical parametric oscillator network; A phase / intensity measurer for measuring the phase and intensity of the light field in the cavity; An optical modulator for changing the phase difference between light beams to simulate the interaction strength between different spin states; A beam splitter for generating interference effects to simulate the connection relationship between spins in the Ising model; An optical fiber serving as a transmission medium for optical signals.

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