Quantum Information Error Correction Method, Device, Electronic Device and Storage Medium

Abstract

The present application discloses a quantum information error correction method, apparatus, electronic device and storage medium, relating to the technical field of quantum computing, including determining the configuration of a quantum low-density parity-check code according to an X-type parity-check matrix of 36 rows and 72 columns and a Z-type parity-check matrix of 36 rows and 72 columns, and based on this configuration, constructing a quantum low-density parity-check code with 72 data qubits, 12 encoded logical qubits, a code distance of 6, and an encoding rate of 1 / 12, and using this quantum low-density parity-check code to correct quantum information. In the case of encoding the same number of logical qubits and having the same number of correctable errors, the encoding rate of the quantum low-density parity-check code of the present application is higher than that of the surface code, so the number of physical qubits required is less, achieving the technical effect of reducing system complexity.

Description

Technical Field

[0001] This application relates to the field of quantum computing technology, and particularly to a quantum information error correction method, apparatus, electronic device, and storage medium. Background Art

[0002] Quantum computing protects quantum information through quantum error correction codes to reduce the error rate of computing. A broad subclass of quantum error correction codes is stabilizer codes, and the most important subclass of stabilizer codes is quantum low-density parity-check codes. As a typical quantum low-density parity-check code, the surface code can increase the code distance by increasing the number of data qubits, thereby correcting more errors.

[0003] However, the coding rate of the surface code is low. The coding rate is defined as the number of encoded logical qubits divided by the number of physical qubits. A surface code can only encode one logical qubit. Therefore, for the surface code, the coding rate is approximately equal to 1 / n^2, where n is the number of data qubits included in the surface code. When encoding the same number of logical qubits and having the same number of correctable errors, due to the low coding rate of the surface code, a larger number of physical qubits are required. The more physical qubits there are, the more control circuits are needed, and the higher the refrigeration power is, which increases the system complexity. Summary of the Invention

[0004] This application provides a quantum information error correction method, apparatus, electronic device, and storage medium to at least solve the problem in the related art that when encoding the same number of logical qubits and having the same number of correctable errors, due to the low coding rate of the surface code, a larger number of physical qubits are required. The more physical qubits there are, the more control circuits are needed, and the higher the refrigeration power is, which increases the system complexity.

[0005] This application provides a quantum information error correction method, including:

[0006] Based on a 6×6 cyclic shift matrix and a 6×6 identity matrix, through a direct product operation, construct a 36×36 first matrix and a 36×36 second matrix;

[0007] Based on the first matrix and the second matrix, determine a third matrix and a fourth matrix through the following formula:

[0008]

[0009]

[0010] where A is the third matrix and B is the fourth matrix, is the first matrix, is the second matrix;

[0011] Based on the third matrix and the fourth matrix, construct an X-type parity-check matrix with 36 rows and 72 columns and a Z-type parity-check matrix with 36 rows and 72 columns;

[0012] Based on the X-type parity-check matrix and the Z-type parity-check matrix, determine the configuration of the quantum low-density parity-check code, where the configuration is used to characterize the mutual relationship among data qubits, auxiliary qubits, and stabilizer operators in the quantum low-density parity-check code;

[0013] Based on the configuration of the quantum low-density parity-check code, construct a quantum low-density parity-check code with 72 data qubits, 12 encoded logical qubits, a code distance of 6, and an encoding rate of 1 / 12;

[0014] Encode the quantum information to be error-corrected into the quantum states of the data qubits in the quantum low-density parity-check code;

[0015] Measure the auxiliary qubits in the quantum low-density parity-check code to determine the eigenvalues of the stabilizer operators;

[0016] Based on the eigenvalues of the stabilizer operators, determine and correct the errors in the quantum information to be error-corrected.

[0017] This application also provides a superconducting quantum computing platform, which is used to determine and correct the errors in the quantum information to be error-corrected based on any of the above quantum information error correction methods.

[0018] This application also provides a quantum information error correction device, including:

[0019] A first construction module, configured to construct a 36×36 first matrix and a 36×36 second matrix through a direct product operation based on a 6×6 cyclic shift matrix and a 6×6 identity matrix;

[0020] A first determination module, configured to determine a third matrix and a fourth matrix based on the first matrix and the second matrix through the following formula:

[0021]

[0022]

[0023] where A is the third matrix and B is the fourth matrix, is the first matrix, is the second matrix;

[0024] A second construction module, configured to construct a 36×72 X-type parity-check matrix and a 36×72 Z-type parity-check matrix based on the third matrix and the fourth matrix;

[0025] A second determination module, configured to determine the configuration of a quantum low-density parity-check code based on an X-type parity-check matrix and a Z-type parity-check matrix, where the configuration is used to characterize the mutual relationship among data qubits, auxiliary qubits, and stabilizer operators in the quantum low-density parity-check code;

[0026] A third construction module, configured to construct a quantum low-density parity-check code with 72 data qubits, 12 encoded logical qubits, a code distance of 6, and an encoding rate of 1 / 12 based on the configuration of the quantum low-density parity-check code;

[0027] An encoding module, configured to encode the quantum information to be error-corrected into the quantum states of the data qubits in the quantum low-density parity-check code;

[0028] A third determination module, configured to measure the auxiliary qubits in the quantum low-density parity-check code to determine the eigenvalues of the stabilizer operators;

[0029] A fourth determination module, configured to determine and correct the errors in the quantum information to be error-corrected based on the eigenvalues of the stabilizer operators.

[0030] This application also provides an electronic device, including: a memory, configured to store a computer program; a processor, configured to implement the steps of any of the above quantum information error correction methods when executing the computer program.

[0031] This application also provides a computer-readable storage medium, in which a computer program is stored, where the computer program implements the steps of any of the above quantum information error correction methods when executed by a processor.

[0032] This application also provides a computer program product, including a computer program, where the computer program implements the steps of any of the above quantum information error correction methods when executed by a processor.

[0033] With this application, based on a 6-row and 6-column cyclic shift matrix and a 6-row and 6-column identity matrix, through a direct product operation, a 36-row and 36-column first matrix and a 36-row and 36-column second matrix are constructed; based on the first matrix and the second matrix, a 36-row and 36-column third matrix and a 36-row and 36-column fourth matrix are constructed; based on the third matrix and the fourth matrix, a 36-row and 72-column X-type parity-check matrix and a 36-row and 72-column Z-type parity-check matrix are constructed; based on the X-type parity-check matrix and the Z-type parity-check matrix, the configuration of the quantum low-density parity-check code is determined, and the configuration is used to characterize the mutual relationship among data qubits, auxiliary qubits, and stabilizer operators in the quantum low-density parity-check code; based on the configuration of the quantum low-density parity-check code, a quantum low-density parity-check code with 72 data qubits, 12 encoded logical qubits, a code distance of 6, and an encoding rate of 1 / 12 is constructed; the quantum information to be error-corrected is encoded into the quantum states of the data qubits in the quantum low-density parity-check code; the auxiliary qubits in the quantum low-density parity-check code are measured to determine the eigenvalues of the stabilizer operators; based on the eigenvalues of the stabilizer operators, the errors in the quantum information to be error-corrected are determined and corrected. When encoding the same number of logical qubits and having the same number of correctable errors, the encoding rate of the quantum low-density parity-check code of this application is higher than that of the surface code, so the number of physical qubits required is less, solving the technical problem in the related art that due to the low encoding rate, when encoding the same number of logical qubits and having the same number of correctable errors, the number of physical qubits required is large, increasing the system complexity, and achieving the technical effect of reducing the system complexity. Description of the Drawings

[0034] To more clearly illustrate the embodiments of this application, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of this application. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0035] Figure 1 Flow chart of a quantum information error correction method provided by an embodiment of this application;

[0036] Figure 2 Flow chart of a quantum information error correction method provided by an embodiment of this application;

[0037] Figure 3 Arrangement diagram of physical qubits in a quantum low-density parity-check code provided by an embodiment of this application;

[0038] Figure 4 Schematic diagram of the first circuit on the first surface provided by an embodiment of this application;

[0039] Figure 5 Schematic diagram of a part of the second circuit on the second surface provided by the embodiment of the present application;

[0040] Figure 6 Schematic diagram of the second circuit after continuous movement provided by the embodiment of the present application.

[0041] Figure 7 Structural block diagram of a quantum information error correction device provided by the embodiment of the present application;

[0042] Figure 8 Structural block diagram of an electronic device provided by the embodiment of the present application. Detailed implementation manners

[0043] Next, the technical solutions in the embodiments of the present application will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the protection scope of the present application.

[0044] It should be noted that in the description of the present application, the terms "including", "comprising" or any other variant thereof are intended to cover a non-exclusive inclusion, so that a process, method, article or device including a series of elements not only includes those elements, but also includes other elements not expressly listed, or further includes elements inherent to such process, method, article or device. The terms "first", "second", etc. in the present application are used to distinguish similar objects, rather than to describe a specific order or sequence.

[0045] In order to enable those skilled in the art of the present technology to better understand the solution of the present application, the present application will be further described in detail below in conjunction with the accompanying drawings and specific implementation manners.

[0046] Quantum computing, as a computing paradigm that is completely different from the classical computing principle, relies on unique characteristics such as quantum coherence and quantum entanglement, enabling specific quantum algorithms to exhibit significant advantages over classical algorithms. Taking the public key cryptosystem as an example, its security depends on the complexity of large number factorization. In the field of classical computing, this complexity grows exponentially with the number of digits of an integer. However, the Shor algorithm based on the principles of quantum mechanics can easily complete large number factorization in polynomial time.

[0047] Classical information uses bits as the basic unit, while the basic unit of quantum information is the qubit. In experiments, two-level systems are usually used to implement qubits. However, qubits are extremely fragile, and factors such as temperature, electromagnetic fields, and cosmic rays in the external environment can all destroy their quantum properties. In addition, quantum computing requires the construction of quantum circuits through a large number of quantum gate operations, and the interference of noise makes the quantum gate operations have a relatively high error rate. Currently, the error rate that can be guaranteed by technology is roughly on the order of 10^(-3). However, for the successful operation of large-scale quantum algorithms, a lower error rate is required, generally reaching between 10^(-9) and 10^(-15).

[0048] To reduce the error rate, just as classical error-correcting codes protect classical information, quantum error-correcting codes are used to protect quantum information. Quantum error-correcting codes use multiple data qubits, leveraging the property of quantum entanglement to encode a logical qubit, and by continuously detecting and correcting errors, effectively protect the logical qubit. Implementing quantum error correction is an essential step towards large-scale quantum computing.

[0049] In quantum error-correcting codes, stabilizer codes are a widely existing subclass. Their significant feature is the existence of a set of mutually commuting stabilizer operators, and errors are detected by measuring these stabilizer operators. Quantum low-density parity-check codes are the most important subclass of stabilizer codes. Their uniqueness lies in that each stabilizer operator contains only a small number of Pauli operators, and each qubit only interacts with a small number of stabilizer operators. Currently, surface codes are recognized as one of the most promising quantum codes, and at the same time, they are also a typical quantum low-density parity-check code.

[0050] The data qubits of surface codes are arranged at the lattice points of a square lattice in a plane. In the surface code system, the stabilizer operators have unique rules: the stabilizer operators located inside the lattice are composed of the product of 4 Pauli operators, and the stabilizer operators at the boundary are composed of the product of 2 Pauli operators, and all stabilizer operators commute with each other. These stabilizer operators can be divided into two categories, one is the product of 4 or 2 X operators, and the other is the product of 4 or 2 Z operators. For a surface code containing n data qubits, there are (n - 1) independent stabilizer operators. The measurement of the stabilizer operators is achieved through a specific method, that is, by using the auxiliary qubits located on the lattice plane, making them coupled to the nearest 4 or 2 data qubits through a Controlled NOT gate (abbreviation: CNOT), and then measuring the auxiliary qubits to complete the measurement of the stabilizer operators. Based on the properties of stabilizer codes, the number of logical qubits k can be obtained by subtracting the number of independent stabilizer operators from the number of data qubits n. Therefore, surface codes can only encode 1 logical qubit.

[0051] The significant advantage of the surface code is that by increasing the number n of data qubits, the code distance d can be improved, thereby enhancing the error correction ability and reducing the error rate of logical qubits. Currently, researchers have implemented small-scale surface codes on experimental platforms such as superconducting quantum circuits and neutral atoms, and preliminarily verified this characteristic. Looking at future development, superconducting quantum circuits are regarded as a highly potential quantum computing platform because of their fast gate operation speed, which can complete practical quantum algorithms in a shorter time.

[0052] However, the surface code also has obvious defects. Its coding rate r is relatively low. The coding rate is defined as the ratio of the number of logical qubits to the number of physical qubits (the sum of the number of data qubits and the number of auxiliary qubits). Since the surface code can only encode 1 logical qubit, its coding rate is approximately 1 / n^2.

[0053] In the field of quantum error correction codes, the characteristics of quantum error correction codes are usually described by three parameters [[n, k, d]]. Among them, n represents the number of data qubits, k represents the number of encoded logical qubits, and d is the code distance. The code distance is defined as the minimum weight of the logical operator (i.e., the number of operators containing non-identity matrices). The number of errors t that a quantum error correction code can correct is related to the code distance d, and t is the largest integer not greater than [(d - 1) / 2].

[0054] Taking the implementation of 12 logical qubits on a superconducting quantum computing platform as an example, 12 surface codes are required. If each surface code can correct 2 errors, each surface code requires at least 5×5, that is, 25 data qubits and 24 auxiliary qubits, and finally forms an error correction code in the form of [[300, 12, 5]], involving 300 data qubits, 288 auxiliary qubits, a total of 588 physical qubits, and the coding rate is only 1 / 49.

[0055] When encoding the same number of logical qubits and with the same number of correctable errors, due to the low coding rate of the surface code, a larger number of physical qubits are required. In a superconducting quantum computing platform, the more physical qubits there are, the more control circuits are needed, and the higher the cooling power, which increases the system complexity.

[0056] Moreover, quantum computing often requires multiple logical qubits to work together. However, due to the power limitation of the dilution refrigerator, different surface codes may be scattered in different dilution refrigerators, and communicating between different surface codes will bring additional noise and signal delay.

[0057] In view of the above problems, the embodiments of the present application provide a quantum information error correction method, apparatus, electronic device, and storage medium. By using a 6×6 cyclic shift matrix and a 6×6 identity matrix, a 36×36 first matrix and a 36×36 second matrix are constructed through a direct product operation; based on the first matrix and the second matrix, a 36×36 third matrix and a 36×36 fourth matrix are constructed; based on the third matrix and the fourth matrix, a 36×72 X-type parity-check matrix and a 36×72 Z-type parity-check matrix are constructed; based on the X-type parity-check matrix and the Z-type parity-check matrix, the configuration of the quantum low-density parity-check code is determined, and the configuration is used to characterize the mutual relationship between data qubits, auxiliary qubits, and stabilizer operators in the quantum low-density parity-check code; based on the configuration of the quantum low-density parity-check code, a quantum low-density parity-check code with 72 data qubits, 12 encoded logical qubits, a code distance of 6, and an encoding rate of 1 / 12 is constructed; the quantum information to be error-corrected is encoded into the quantum state of the data qubits in the quantum low-density parity-check code; the auxiliary qubits in the quantum low-density parity-check code are measured to determine the eigenvalues of the stabilizer operators; based on the eigenvalues of the stabilizer operators, the errors in the quantum information to be error-corrected are determined and corrected. When encoding the same number of logical qubits and having the same number of correctable errors, the encoding rate of the quantum low-density parity-check code of the present application is higher than that of the surface code, so the number of physical qubits required is less, solving the technical problem in the related art that due to the low encoding rate, when encoding the same number of logical qubits and having the same number of correctable errors, the number of physical qubits required is large, increasing the system complexity, and achieving the technical effect of reducing the system complexity.

[0058] It can be understood that the quantum low-density parity-check code provided by the present application can be expressed as [[72, 12, 6]]. From the encoding rate of 1 / 12, it can be known that the number of auxiliary qubits is 72, and the number of physical qubits is 144. Compared with the surface code [[300, 12, 5]] encoding the same number of logical qubits and having the same error correction level, the encoding rate of the quantum low-density parity-check code provided by the present application is more than 4 times that of the surface code, and the number of physical qubits required is greatly reduced, reducing the number of control circuits, reducing the cooling power, and reducing the system complexity. And because the number of physical qubits required for the quantum low-density parity-check code provided by the present application is small, it only needs to be placed in one dilution refrigerator, solving the problem that the error correction codes on superconducting quantum chips in different dilution refrigerators need to communicate, bringing additional noise and signal delay.

[0059] The embodiments of the present application provide a quantum information error correction method, which is applied to a superconducting quantum computing platform. Figure 1The flowchart of the quantum information error correction method provided by the embodiments of this application is as follows Figure 1 As shown, this process includes the following steps:

[0060] Step S101: Based on a 6×6 cyclic shift matrix and a 6×6 identity matrix, through the direct product operation, construct a 36×36 first matrix and a 36×36 second matrix.

[0061] Among them, in the theory of error-correcting codes, the numbers in the matrix are only 0 and 1, and 0 and 1 form a number field, and the addition and multiplication in it satisfy Boolean algebra.

[0062] The cyclic shift matrix in this embodiment is: .

[0063] The identity matrix is .

[0064] Step S102: Based on the first matrix and the second matrix, determine the third matrix and the fourth matrix through the formula.

[0065] Among them, the formula is as follows:

[0066]

[0067]

[0068] Among them, A is the third matrix, B is the fourth matrix, is the first matrix, is the second matrix.

[0069] It can be understood that both the third matrix and the fourth matrix are 36×36 matrices.

[0070] Step S103: Based on the third matrix and the fourth matrix, construct a 36×72 X-type parity-check matrix and a 36×72 Z-type parity-check matrix.

[0071] Among them, the quantum low-density parity-check code proposed by the embodiments of this application is a Calderbank-Shor-Steane code (abbreviation: CSS code). The stabilizer operators of the CSS code are divided into two types: X-type stabilizer operators and Z-type stabilizer operators, which are respectively determined by the corresponding parity-check matrices, and the parity-check matrices also determine the values of each parameter of the quantum low-density parity-check code [[n, k, d]].

[0072] The X-type stabilizer operator is determined by the X-type parity-check matrix, and the Z-type stabilizer operator is determined by the Z-type parity-check matrix.

[0073] Each row of the X-type parity-check matrix has six 1s and sixty-six 0s. The number of rows of the X-type parity-check matrix, which is 36, is the number of X-type stabilizer operators, and the number of columns of the X-type parity-check matrix, which is 72, is the number of data qubits.

[0074] Each row of the Z-type parity-check matrix has six 1s and sixty-six 0s. The number of rows of the Z-type parity-check matrix, which is 36, is the number of Z-type stabilizer operators, and the number of columns of the Z-type parity-check matrix, which is 72, is the number of data qubits.

[0075] The X-type parity-check matrix indicates that the parity-check matrix is related to the bit-flip errors of the detection qubits.

[0076] The Z-type parity-check matrix indicates that the parity-check matrix is related to the phase-flip errors of the detection qubits.

[0077] In step S104, based on the X-type parity-check matrix and the Z-type parity-check matrix, determine the configuration of the quantum low-density parity-check code, where the configuration is used to characterize the mutual relationship between the data qubits, the auxiliary qubits, and the stabilizer operators in the quantum low-density parity-check code.

[0078] Among them, according to the X-type parity-check matrix and the Z-type parity-check matrix, it can be known that each stabilizer operator acts on six data qubits. According to the configuration of the stabilizer operator, the corresponding auxiliary qubits need to be connected to the six data qubits by circuits to generate coupling.

[0079] According to the theory of quantum error-correcting codes, the quantum low-density parity-check code can be determined as [[n, k, d]] = [[72, 12, 6]] through the X-type parity-check matrix and the Z-type parity-check matrix.

[0080] Among them, n is the number of data qubits, and the number of data qubits is the same as the number of columns of the X-type parity-check matrix, which is 72.

[0081] According to the formula , k can be determined to be 12. Here, dim is the dimension of the space. is the null space of matrix A, is the null space of matrix B.

[0082] According to the formula , d = 6 can be determined. Among them, is the null space of the X-type parity-check matrix , is the linear space spanned by all row vectors of the Z-type parity-check matrix ; denotes the set difference, which means all elements that belong to but do not belong to vector is the Hamming weight refers to the smallest number in the set

[0083] Step S105: Based on the configuration of the quantum low-density parity-check code, construct a quantum low-density parity-check code with 72 data qubits, 12 encoded logical qubits, a code distance of 6, and an encoding rate of 1 / 12

[0084] Among them, "low-density" refers to the sparsity of the parity-check matrix. Specifically, this means that each row and column of the parity-check matrix contains very few non-zero elements (usually 1), relative to the entire matrix

[0085] Step S106: Encode the quantum information to be error-corrected into the quantum states of the data qubits in the quantum low-density parity-check code

[0086] Among them, the quantum information that needs to be error-corrected is stored into the quantum states of the data qubits according to the specific encoding rules of the quantum low-density parity-check code. In quantum computing, quantum information is vulnerable to noise interference and errors, and encoding is the primary link in error correction. By encoding logical qubits (carrying actual information) into multiple data qubits and utilizing characteristics such as quantum entanglement, the information is made redundant, providing a basis for subsequent error detection and correction

[0087] Step S107: Measure the auxiliary qubits in the quantum low-density parity-check code to determine the eigenvalues of the stabilizer operators

[0088] Among them, the auxiliary qubits are introduced to assist in error detection. Measuring them can obtain the eigenvalues of the stabilizer operators. The stabilizer operators are a set of operators composed of Pauli operators (such as Pauli X, Z operators, etc.) and commute with each other. In quantum error correction, the stabilizer operators interact with the quantum state, and measuring the auxiliary qubits can obtain information about the result of the action of the stabilizer operators, that is, the eigenvalues. The eigenvalues reflect information such as whether the quantum state has an error and the type of error

[0089] Step S108: Based on the eigenvalues of the stabilizer operators, determine and correct the errors in the quantum information to be error-corrected

[0090] Among them, according to the eigenvalues of the stabilizer operators obtained in step S107, judge the specific situation of the errors in the quantum information to be error-corrected, such as the error position, the type of error (bit flip or phase flip), etc., that is, determine the error syndrome. Then, based on the error syndrome, use corresponding quantum gate operations and other means to correct the errors and restore the original state of the quantum information

[0091] The quantum information error correction method provided by the embodiments of the present application constructs a 36-row and 36-column first matrix and a 36-row and 36-column second matrix through a direct product operation based on a 6-row and 6-column cyclic shift matrix and a 6-row and 6-column identity matrix; constructs a 36-row and 36-column third matrix and a 36-row and 36-column fourth matrix based on the first matrix and the second matrix; constructs a 36-row and 72-column X-type parity check matrix and a 36-row and 72-column Z-type parity check matrix based on the third matrix and the fourth matrix; determines the configuration of the quantum low-density parity check code based on the X-type parity check matrix and the Z-type parity check matrix, and the configuration is used to characterize the mutual relationship among data qubits, auxiliary qubits, and stabilizer operators in the quantum low-density parity check code; constructs a quantum low-density parity check code with 72 data qubits, 12 encoded logical qubits, a code distance of 6, and an encoding rate of 1 / 12 based on the configuration of the quantum low-density parity check code; encodes the quantum information to be error-corrected into the quantum state of the data qubits in the quantum low-density parity check code; measures the auxiliary qubits in the quantum low-density parity check code to determine the eigenvalues of the stabilizer operators; and determines and corrects the errors in the quantum information to be error-corrected based on the eigenvalues of the stabilizer operators. In the case of encoding the same number of logical qubits and having the same number of correctable errors, the encoding rate of the quantum low-density parity check code of the present application is higher than that of the surface code, so the number of physical qubits required is less, solving the technical problem in the related art that due to the low encoding rate, in the case of encoding the same number of logical qubits and having the same number of correctable errors, the number of physical qubits required is large, increasing the system complexity, and achieving the technical effect of reducing the system complexity.

[0092] An embodiment of the present application provides a quantum information error correction method, which is applied to a superconducting quantum computing platform. Figure 2 It is a flowchart of the quantum information error correction method provided by the embodiments of the present application. As Figure 2 shown, the process includes the following steps:

[0093] Step S201: Based on a 6-row and 6-column cyclic shift matrix and a 6-row and 6-column identity matrix, construct a 36-row and 36-column first matrix and a 36-row and 36-column second matrix through a direct product operation.

[0094] Specifically, the above step S201 includes:

[0095] Step S2011: Based on a 6-row and 6-column cyclic shift matrix and a 6-row and 6-column identity matrix, determine the first matrix through a formula. The formula is as follows:

[0096]

[0097] Specifically, x can be written as a block diagonal matrix of 6 rows and 6 columns, with each block being a matrix of 6 rows and 6 columns, as shown below:

[0098]

[0099] Step S2012: Based on a 6×6 cyclic shift matrix and a 6×6 identity matrix, determine a second matrix through a formula. The formula is as follows:

[0100]

[0101] Where, is a 6×6 identity matrix, is a direct product operation, is a 6×6 cyclic shift matrix.

[0102] Specifically, can be written as a block diagonal matrix of 6 rows and 6 columns, with each block being a matrix of 6 rows and 6 columns, as shown below:

[0103]

[0104] Step S202: Based on the first matrix and the second matrix, determine a third matrix and a fourth matrix through a formula.

[0105] The formula is as follows:

[0106]

[0107]

[0108] Where A is the third matrix and B is the fourth matrix, is the first matrix, is the second matrix.

[0109] For details, please refer to Figure 1 Step S102 of the embodiment shown, which will not be elaborated here.

[0110] Step S203: Based on the third matrix and the fourth matrix, construct a 36×72 X-type parity-check matrix and a 36×72 Z-type parity-check matrix. For details, please refer to Figure 1 Step S103 of the embodiment shown, which will not be elaborated here.

[0111] Step S204: Based on the X-type parity-check matrix and the Z-type parity-check matrix, determine the configuration of the quantum low-density parity-check code, where the configuration is used to characterize the mutual relationship between data qubits, auxiliary qubits, and stabilizer operators in the quantum low-density parity-check code. For details, please refer to Figure 1 Step S104 of the embodiment shown, which will not be elaborated here.

[0112] Step S205: Based on the configuration of the quantum low-density parity-check code, construct a quantum low-density parity-check code with 72 data qubits, 12 encoded logical qubits, a code distance of 6, and an encoding rate of 1 / 12. For details, please refer to Figure 1 Step S105 of the illustrated embodiment, which will not be elaborated here.

[0113] Step S206: Encode the quantum information to be error-corrected into the quantum states of the data qubits in the quantum low-density parity-check code. For details, please refer to Figure 1 Step S106 of the illustrated embodiment, which will not be elaborated here.

[0114] Step S207: Measure the auxiliary qubits in the quantum low-density parity-check code to determine the eigenvalues of the stabilizer operators. For details, please refer to Figure 1 Step S107 of the illustrated embodiment, which will not be elaborated here.

[0115] Step S208: Based on the eigenvalues of the stabilizer operators, determine and correct the errors in the quantum information to be error-corrected. For details, please refer to Figure 1 Step S108 of the illustrated embodiment, which will not be elaborated here.

[0116] In some alternative embodiments, the above Step S204 includes:

[0117] Step a1: Based on the number of columns of the X-type parity-check matrix, determine the number of data qubits in the quantum low-density parity-check code.

[0118] Wherein, the number of data qubits in the quantum low-density parity-check code is the same as the number of columns of the X-type parity-check matrix, that is, the quantum low-density parity-check code includes 72 data qubits.

[0119] Step a2: Based on the number of rows of the X-type parity-check matrix, determine the number of X-type auxiliary qubits in the quantum low-density parity-check code.

[0120] The number of X-type auxiliary qubits in the quantum low-density parity-check code is the same as the number of rows of the X-type parity-check matrix, that is, the quantum low-density parity-check code includes 36 X-type auxiliary qubits.

[0121] Step a3: Based on the number of rows of the Z-type parity-check matrix, determine the number of Z-type auxiliary qubits in the quantum low-density parity-check code.

[0122] The number of Z-type auxiliary qubits in the quantum low-density parity-check code is the same as the number of rows of the Z-type parity-check matrix, that is, the quantum low-density parity-check code includes 36 Z-type auxiliary qubits.

[0123] Step a4: For each row in the X-type parity-check matrix, substitute the first preset character in this row with the Pauli X operator, substitute the second preset character in this row with the 2×2 identity matrix, and determine the X-type stabilizer operator corresponding to this row.

[0124] Among them, the first preset character is 1, and the second preset character is 0. Substitute 1 with the Pauli X operator, and this Pauli X operator acts on the corresponding qubit. Substitute 0 with the identity matrix, and this identity matrix acts on the corresponding qubit. According to the above substitution, the specific form of each X-type stabilizer operator can be completely determined. Since the X-type parity-check matrix has 36 rows, the number of corresponding X-type stabilizer operators is 36.

[0125] The Pauli X operator is also called the bit-flip operator, and its matrix form is X = .

[0126] Step a5: For each row in the Z-type parity-check matrix, substitute the first preset character in this row with the Pauli Z operator, substitute the second preset character in this row with the 2×2 identity matrix, and determine the Z-type stabilizer operator corresponding to this row.

[0127] Substitute 1 with the Pauli Z operator, and this Pauli Z operator acts on the corresponding qubit. Substitute 0 with the identity matrix, and this identity matrix acts on the corresponding qubit. According to the above substitution, the specific form of each Z-type stabilizer operator can be completely determined. Since the Z-type parity-check matrix has 36 rows, the number of corresponding Z-type stabilizer operators is 36.

[0128] The Pauli Z operator is also called the phase-flip operator, and its matrix form is Z = .

[0129] Step a6: Based on the number of data qubits, the number of X-type auxiliary qubits, the number of Z-type auxiliary qubits, the X-type stabilizer operators, the Z-type stabilizer operators, the X-type parity-check matrix, and the Z-type parity-check matrix, determine the configuration of the quantum low-density parity-check matrix.

[0130] Among them, the auxiliary qubits include X-type auxiliary qubits and Z-type auxiliary qubits, the stabilizer operators include X-type stabilizer operators and Z-type stabilizer operators, and all the stabilizer operators commute with each other in pairs.

[0131] It should be noted that according to the properties of the cyclic shift matrix, AB + BA = 0 can be obtained, so the stabilizer operators in the quantum low-density parity-check matrix commute with each other in pairs.

[0132] In some alternative embodiments, the above step a6 includes:

[0133] Step a61: Determine the number of physical qubits based on the number of data qubits, the number of X-type auxiliary qubits, and the number of Z-type auxiliary qubits. The physical qubits include data qubits, X-type auxiliary qubits, and Z-type auxiliary qubits.

[0134] Among them, in the embodiments of the present application, the number of physical qubits is 144.

[0135] Step a62: Determine the arrangement rule of physical qubits based on the number of physical qubits.

[0136] Step a63: Based on the X-type parity-check matrix and the Z-type parity-check matrix, determine the connection relationship between physical qubits, the first target data qubits acted on by the X-type stabilizer operator, and the second target data qubits acted on by the Z-type stabilizer operator.

[0137] Among them, the configuration of the quantum low-density parity-check matrix includes the arrangement rule of physical qubits, the connection relationship between physical qubits, the first target data qubits acted on by the X-type stabilizer operator, and the second target data qubits acted on by the Z-type stabilizer operator.

[0138] The quantum information error correction method provided by the embodiments of the present application determines the arrangement rule based on the number of physical qubits; through the X-type parity-check matrix and the Z-type parity-check matrix, it determines the connection relationship between physical qubits and the target data qubits acted on by the stabilizer operator, ensuring the accuracy of the generated quantum low-density parity-check code.

[0139] In some alternative embodiments, the above step a62 includes:

[0140] Step a621: Based on the number of physical qubits, determine that all physical qubits are arranged at the vertices of a square lattice in a 12-row and 12-column arrangement form, the row numbers increase from top to bottom, the column numbers increase from left to right, and all physical qubits are on a plane with periodic boundary conditions in both the horizontal and vertical directions.

[0141] Among them, the periodic boundary condition assumes that the boundaries of the system are connected, so that leaving one side of the system in a certain direction will re-enter from the other side. The main purpose is to connect the boundaries of the system to form a closed space.

[0142] The quantum information error correction method provided by the embodiments of the present application, by placing all physical qubits on a plane, since the number of physical qubits is small, only one dilution refrigerator is needed, solving the communication problem of error-correcting codes on superconducting quantum chips in different dilution refrigerators.

[0143] In some alternative embodiments, the above quantum information error correction method further includes:

[0144] Step b1, set the arrangement pattern of the physical quantum bits in the odd rows of the 12×12 matrix such that the X-type auxiliary quantum bits and the first data quantum bits are arranged alternately from left to right, where the leftmost one is the X-type auxiliary quantum bit and the rightmost one is the first data quantum bit.

[0145] Among them, the data quantum bits include the first data quantum bits and the second data quantum bits. The number of the first data quantum bits is 36, and the number of the second data quantum bits is 36.

[0146] Figure 3 It is a schematic diagram of the arrangement of the physical quantum bits in the quantum low-density parity-check code provided by the embodiment of the present application. Among them, the black circles represent the first data quantum bits, the white circles represent the second data quantum bits, the squares marked with X represent the X-type auxiliary quantum bits, and the squares marked with Z represent the Z-type auxiliary quantum bits.

[0147] As Figure 3 shown, the arrangement pattern of the physical quantum bits in the odd rows is that, from left to right, they are arranged in the order of X-type auxiliary quantum bit, first data quantum bit, X-type auxiliary quantum bit, first data quantum bit, X-type auxiliary quantum bit, first data quantum bit, X-type auxiliary quantum bit, first data quantum bit, X-type auxiliary quantum bit, first data quantum bit, X-type auxiliary quantum bit, first data quantum bit.

[0148] It can be understood that due to the periodic boundary condition in the horizontal direction, the 12 physical quantum bits arranged in this order form a ring with a period of 6.

[0149] Step b2, set the arrangement pattern of the physical quantum bits in the even rows of the 12×12 matrix such that the second data quantum bits and the Z-type auxiliary quantum bits are arranged alternately from left to right, where the leftmost one is the second data quantum bit and the rightmost one is the Z-type auxiliary quantum bit.

[0150] As Figure 3 shown, the arrangement pattern of the physical quantum bits in the even rows is that, from left to right, they are arranged in the order of second data quantum bit, Z-type auxiliary quantum bit, second data quantum bit, Z-type auxiliary quantum bit, second data quantum bit, Z-type auxiliary quantum bit, second data quantum bit, Z-type auxiliary quantum bit, second data quantum bit, Z-type auxiliary quantum bit, second data quantum bit, Z-type auxiliary quantum bit.

[0151] It can be understood that due to the periodic boundary condition in the horizontal direction, the 12 physical quantum bits arranged in this order form a ring with a period of 6.

[0152] The quantum information error correction method provided by the embodiments of the present application ensures the accurate generation of corresponding quantum low-density parity-check codes by clarifying the arrangement of physical qubits in odd rows and even rows. Due to the periodic boundary conditions in the horizontal direction, the physical qubits in odd rows and even rows respectively form a cyclic structure with a period of 6. This symmetry and periodicity enhance the stability of the system and simplify the complexity in the evolution of quantum states.

[0153] In some alternative embodiments, step a63 includes:

[0154] Step a631: Divide the X-type parity-check matrix into a first X-type parity-check matrix and a second X-type parity-check matrix, where each row of the first X-type parity-check matrix and the second X-type parity-check matrix includes three first preset characters.

[0155] The sum of the first X-type parity-check matrix and the second X-type parity-check matrix is the X-type parity-check matrix.

[0156] Step a632: Divide the Z-type parity-check matrix into a first Z-type parity-check matrix and a second Z-type parity-check matrix, where each row of the first Z-type parity-check matrix and the second Z-type parity-check matrix includes three first preset characters.

[0157] The sum of the first Z-type parity-check matrix and the second Z-type parity-check matrix is the Z-type parity-check matrix.

[0158] For the X-type parity-check matrix and the Z-type parity-check matrix, each row has 6 1s, corresponding to the stabilizer operator acting on 6 data qubits.

[0159] Each row of the first X-type parity-check matrix and the first Z-type parity-check matrix has only 3 1s, corresponding to the stabilizer operator acting on the corresponding 3 data qubits.

[0160] Each row of the second X-type parity-check matrix and the second Z-type parity-check matrix has only 3 1s, corresponding to the stabilizer operator acting on the corresponding 3 data qubits.

[0161] Step a633: Based on the first X-type parity-check matrix, the second X-type parity-check matrix, the first Z-type parity-check matrix, and the second Z-type parity-check matrix, determine the connection relationship between physical qubits, the first target data qubits on which the X-type stabilizer operator acts, and the second target data qubits on which the Z-type stabilizer operator acts.

[0162] In some alternative embodiments, step a631 includes:

[0163] Step a6311, divide the X - type parity - check matrix into a first X - type parity - check matrix and a second X - type parity - check matrix based on the following formula:

[0164]

[0165]

[0166]

[0167] wherein, is the X - type parity - check matrix, is the first X - type parity - check matrix, is the second X - type parity - check matrix.

[0168] It can be seen that the first X - type parity - check matrix and the second X - type parity - check matrix are divided into left and right parts by a vertical line. The left part only acts on the second data qubit, and the right part only acts on the first data qubit.

[0169] In some alternative embodiments, the above - mentioned step a632 includes:

[0170] Step a6321, divide the Z - type parity - check matrix into a first Z - type parity - check matrix and a second Z - type parity - check matrix based on the following formula:

[0171]

[0172]

[0173]

[0174] wherein, is the Z - type parity - check matrix, is the first Z - type parity - check matrix, is the second Z - type parity - check matrix, is the transpose matrix of the second matrix, is the transpose matrix of the first matrix.

[0175] It can be seen that the first Z - type parity - check matrix and the second Z - type parity - check matrix are divided into left and right parts by a vertical line. The left part only acts on the second data qubit, and the right part only acts on the first data qubit.

[0176] In some alternative embodiments, the above - mentioned step a633 includes:

[0177] Step a6331: Based on the first X-type parity-check matrix, determine that each X-type auxiliary qubit is connected to the second data qubit nearest to it above, the second data qubit nearest to it below, and the first data qubit nearest to it on the right.

[0178] Step a6332: Based on the second X-type parity-check matrix, determine that each X-type auxiliary qubit is connected to the third second data qubit on the right of the second data qubit second-nearest to it above, the first data qubit nearest to it on the left, and the third first data qubit below the first data qubit second-nearest to it on the left.

[0179] Step a6333: Based on the first Z-type parity-check matrix, determine that each Z-type auxiliary qubit is connected to the first data qubit nearest to it above, the first data qubit nearest to it below, and the second data qubit nearest to it on the left.

[0180] Step a6334: Based on the second Z-type parity-check matrix, determine that each Z-type auxiliary qubit is connected to the second data qubit nearest to it on the right, the third second data qubit above the second data qubit second-nearest to it on the right, and the third first data qubit on the left of the first data qubit second-nearest to it below.

[0181] Step a6335: Based on the connection relationship between the X-type auxiliary qubits and the first and second data qubits, determine the first target data qubits on which the X-type stabilizer operator acts.

[0182] Step a6336: Based on the connection relationship between the Z-type auxiliary qubits and the first and second data qubits, determine the second target data qubits on which the Z-type stabilizer operator acts.

[0183] In some alternative embodiments, the above step a6335 includes:

[0184] Step a63351: For any X-type stabilizer operator, determine that the first and second data qubits connected to the X-type auxiliary qubit corresponding to this X-type stabilizer operator are the first target data qubits on which this X-type stabilizer operator acts.

[0185] Wherein, one X-type stabilizer operator corresponds to one X-type auxiliary qubit.

[0186] In some alternative embodiments, the above step a6336 includes:

[0187] Step a63361: For any Z-type stabilizer operator, determine that the first data qubit and the second data qubit connected by the Z-type auxiliary qubit corresponding to the Z-type stabilizer operator are the second target data qubits on which the Z-type stabilizer operator acts;

[0188] Among them, one Z-type stabilizer operator corresponds to one Z-type auxiliary qubit.

[0189] In some alternative embodiments, the above quantum information error correction method further includes:

[0190] Step c1: The first circuit connected based on the connection relationship between physical qubits determined by the first X-type parity check matrix and the first Z-type parity check matrix is located on the first surface of the plane.

[0191] Figure 4 It is a schematic diagram of the first circuit on the first surface provided by the embodiment of the present application. As Figure 4 shown, the circuit is represented by a dotted line and is determined based on the connection relationship between physical qubits determined by the above steps a6331 and a6333. Due to the periodic boundary condition, the first circuit forms 6 mutually independent circular ring structures, and all circuits do not cross lines. The first surface may be the upper surface of the plane.

[0192] Step c2: The second circuit connected based on the connection relationship between physical qubits determined by the second X-type parity check matrix and the second Z-type parity check matrix is located on the second surface of the plane.

[0193] Figure 5 It is a schematic diagram of a part of the second circuit on the second surface provided by the embodiment of the present application. As Figure 5 shown, the circuit is represented by a solid line and is determined based on the connection relationship between physical qubits determined by the above steps a6332 and a6334. The second surface may be the lower surface of the plane.

[0194] It should be noted that since the superconducting qubits and the circuits are located on a two-dimensional plane, the circuits on the superconducting quantum chip must satisfy that the circuits cannot cross lines. Therefore, in the embodiment of the present application, the circuits are divided into a first circuit and a second circuit. The first circuit is located on the upper surface of the plane, and the second circuit is located on the lower surface of the plane, so that all circuits can avoid crossing lines.

[0195] The quantum information error correction method provided by the embodiment of the present application divides the circuits into a first circuit and a second circuit. The first circuit is located on the upper surface of the plane, and the second circuit is located on the lower surface of the plane, effectively avoiding the problem of circuit cross-line crossing. This design meets the actual requirements of the superconducting quantum chip and ensures that the qubits and circuits can operate stably on a two-dimensional plane.

[0196] In some alternative embodiments, the above quantum information error correction method further includes:

[0197] Step d1: Continuously move the second line until the principle of non-crossing of lines is satisfied.

[0198] As Figure 5 shown, there may be a phenomenon of cross-line crossing between the second lines. In order to satisfy the principle of non-crossing of lines, due to the periodic boundary conditions, the type-B lines can be changed into 6 independent circular ring structures through continuous movement, that is, non-crossing movement of the lines, and all lines do not cross each other.

[0199] Figure 6 This is a schematic diagram of the second line after continuous movement provided by the embodiment of the present application. As Figure 6 shown, Figure 6 the dotted line in

[0200] shows that the second line after continuous movement satisfies the principle of non-crossing of lines. The quantum information error correction method provided by the embodiment of the present application makes all lines finally satisfy the principle of non-crossing of lines through continuous movement of the second line. This operation ensures that the line layout on the superconducting quantum chip meets the requirements of physical implementation and avoids signal interference or short-circuit problems caused by line crossing.

[0201] In some alternative embodiments, the above step S203 includes:

[0202] Step e1: Horizontally place the third matrix and the fourth matrix side by side to construct an X-type parity check matrix with 36 rows and 72 columns.

[0203] Among them, the X-type parity check matrix can be expressed as .

[0204] Step e2: Based on the third matrix and the fourth matrix, determine the transpose matrix of the third matrix and the transpose matrix of the fourth matrix.

[0205] Step e3: Horizontally place the transpose matrix of the fourth matrix and the transpose matrix of the third matrix side by side to construct a Z-type parity check matrix with 36 rows and 72 columns.

[0206] Among them, the Z-type parity check matrix can be expressed as , where is the transpose matrix of the third matrix, is the transpose matrix of the fourth matrix.

[0207] Through the description of the above embodiments, those skilled in the art can clearly understand that the method according to the above embodiments can be implemented by means of software plus a necessary general hardware platform. Of course, it can also be implemented by hardware, but in many cases the former is a better implementation method.

[0208] An embodiment of the present application also provides a superconducting quantum platform, and the superconducting quantum computing platform is used to determine and correct the errors of the quantum information to be error-corrected based on any one of the above quantum information error correction methods.

[0209] It should be noted that since the physical qubits are located on a plane and the circuits are respectively located on the upper surface and the lower surface of the plane, the quantum low-density parity-check code of the embodiment of the present application can be implemented using a superconducting quantum computing platform in principle. When implementing this quantum low-density parity-check code, the read cavity and the control line can be placed above and below the plane, where the read cavity is used to read the state of the superconducting qubit, and the control line is used to implement the manipulation of the superconducting qubit.

[0210] An embodiment of the present application also provides a quantum information error correction device, as Figure 7 shown, including:

[0211] A first construction module 701, configured to construct a 36-row and 36-column first matrix and a 36-row and 36-column second matrix through a direct product operation based on a 6-row and 6-column cyclic shift matrix and a 6-row and 6-column identity matrix.

[0212] A first determination module 702, configured to determine a third matrix and a fourth matrix based on the first matrix and the second matrix through the following formula:

[0213]

[0214]

[0215] where A is the third matrix and B is the fourth matrix, is the first matrix, is the second matrix.

[0216] A second construction module 703, configured to construct a 36-row and 72-column X-type parity-check matrix and a 36-row and 72-column Z-type parity-check matrix based on the third matrix and the fourth matrix.

[0217] A second determination module 704, configured to determine the configuration of the quantum low-density parity-check code based on the X-type parity-check matrix and the Z-type parity-check matrix, and the configuration is used to characterize the mutual relationship between the data qubits, the auxiliary qubits, and the stabilizer operators in the quantum low-density parity-check code.

[0218] The third construction module 705 is used to construct a quantum low-density parity-check code with 72 data qubits, 12 encoded logical qubits, a code distance of 6, and an encoding rate of 1 / 12 based on the configuration of the quantum low-density parity-check code.

[0219] The encoding module 706 is used to encode the quantum information to be error-corrected into the quantum states of the data qubits in the quantum low-density parity-check code.

[0220] The third determination module 707 is used to measure the auxiliary qubits in the quantum low-density parity-check code and determine the eigenvalues of the stabilizer operators.

[0221] The fourth determination module 708 is used to determine and correct the errors in the quantum information to be error-corrected based on the eigenvalues of the stabilizer operators.

[0222] In some alternative embodiments, the first construction module 701 includes:

[0223] The first determination unit is used to determine the first matrix based on a 6×6 cyclic shift matrix and a 6×6 identity matrix through the following formula:

[0224]

[0225] The second determination unit is used to determine the second matrix based on a 6×6 cyclic shift matrix and a 6×6 identity matrix through the following formula:

[0226]

[0227] Where is a 6×6 identity matrix, is the direct product operation, is a 6×6 cyclic shift matrix.

[0228] In some alternative embodiments, the second determination module 704 includes:

[0229] The third determination unit is used to determine the number of data qubits in the quantum low-density parity-check code based on the number of columns of the X-type parity-check matrix.

[0230] The fourth determination unit is used to determine the number of X-type auxiliary qubits in the quantum low-density parity-check code based on the number of rows of the X-type parity-check matrix.

[0231] The fifth determination unit is used to determine the number of Z-type auxiliary qubits in the quantum low-density parity-check code based on the number of rows of the Z-type parity-check matrix.

[0232] A sixth determination unit, configured to, for each row in the X-type parity check matrix, substitute the first preset character in the row with a Pauli X operator, substitute the second preset character in the row with a 2×2 identity matrix, and determine the X-type stabilizer operator corresponding to the row.

[0233] A seventh determination unit, configured to, for each row in the Z-type parity check matrix, substitute the first preset character in the row with a Pauli Z operator, substitute the second preset character in the row with a 2×2 identity matrix, and determine the Z-type stabilizer operator corresponding to the row.

[0234] An eighth determination unit, configured to determine the configuration of the quantum low-density parity check matrix based on the number of data qubits, the number of X-type auxiliary qubits, the number of Z-type auxiliary qubits, the X-type stabilizer operators, the Z-type stabilizer operators, the X-type parity check matrix, and the Z-type parity check matrix.

[0235] Wherein, the auxiliary qubits include X-type auxiliary qubits and Z-type auxiliary qubits, the stabilizer operators include X-type stabilizer operators and Z-type stabilizer operators, and all the stabilizer operators commute with each other in pairs.

[0236] In some alternative embodiments, the eighth determination unit includes:

[0237] A ninth determination unit, configured to determine the number of physical qubits based on the number of data qubits, the number of X-type auxiliary qubits, and the number of Z-type auxiliary qubits, where the physical qubits include data qubits, X-type auxiliary qubits, and Z-type auxiliary qubits.

[0238] A tenth determination unit, configured to determine the arrangement rule of the physical qubits based on the number of physical qubits.

[0239] An eleventh determination unit, configured to determine the connection relationship between the physical qubits, the first target data qubits acted on by the X-type stabilizer operators, and the second target data qubits acted on by the Z-type stabilizer operators based on the X-type parity check matrix and the Z-type parity check matrix.

[0240] Wherein, the configuration of the quantum low-density parity check matrix includes the arrangement rule of the physical qubits, the connection relationship between the physical qubits, the first target data qubits acted on by the X-type stabilizer operators, and the second target data qubits acted on by the Z-type stabilizer operators.

[0241] In some alternative embodiments, the tenth determination unit includes:

[0242] A twelfth determination unit, configured to determine, based on the number of physical qubits, that all physical qubits are arranged at the vertices of a square lattice in a 12-row and 12-column arrangement form, where the row numbers increase from top to bottom, the column numbers increase from left to right, and all physical qubits are located on a plane with periodic boundary conditions in both the horizontal and vertical directions.

[0243] In some alternative embodiments, the quantum information error correction device further includes:

[0244] A first setting unit, configured to set the arrangement mode of the physical qubits in the odd rows of the 12 rows and 12 columns as an alternating arrangement of X-type auxiliary qubits and first data qubits from left to right, where the leftmost one is an X-type auxiliary qubit and the rightmost one is a first data qubit.

[0245] A second setting unit, configured to set the arrangement mode of the physical qubits in the even rows of the 12 rows and 12 columns as an alternating arrangement of second data qubits and Z-type auxiliary qubits from left to right, where the leftmost one is a second data qubit and the rightmost one is a Z-type auxiliary qubit.

[0246] Wherein, the data qubits include a first data qubit and a second data qubit.

[0247] In some alternative embodiments, the eleventh determination unit includes:

[0248] A first partitioning unit, configured to partition the X-type parity check matrix into a first X-type parity check matrix and a second X-type parity check matrix, where each row of the first X-type parity check matrix and the second X-type parity check matrix includes three first preset characters.

[0249] A second partitioning unit, configured to partition the Z-type parity check matrix into a first Z-type parity check matrix and a second Z-type parity check matrix, where each row of the first Z-type parity check matrix and the second Z-type parity check matrix includes three first preset characters.

[0250] A thirteenth determination unit, configured to determine the connection relationship between physical qubits, the first target data qubits acted on by the X-type stabilizer operator, and the second target data qubits acted on by the Z-type stabilizer operator based on the first X-type parity check matrix, the second X-type parity check matrix, the first Z-type parity check matrix, and the second Z-type parity check matrix.

[0251] In some alternative embodiments, the first partitioning unit includes:

[0252] A first sub-partitioning unit, configured to partition the X-type parity check matrix into a first X-type parity check matrix and a second X-type parity check matrix based on the following formula:

[0253]

[0254]

[0255]

[0256] Among them, is an X-type parity-check matrix, is the first X-type parity-check matrix, is the second X-type parity-check matrix.

[0257] In some alternative embodiments, the second partitioning unit includes:

[0258] A second sub-partitioning unit, configured to partition a Z-type parity-check matrix into a first Z-type parity-check matrix and a second Z-type parity-check matrix based on the following formula:

[0259]

[0260]

[0261]

[0262] Among them, is a Z-type parity-check matrix, is the first Z-type parity-check matrix, is the second Z-type parity-check matrix, is the transpose matrix of the second matrix, is the transpose matrix of the first matrix.

[0263] In some alternative embodiments, the thirteenth determination unit includes:

[0264] A fourteenth determination unit, configured to determine, based on the first X-type parity-check matrix, that each X-type auxiliary qubit is connected to the second data qubit that is the nearest neighbor above it, the second data qubit that is the nearest neighbor below it, and the first data qubit that is the nearest neighbor to its right.

[0265] A fifteenth determination unit, configured to determine, based on the second X-type parity-check matrix, that each X-type auxiliary qubit is connected to the third second data qubit on the right of the second data qubit that is the second nearest neighbor above it, the first data qubit that is the nearest neighbor to its left, and the third first data qubit below the first data qubit that is the second nearest neighbor to its left.

[0266] A sixteenth determination unit, configured to determine, based on a first Z-type parity check matrix, that each Z-type auxiliary qubit is connected to a first data qubit that is the nearest neighbor above it, a first data qubit that is the nearest neighbor below it, and a second data qubit that is the nearest neighbor to its left.

[0267] A seventeenth determination unit, configured to determine, based on a second Z-type parity check matrix, that each Z-type auxiliary qubit is connected to a second data qubit that is the nearest neighbor to its right, a third second data qubit above the second data qubit that is the second nearest neighbor to its right, and a third first data qubit to the left of the first data qubit that is the second nearest neighbor below it.

[0268] An eighteenth determination unit, configured to determine a first target data qubit on which an X-type stabilizer operator acts, based on the connection relationship between an X-type auxiliary qubit and first and second data qubits.

[0269] A nineteenth determination unit, configured to determine a second target data qubit on which a Z-type stabilizer operator acts, based on the connection relationship between a Z-type auxiliary qubit and first and second data qubits.

[0270] In some alternative embodiments, the eighteenth determination unit includes:

[0271] A twentieth determination unit, configured to, for any X-type stabilizer operator, determine the first data qubit and the second data qubit connected to the X-type auxiliary qubit corresponding to the X-type stabilizer operator as the first target data qubit on which the X-type stabilizer operator acts.

[0272] Wherein, one X-type stabilizer operator corresponds to one X-type auxiliary qubit.

[0273] In some alternative embodiments, the nineteenth determination unit includes:

[0274] A twenty-first determination unit, configured to, for any Z-type stabilizer operator, determine the first data qubit and the second data qubit connected to the Z-type auxiliary qubit corresponding to the Z-type stabilizer operator as the second target data qubit on which the Z-type stabilizer operator acts.

[0275] Wherein, one Z-type stabilizer operator corresponds to one Z-type auxiliary qubit.

[0276] In some alternative embodiments, the quantum information error correction device further includes:

[0277] A twenty-second determination unit, configured to determine that a first circuit connected based on the connection relationship between physical qubits determined by a first X-type parity check matrix and a first Z-type parity check matrix is located on a first surface of a plane.

[0278] The twenty-third determination unit is configured to determine that the second line connected based on the connection relationship between the physical qubits determined by the second X-type parity check matrix and the second Z-type parity check matrix is located on the second surface of the plane.

[0279] In some alternative embodiments, the quantum information error correction device further includes:

[0280] A moving unit configured to continuously move the second line until the principle of non-crossing of lines is satisfied.

[0281] In some alternative embodiments, the second construction module 703 includes:

[0282] A first construction unit configured to horizontally arrange and place the third matrix and the fourth matrix to construct an X-type parity check matrix with 36 rows and 72 columns.

[0283] A twenty-fourth determination unit configured to determine the transposed matrix of the third matrix and the transposed matrix of the fourth matrix based on the third matrix and the fourth matrix.

[0284] A second construction unit configured to horizontally arrange and place the transposed matrix of the fourth matrix and the transposed matrix of the third matrix to construct a Z-type parity check matrix with 36 rows and 72 columns.

[0285] For the description of the features in the corresponding embodiments of the quantum information error correction device, reference can be made to the relevant descriptions in the corresponding embodiments of the quantum information error correction method, which will not be elaborated here one by one.

[0286] An embodiment of the present application further provides an electronic device, as Figure 8 shown, including a processor 801 and a memory 802. The memory 802 stores a computer program, and the processor 801 is configured to run the computer program to execute the steps in any one of the above embodiments of the quantum information error correction method.

[0287] An embodiment of the present application further provides a computer-readable storage medium storing a computer program, wherein the computer program is configured to execute the steps in any one of the above embodiments of the quantum information error correction method when running.

[0288] In an exemplary embodiment, the above computer-readable storage medium may include, but is not limited to: various media such as a USB flash drive, a read-only memory (ROM for short), a random access memory (RAM for short), a mobile hard disk, a magnetic disk, or an optical disc that can store a computer program.

[0289] Embodiments of the present application also provide a computer program product. The computer program product includes a computer program, and when the computer program is executed by a processor, it implements the steps in any of the above-described embodiments of the quantum information error correction method.

[0290] Embodiments of the present application also provide another computer program product, including a non-volatile computer-readable storage medium. The non-volatile computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, it implements the steps in any of the above-described embodiments of the quantum information error correction method.

[0291] Those skilled in the art can further realize that the units and algorithm steps of each example described in combination with the embodiments disclosed herein can be implemented by electronic hardware, computer software, or a combination of the two. To clearly illustrate the interchangeability of hardware and software, the components and steps of each example have been generally described according to their functions in the above description. Whether these functions are executed in a hardware or software manner depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered to exceed the scope of the present application.

[0292] The above has introduced in detail a quantum information error correction method, apparatus, electronic device, and storage medium provided by the present application. Specific examples are used in this article to elaborate on the principle and implementation manner of the present application. The description of the above embodiments is only used to help understand the method and its core idea of the present application. It should be noted that for those of ordinary skill in the art in the technical field, without departing from the principle of the present application, several improvements and modifications can be made to the present application, and these improvements and modifications also fall within the protection scope of the claims of the present application.

Claims

1. A quantum information error correction method, characterized in that: include: Based on the 6-row 6-column cyclic shift matrix and the 6-row 6-column identity matrix, a first matrix with 36 rows and 36 columns and a second matrix with 36 rows and 36 columns are constructed by direct product operation; Based on the first matrix and the second matrix, the third matrix and the fourth matrix are determined by the following formula: Among them, A is the third matrix, B is the fourth matrix, is the first matrix, is the second matrix; Based on the third matrix and the fourth matrix, construct an X-type parity check matrix with 36 rows and 72 columns and a Z-type parity check matrix with 36 rows and 72 columns; Determining a configuration of a quantum low-density parity-check code based on the X-type parity-check matrix and the Z-type parity-check matrix, wherein the configuration is used to characterize the relationship between data qubits, auxiliary qubits, and stabilizer operators in the quantum low-density parity-check code; Based on the configuration of the quantum low-density parity-check code, a quantum low-density parity-check code with 72 data qubits, 12 encoded logical qubits, a code distance of 6, and a coding rate of 1 / 12 is constructed; Encoding the quantum information to be corrected into the quantum state of the data quantum bit in the quantum low-density parity-check code; Measuring the auxiliary quantum bits in the quantum low-density parity-check code to determine the eigenvalues ​​of the stabilizer operator; Based on the eigenvalue of the stabilizer operator, errors in the quantum information to be corrected are determined and corrected.

2. The method according to claim 1, characterized in that The method of constructing a first matrix with 36 rows and 36 columns and a second matrix with 36 rows and 36 columns by direct product operation based on a 6-row and 6-column cyclic shift matrix and a 6-row and 6-column identity matrix includes: Based on a 6-row 6-column cyclic shift matrix and a 6-row 6-column identity matrix, the first matrix is ​​determined by the following formula: Based on the 6-row 6-column cyclic shift matrix and the 6-row 6-column identity matrix, the second matrix is ​​determined by the following formula: in, is the identity matrix with 6 rows and 6 columns, is the direct product operation, is a 6-row 6-column cyclic shift matrix.

3. The method according to claim 1, characterized in that The step of determining the configuration of a quantum low-density parity check code based on the X-type parity check matrix and the Z-type parity check matrix comprises: Determining the number of data qubits in the quantum low-density parity-check code based on the number of columns of the X-type parity-check matrix; Determining the number of X-type auxiliary quantum bits of the quantum low-density parity-check code based on the number of rows of the X-type parity-check matrix; Determining the number of Z-type auxiliary quantum bits in the quantum low-density parity-check code based on the number of rows of the Z-type parity-check matrix; For each row in the X-type parity check matrix, replace the first preset character in the row with the Pauli X operator, replace the second preset character in the row with a 2-row 2-column identity matrix, and determine the X-type stable sub-operator corresponding to the row; For each row in the Z-type parity check matrix, replace the first preset character in the row with the Pauli Z operator, replace the second preset character in the row with a 2-row 2-column identity matrix, and determine the Z-type stabilizer operator corresponding to the row; Determining a configuration of a quantum low-density parity check matrix based on the number of data qubits, the number of X-type auxiliary qubits, the number of Z-type auxiliary qubits, the X-type stabilizer operator, the Z-type stabilizer operator, the X-type parity check matrix, and the Z-type parity check matrix; Among them, the auxiliary quantum bits include X-type auxiliary quantum bits and Z-type auxiliary quantum bits, the stabilizer operators include X-type stabilizer operators and Z-type stabilizer operators, and all stabilizer operators commutate pairwise.

4. The method according to claim 3, characterized in that The determining of the configuration of a quantum low-density parity check matrix based on the number of data qubits, the number of X-type auxiliary qubits, the number of Z-type auxiliary qubits, the X-type stabilizer operator, the Z-type stabilizer operator, the X-type parity check matrix, and the Z-type parity check matrix comprises: Determining the number of physical qubits based on the number of the data qubits, the number of the X-type auxiliary qubits, and the number of the Z-type auxiliary qubits, the physical qubits including the data qubits, the X-type auxiliary qubits, and the Z-type auxiliary qubits; Determining an arrangement rule of the physical quantum bits based on the number of the physical quantum bits; Based on the X-type parity check matrix and the Z-type parity check matrix, determining a connection relationship between physical qubits, a first target data qubit acted upon by the X-type stabilizer operator, and a second target data qubit acted upon by the Z-type stabilizer operator; Among them, the configuration of the quantum low-density parity check matrix includes the arrangement rules of physical quantum bits, the connection relationship between physical quantum bits, the first target data quantum bit acted by the X-type stabilizer operator and the second target data quantum bit acted by the Z-type stabilizer operator.

5. The method according to claim 4, characterized in that The step of determining an arrangement rule of physical quantum bits based on the number of physical quantum bits includes: Based on the number of the physical quantum bits, it is determined that all physical quantum bits are arranged at the vertices of the square lattice in an arrangement of 12 rows and 12 columns, with the row numbers increasing from top to bottom and the column numbers increasing from left to right, and all physical quantum bits are located on a plane with periodic boundary conditions in both the horizontal and vertical directions.

6. The method according to claim 5, characterized in that The method further comprises: The physical qubits in the odd-numbered rows of the 12 rows and 12 columns are arranged in such a way that the X-type auxiliary qubits and the first data qubits are arranged alternately from left to right, wherein the leftmost side is the X-type auxiliary qubit and the rightmost side is the first data qubit; The physical qubits in the even-numbered rows of the 12 rows and 12 columns are arranged in such a way that the second data qubits and the Z-type auxiliary qubits are arranged alternately from left to right, wherein the leftmost side is the second data qubit and the rightmost side is the Z-type auxiliary qubit; The data qubits include a first data qubit and a second data qubit.

7. The method according to claim 6, characterized in that The determining, based on the X-type parity check matrix and the Z-type parity check matrix, a connection relationship between physical quantum bits, a first target data quantum bit acted upon by the X-type stabilizer operator, and a second target data quantum bit acted upon by the Z-type stabilizer operator comprises: Dividing the X-type parity check matrix into a first X-type parity check matrix and a second X-type parity check matrix, wherein each row of the first X-type parity check matrix and the second X-type parity check matrix includes three first preset characters; Dividing the Z-type parity check matrix into a first Z-type parity check matrix and a second Z-type parity check matrix, wherein each row of the first Z-type parity check matrix and the second Z-type parity check matrix includes three first preset characters; Based on the first X-type parity check matrix, the second X-type parity check matrix, the first Z-type parity check matrix and the second Z-type parity check matrix, a connection relationship between physical quantum bits, a first target data quantum bit acted upon by the X-type stabilizer operator, and a second target data quantum bit acted upon by the Z-type stabilizer operator are determined.

8. The method according to claim 7, characterized in that The step of dividing the X-type parity check matrix into a first X-type parity check matrix and a second X-type parity check matrix comprises: Based on the following formula, the X-type parity check matrix is ​​divided into a first X-type parity check matrix and a second X-type parity check matrix: in, is an X-type parity check matrix, is the first X-type parity check matrix, is the second X-type parity check matrix.

9. The method according to claim 7, characterized in that: The step of dividing the Z-type parity check matrix into a first Z-type parity check matrix and a second Z-type parity check matrix comprises: Based on the following formula, the Z-type parity check matrix is ​​divided into a first Z-type parity check matrix and a second Z-type parity check matrix: in, is a Z-type parity check matrix, is the first Z-type parity check matrix, is the second Z-type parity check matrix, is the transposed matrix of the second matrix, is the transposed matrix of the first matrix.

10. The method according to claim 7, characterized in that The determining, based on the first X-type parity check matrix, the second X-type parity check matrix, the first Z-type parity check matrix, and the second Z-type parity check matrix, a connection relationship between physical quantum bits, a first target data quantum bit acted upon by the X-type stabilizer operator, and a second target data quantum bit acted upon by the Z-type stabilizer operator, comprises: Based on the first X-type parity check matrix, determine that each X-type auxiliary qubit is connected to a second data qubit located at its upper nearest neighbor, a second data qubit located at its lower nearest neighbor, and a first data qubit located at its right nearest neighbor; Based on the second X-type parity check matrix, determine that each X-type auxiliary qubit is connected to the third second data qubit to the right of the second data qubit located above the second nearest neighbor, the first data qubit located to the left of the first nearest neighbor, and the third first data qubit below the first data qubit located to the left of the second nearest neighbor; Based on the first Z-type parity check matrix, determine that each Z-type auxiliary qubit is connected to a first data qubit located at a nearest neighbor above it, a first data qubit located at a nearest neighbor below it, and a second data qubit located at a nearest neighbor to its left; Based on the second Z-type parity check matrix, determine that each Z-type auxiliary qubit is connected to the second data qubit located at the nearest neighbor on the right, the third second data qubit above the second data qubit located at the next nearest neighbor on the right, and the third first data qubit to the left of the first data qubit located at the next nearest neighbor below; Determining a first target data qubit on which the X-type stabilizer operator acts based on a connection relationship between the X-type auxiliary qubit and the first data qubit and the second data qubit; Based on the connection relationship between the Z-type auxiliary qubit and the first data qubit and the second data qubit, a second target data qubit on which the Z-type stabilizer operator acts is determined.

11. The method according to claim 10, characterized in that The determining, based on the connection relationship between the X-type auxiliary qubit and the first data qubit and the second data qubit, of the first target data qubit acted upon by the X-type stabilizer operator comprises: For any X-type stabilizer operator, determine the first data qubit and the second data qubit connected to the X-type auxiliary qubit corresponding to the X-type stabilizer operator as the first target data qubit acted upon by the X-type stabilizer operator; Among them, one X-type stabilizer operator corresponds to one X-type auxiliary quantum bit.

12. The method according to claim 10, characterized in that The determining, based on the connection relationship between the Z-type auxiliary qubit and the first data qubit and the second data qubit, of the second target data qubit on which the Z-type stabilizer operator acts comprises: For any Z-type stabilizer operator, determining a first data qubit and a second data qubit connected to a Z-type auxiliary qubit corresponding to the Z-type stabilizer operator as a second target data qubit acted upon by the Z-type stabilizer operator; Among them, one Z-type stabilizer operator corresponds to one Z-type auxiliary quantum bit.

13. The method according to claim 10, characterized in that The method further comprises: A first line connected based on a connection relationship between physical quantum bits determined by the first X-type parity check matrix and the first Z-type parity check matrix is ​​located on a first surface of the plane; A second line that connects the physical quantum bits based on the connection relationship between the second X-type parity check matrix and the second Z-type parity check matrix is ​​located on the second surface of the plane.

14. The method according to claim 13, characterized in that The method further comprises: The second line is continuously moved until the line does not cross the line principle is met.

15. The method according to claim 1, characterized in that The step of constructing an X-type parity check matrix with 36 rows and 72 columns and a Z-type parity check matrix with 36 rows and 72 columns based on the third matrix and the fourth matrix comprises: Placing the third matrix and the fourth matrix side by side horizontally to construct an X-type parity check matrix with 36 rows and 72 columns; Based on the third matrix and the fourth matrix, determining a transposed matrix of the third matrix and a transposed matrix of the fourth matrix; The transposed matrix of the fourth matrix and the transposed matrix of the third matrix are placed side by side horizontally to construct a Z-type parity check matrix with 36 rows and 72 columns.

16. A superconducting quantum computing platform, characterized in that: The superconducting quantum computing platform is used to determine and correct errors in quantum information to be corrected based on the quantum information error correction method according to any one of claims 1 to 15.

17. A quantum information error correction device, characterized in that: include: A first construction module is used to construct a first matrix with 36 rows and 36 columns and a second matrix with 36 rows and 36 columns through a direct product operation based on a 6-row 6-column cyclic shift matrix and a 6-row 6-column identity matrix; The first determination module is used to determine the third matrix and the fourth matrix based on the first matrix and the second matrix by the following formula: Among them, A is the third matrix, B is the fourth matrix, is the first matrix, is the second matrix; A second construction module is used to construct an X-type parity check matrix with 36 rows and 72 columns and a Z-type parity check matrix with 36 rows and 72 columns based on the third matrix and the fourth matrix; A second determination module is used to determine a configuration of a quantum low-density parity-check code based on the X-type parity-check matrix and the Z-type parity-check matrix, wherein the configuration is used to characterize the relationship between data quantum bits, auxiliary quantum bits, and stabilizer operators in the quantum low-density parity-check code; A third construction module is used to construct a quantum low-density parity-check code with 72 data qubits, 12 encoded logical qubits, a code distance of 6, and a coding rate of 1 / 12 based on the configuration of the quantum low-density parity-check code; An encoding module, used for encoding the quantum information to be corrected into the quantum state of the data quantum bit in the quantum low-density parity-check code; A third determination module is used to measure the auxiliary quantum bits in the quantum low-density parity-check code to determine the eigenvalue of the stabilizer operator; The fourth determination module is used to determine and correct errors in the quantum information to be corrected based on the eigenvalue of the stabilizer operator.

18. An electronic device, characterized in that: include: Memory for storing computer programs; A processor, configured to implement the steps of the quantum information error correction method according to any one of claims 1 to 15 when executing the computer program.

19. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, wherein the computer program, when executed by a processor, implements the steps of the quantum information error correction method according to any one of claims 1 to 15.

20. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the quantum information error correction method according to any one of claims 1 to 15 are implemented.

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