High-performance decoding method for quantum low-density parity check codes

Abstract

The invention discloses a high-performance decoding method for quantum low-density parity check codes, and belongs to the technical field of quantum computing. Comprising the following steps: solving a transformation matrix and a permutation matrix through a matrix decoupling strategy optimized by an off-line satisfiability modulus theory, and equivalently transforming an original check matrix into a diagonal block matrix and any sparse matrix; the method comprises the following steps: decomposing an error mode into a left error corresponding to a diagonal block matrix and a right error corresponding to any sparse matrix through an online hierarchical greedy decoding algorithm, guessing an error bit of the right error, and then calculating an error symptom corresponding to the left error based on any sparse matrix; then the error symptom is divided according to the diagonal block matrixes for parallel decoding, decoding results of all the block matrixes are combined to form a left error, and finally the left error and the right error are spliced to obtain a complete error mode. According to the method, accurate and real-time decoding of the qLDPC code can be realized, and the method is applied to the frontier fields of quantum communication, quantum calculation and the like.

Description

Technical Field

[0001] The present invention belongs to the field of quantum computing technology, and in particular relates to a high-performance decoding method for quantum low-density parity-check codes. Background Art

[0002] Quantum error correction (QEC) is crucial for achieving large-scale, fault-tolerant quantum computing. QEC relies on error-correcting codes, which encode multiple physical qubits into a single logical qubit, protecting the information contained in the logical qubit through redundant coding. Among various error-correcting codes, surface codes have been widely studied and experimentally implemented due to their high noise threshold and locality-friendly structure. However, surface codes suffer from poor scalability: due to their unique planar lattice structure, surface codes require hundreds or even thousands of physical qubits to encode a single logical qubit, resulting in a significant physical resource overhead that limits the feasibility of building large-scale, fault-tolerant quantum systems.

[0003] Quantum low-density parity-check (qLDPC) codes offer a promising alternative. qLDPC codes are defined by a binary sparse parity check matrix (containing only 0s and 1s), where each row of the parity check matrix corresponds to a stabilizer and each column corresponds to a data qubit. A 1 in the parity check matrix indicates that the associated stabilizer acts on that data qubit. This sparse parity check matrix enables an asymptotically constant coding rate, making qLDPC codes more economical in physical qubit resources than surface codes. Notably, in 2024, IBM introduced bivariate cyclic (BB) codes, a family of qLDPC codes that achieve a high error threshold of 0.7% and can save 10 times the physical qubit overhead compared to surface codes. This suggests that qLDPC codes have great potential as a scalable architectural solution for superconducting quantum computing platforms.

[0004] In addition to selecting a suitable error-correcting code, an accurate, real-time decoder also plays a key role in QEC. On the quantum computer side, parity qubits interact with nearby data qubits and periodically extract error symptoms. On the classical decoder side, the decoder uses these error symptoms to infer and correct errors in the data qubits before entering the next QEC cycle. The decoder must be accurate because any incorrect corrections can lead to logical errors that propagate through the quantum circuit and ultimately cause the computation to fail. At the same time, the decoder must run in real time. If decoding lags behind the generation of error symptoms, the system will continue to accumulate error symptoms, where unprocessed data will delay subsequent quantum operations. This delay overhead grows exponentially with the depth of the circuit.

[0005] The simple, regular two-dimensional grid structure of surface codes facilitates real-time decoders, such as the minimum weight perfect matching (MWPM) algorithm based on graph matching. However, due to the structural differences in error-correcting codes, the MWPM decoding algorithm cannot be directly and efficiently applied to qLDPC codes. This is because, in qLDPC codes, each data qubit is connected to two or more parity qubits, forming a hypergraph structure rather than a simple graph. The resulting computational complexity renders the MWPM algorithm ineffective, as matching in a hypergraph is an NP-hard problem. Therefore, the decoding algorithms for qLDPC codes differ significantly from those for surface codes.

[0006] The most representative decoding algorithms for qLDPC codes are belief propagation (BP) and belief propagation with ordered statistical decoding (BP+OSD). BP is a message passing algorithm that iteratively updates approximate error probabilities for data qubits, improving these approximate probabilities with each iteration, ideally converging to the most likely error pattern. If BP fails to converge, BP+OSD invokes OSD to post-process the decoding results. OSD first sorts the data qubits according to BP's error probabilities. It then selects a subset of qubits, hypothesizes a possible error pattern, and solves a restricted linear system to test whether the pattern matches the observed error symptoms. This process is repeated for many candidate error patterns to find the most likely one.

[0007] However, BP and BP+OSD cannot simultaneously achieve high decoding accuracy and low decoding latency. BP, due to its low complexity and high parallelism, holds promise for real-time decoding and is suitable for deployment on hardware platforms such as FPGAs and ASICs. However, BP suffers from low accuracy due to a phenomenon known as "quantum degeneracy," where different error modes can produce the same error symptoms. This problem arises because the number of columns in the parity check matrix far exceeds the number of rows. BP does not account for this degeneracy, resulting in BP often converging to incorrect results. Although BP+OSD improves accuracy by using OSD, its decoding latency is very high due to high-complexity operations such as sorting and solving linear systems. These computationally intensive operations make BP+OSD unsuitable for real-time decoding. This trade-off between accuracy and latency highlights the urgent need for theoretical research on high-performance qLDPC decoding algorithms to address this research gap. Summary of the Invention

[0008] In view of the above, the purpose of the present invention is to provide a high-performance decoding method for quantum low-density parity-check codes, which decouples the check matrix through a matrix decoupling strategy optimized by offline satisfiability modulo theory (SMT), and solves the error pattern based on the decoupled check matrix through an online hierarchical greedy decoding algorithm to solve the limitations of the existing qLDPC decoding algorithm in the trade-off between accuracy and delay, thereby achieving accurate and real-time decoding of qLDPC codes. It can be applied to cutting-edge fields such as quantum communication and quantum computing that have extremely high requirements for data reliability and real-time performance.

[0009] To achieve the above-mentioned purpose, the present invention provides the following technical solutions: An embodiment of the present invention provides a high-performance decoding method for quantum low-density parity-check codes, comprising the following steps: Through the matrix decoupling strategy optimized by offline satisfiability modulo theory, the transformation matrix and permutation matrix are solved to transform the original check matrix into a diagonal block matrix and an arbitrary sparse matrix. Through an online hierarchical greedy decoding algorithm, the error pattern is decomposed into a left error corresponding to a diagonal block matrix and a right error corresponding to an arbitrary sparse matrix. The error bits of the right error are first guessed, and then the error symptom corresponding to the left error is calculated based on an arbitrary sparse matrix. The error symptom is then divided according to the diagonal block matrix for parallel decoding, and the decoding results of all the block matrices are merged to form the left error. Finally, the left error and the right error are spliced ​​to obtain the complete error pattern.

[0010] Preferably, the matrix decoupling strategy optimized by offline satisfiability modulo theory, which solves the transformation matrix and the permutation matrix to equivalently transform the original check matrix into a diagonal block matrix and an arbitrary sparse matrix, includes: The matrix decoupling strategy of offline satisfiability modulo theory optimization first solves the specific transformation matrix by using the satisfiability modulo theory solver under the constraints. and permutation matrix And maximize the sparsity of the decoupled check matrix, and then convert the check matrix of the original quantum low-density parity check code into By left-multiplying the transformation matrix and right-multiply the permutation matrix Perform equivalent transformation to obtain a diagonal block matrix and any sparse matrix The decoupled check matrix ,in Indicates the A block matrix, Represents the total number of block matrices.

[0011] Preferably, solving the specific transformation matrix and permutation matrix by using a satisfiability modulo theory solver under the constraint conditions includes: The transformation matrix and permutation matrix Set as a Boolean variable and used to represent the decoupled check matrix Elements, set the constraints during the decoupling process as follows: (1) Transformation matrix It is a full-rank matrix, that is, no subset of rows can be XORed to the zero vector; (2) Permutation matrix Each row and column must contain only one non-zero element; (3) Decoupling check matrix A specific shape that meets the definition The constraints are as follows: i, each block in the decoupled parity check matrix must have the same shape; ii, except for sparse matrices Besides, all elements outside the block must be zero; iii. Each block in the decoupled check matrix must contain an identity matrix; The objective function is set to seek to minimize the decoupled check matrix The total number of non-zero elements in , and then the specific transformation matrix is ​​obtained by the satisfiability module theory solver based on the constraints and objective function. and permutation matrix .

[0012] Preferably, decomposing the error pattern into left errors corresponding to a diagonal block matrix and right errors corresponding to an arbitrary sparse matrix comprises: Error Mode Split into left error and right error Two-part vector, Corresponding to the diagonal block matrix , Corresponding to the sparse matrix , expressed as: , , in, is the error pattern after substitution, is the original error pattern, is the error symptom after transformation, is the original error symptom, It is an exclusive OR operation.

[0013] Preferably, the step of first guessing the error bit of the right error and then calculating the error symptom corresponding to the left error based on an arbitrary sparse matrix includes: According to the divided left error and right error, Defined as right error symptoms and moving it to the right side of the equation, we get the left error symptom ,Right now: , First enter the original error symptoms , through the transformation matrix After the transformation, the error symptoms after the transformation are obtained , by successively guessing the right error The error bit and multiplying the sparse matrix Get the right error symptoms ,pass Calculate the left error symptoms for each time .

[0014] Preferably, the step of dividing the error symptom into diagonal block matrices for parallel decoding and combining the decoding results of all the block matrices to obtain the left error comprises: Based on the left error symptoms obtained for each calculation Decompose the matrix into smaller components based on the block , thus transforming into a set of smaller independent decoding problems Then parallel decoding is performed, and the decoding results corresponding to all block matrices are obtained through iterative greedy guessing function decoding and then merged into the current calculation Left error.

[0015] Preferably, the final step of concatenating the left error and the right error to obtain a complete error pattern includes: Concatenate all the left errors and right errors to get the permuted error pattern ,pass Permutation to obtain the complete error pattern .

[0016] Preferably, decoding is performed by a greedy guessing function, comprising: Using the structure of the decoupled check matrix ,in, represents the identity matrix, Represents an arbitrary matrix, and the left error Re-divided into and Two parts, Corresponding to the identity matrix , For any matrix ,according to Reset the decoding constraints to: , The goal of decoding is to minimize the objective function as the likelihood , that is, minimize The number of non-zero values ​​in The number of non-zero values ​​in the quantifier is guessed, starting from the minimum number and gradually increasing until the current target is less than the existing minimum. Then stop the iteration.

[0017] Compared with the prior art, the present invention has the following beneficial effects: (1) This paper designs an offline SMT optimized matrix decoupling strategy. By equivalently converting the original check matrix into a combination of a diagonal block matrix and an arbitrary sparse matrix, the number of columns and rows of each block matrix is ​​very close, thereby effectively alleviating the low decoding accuracy problem caused by quantum degeneracy.

[0018] (2) The present invention designs an online hierarchical greedy decoding algorithm that can maximize the decoding parallelism and make full use of the sparsity of the decoupled block matrix. By iteratively performing greedy guesses, the probability of occurrence of each possible error mode is calculated, and the most likely error mode is continuously approached, thereby significantly reducing the decoding delay. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0020] Figure 1 Schematic diagram of a framework of a high-performance decoding method for quantum low-density parity-check codes provided by an embodiment of the present invention; Figure 2 Schematic diagram of the principle of the matrix decoupling strategy for offline SMT optimization provided by an embodiment of the present invention; Figure 3 : is a pseudo code diagram of an online hierarchical greedy decoding algorithm provided by an embodiment of the present invention; Figure 4 This is an example diagram of the greedy guessing process in the online hierarchical greedy decoding algorithm provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0021] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and do not limit the scope of protection of the present invention.

[0022] The inventive concept of the present invention is that previous decoding algorithms for qLDPC codes cannot achieve high decoding accuracy and low decoding latency at the same time, resulting in the inability to be actually deployed in current fault-tolerant quantum systems. Specifically, the decoding accuracy of the BP algorithm decreases as the code distance of the error-correcting code increases, while the accuracy of an excellent decoding algorithm should increase as the code distance of the error-correcting code increases. This is because an increase in code distance means an increase in error correction capability, and the BP algorithm cannot fully utilize this error correction capability. In addition, in terms of decoding latency, the superconducting quantum platform requires that the decoding time of the decoder must be less than 1μs (microseconds), otherwise it will cause errors to accumulate, and then the quantum error correction will fail. However, the high computational complexity of BP+OSD makes it impossible to deploy on a hardware acceleration platform, and the decoding time is on the order of ms (milliseconds) to s (seconds), which is completely unacceptable. Therefore, to address this problem, an embodiment of the present invention provides a high-performance decoding method for quantum low-density parity-check codes. By proposing an offline SMT-optimized matrix decoupling strategy and an online hierarchical greedy decoding algorithm, it respectively addresses the technical challenges of low precision and high latency faced by current qLDPC decoding algorithms, thereby achieving accurate and real-time decoding of qLDPC codes.

[0023] like Figure 1 As shown, the embodiment provides a high-performance decoding method for quantum low-density parity-check codes, comprising the following steps: S1, through the matrix decoupling strategy optimized by offline satisfiability modulo theory, the transformation matrix and permutation matrix are solved to equivalently transform the original check matrix into a diagonal block matrix and an arbitrary sparse matrix.

[0024] The essential idea of ​​offline decoupling is to use the original large sparse check matrix Divide into a series of independent, smaller sub-matrices. However, this ideal division is not possible in most cases. Therefore, the present invention chooses to divide the original check matrix into a series of independent, smaller sub-matrices. Perform equivalent row-column transformation to transform it into a combination of a diagonal block matrix and an arbitrary sparse matrix. The detailed process is as follows Figure 2 To do this, you need to multiply the original check matrix by a transformation matrix and right-multiply by a permutation matrix . Solve for the optimal matrix and This is a major challenge because it involves a huge search space and requires a huge amount of computation. The present invention solves the problem of decoupling the check matrix by reformulating it as an SMT problem, which allows the use of an SMT solver to find the optimal transformation. The present invention defines a set of solution constraints to ensure that the decoupled matrix conforms to the required structure, with the goal of maximizing sparsity. The transformation matrix and the permutation matrix are represented as Boolean variables, and the number of columns of the decoupled submatrix is ​​closer to the number of rows, thereby effectively alleviating the low-precision problem caused by quantum degeneracy, and the decoupled matrix is ​​then stored for use in the subsequent online hierarchical greedy decoding algorithm.

[0025] S1.1, Mathematical form: This invention aims to The check matrix Apply the following transformation: (1), in, yes The full-rank transformation matrix of yes The permutation matrix of is the decoupled check matrix after row-column transformation. Under this transformation, the maximum likelihood decoding of equation (1) becomes: (2), in, is the error pattern after substitution, is the original error pattern, is the error symptom after transformation, is the original error symptom, is the weight corresponding to each error, In order to recover the optimal original error pattern, the present invention obtains the optimal permuted error pattern by decoding equation (2): and through Restore the optimal original error mode. For the decoupled check matrix , the present invention aims to convert it into the following form: (3), in, is a diagonal block matrix, Indicates the A block matrix, represents the total number of block matrices, is an arbitrary sparse matrix. In order to simplify the subsequent online decoding algorithm, the present invention further requires that each The left side contains an identity matrix. Specifically: (4), in, is the identity matrix, is an arbitrary matrix.

[0026] S1.2, variable definition: The present invention transforms the matrix and permutation matrix Set to a Boolean variable. According to equation (1), The elements can be passed through the variable and To express: (5), in, express No. Rank Elements of the column, and Also represents the row or column index.

[0027] S1.3, Constraints: The following conditions must be met during the decoupling process: (1) Transformation matrix: Transformation matrix Must be a full-rank matrix, meaning that its rows are linearly independent. Specifically, no subset of rows can be XORed to the zero vector: (6), in, Is the non-empty row index subset.

[0028] (2) Permutation matrix: The permutation matrix must satisfy that each row and each column contains only one non-zero element: (7).

[0029] (3) Decoupling check matrix: Decoupling check matrix Must meet the specific shape defined in the present invention, The constraints are as follows: i, each block in the decoupled parity check matrix must have the same shape, expressed as . The total number of rows in each block matrix and the total number of columns The following relationship must be satisfied: (8), in, is the number of blocks, and are the number of rows and columns of the original check matrix.

[0030] ii, except for the sparse matrix on the right side All elements outside the block must be zero, that is: (9).

[0031] iii. Each block in the decoupled check matrix must have an identity matrix on the left, according to equation (4): (10).

[0032] S1.4, Objective function: The present invention aims to make the new check matrix Sparse, to facilitate subsequent hardware acceleration, which means that the present invention seeks to minimize The total number of nonzero elements in : (11).

[0033] The constraints in Eqs. (5) to (10) and the objective in Eq. (11) are then passed to the SMT solver to find the specific transformation matrix and permutation matrix .

[0034] S2, through an online hierarchical greedy decoding algorithm, decomposes the error pattern into a left error corresponding to a diagonal block matrix and a right error corresponding to an arbitrary sparse matrix. First, guess the error bit of the right error and then calculate the error symptom corresponding to the left error based on an arbitrary sparse matrix. Then, the error symptom is divided according to the diagonal block matrix for parallel decoding and the decoding results of all the block matrices are merged to obtain the left error. Finally, the left error and the right error are spliced ​​to obtain the complete error pattern.

[0035] The goal of this invention is to decompose the original decoding problem into a set of smaller decoding problems that can be solved in parallel, and decode the most likely error mode through an online decoding algorithm. In order to address the challenge of high latency, the online decoding algorithm maximizes parallelism and fully utilizes the sparsity in the decoupled sub-calibration matrix to accelerate the decoding process. This is straightforward when is a diagonally block matrix. However, in the case of the present invention, the decoupled check matrix contains a sparse matrix on the right , which requires additional processing. To solve this problem, the present invention will error mode Split into left error and right error Two-part vector, Corresponding to the diagonal block matrix , Corresponding to the sparse matrix . This transforms the constraint into the following form: (12).

[0036] Next, the present invention will Defined as right error symptoms and moving it to the right side of the equation, we get the left error symptom ,Right now: (13).

[0037] This reformulated decoding constraint involves the diagonal block matrix, the left error, and the error symptom corresponding to the left error. Decompose the matrix into smaller components based on the block , thus transforming into a set of smaller independent decoding problems, where each constraint corresponds to a smaller check matrix: (14).

[0038] Furthermore, based on the new problem formulation, the present invention proposes a two-step online hierarchical greedy decoding algorithm, such as Figure 1 (b) and Figure 3 The algorithm first inputs the original error symptoms , based on the transformation matrix Error symptoms after initialization transformation . The right error The initial guess of is set to an all-zero vector, and the initial likelihood of the error pattern is set to infinity. Next, the decoding process is performed by gradually increasing the number of 1s until the maximum iteration limit M is reached. In this paper, a two-step decoding strategy is adopted: first guess the right error , then decode the left error Finally, the best left error obtained by decoding and best right error Perform concatenation and multiply by the permutation matrix , thus obtaining the error pattern of the final output .

[0039] Specifically, the present invention explores possible right errors by flipping one bit at a time , then calculate the left error symptom Then, according to the block matrix, the left error symptoms Split into The present invention uses the GreedyGuess function based on Parallel decoding left error After completion, the right error is updated and the next guessing + decoding process is performed. The weighted sum of the left and right errors is then calculated. At this point, the present invention checks whether the current target is less than the currently found best solution. If so, the best solution is updated for the next iteration. If not, the process is terminated and the currently found best solution is returned.

[0040] GreedyGuess is used to decode the left error under the constraints specified in Equation (14) .like Figure 4 As shown, the structure of the decoupled check matrix is ​​used , the present invention will be left error Re-divided into and Two parts: Corresponding to the identity matrix , For any matrix . Therefore, the decoding constraint can be rewritten as: (15).

[0041] The goal of this invention is to minimize the objective function For the sake of convenience, we assume that the weight of each data qubit is equal, so the above minimization objective function is equivalent to minimizing In order to achieve this, the present invention The number of 1s in the game is guessed, starting from the minimum number and gradually increasing. This search process follows the same Figure 3 A similar method to the algorithm in [1] is used until the current target is smaller than the existing minimum. Then stop the iteration and save the current minimum value and the corresponding left and right errors.

[0042] In summary, the embodiments of the present invention provide a high-performance decoding method for quantum low-density parity-check codes. Experimental verification demonstrates that, on a benchmark test of 12 qLDPC codes, it can achieve decoding accuracy comparable to that of the BP+OSD algorithm. The accuracy for the BB code [[144,12,12]] is even significantly higher than that of the BP+OSD algorithm. Furthermore, the method achieves an average decoding speed improvement of 8.48 times compared to the BP algorithm.

[0043] The specific implementation methods described above provide a detailed description of the technical solutions and beneficial effects of the present invention. It should be understood that the above is only the most preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, supplements and equivalent substitutions made within the scope of the principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A high-performance decoding method for quantum low-density parity-check codes, characterized in that: The following steps are involved: Through the matrix decoupling strategy optimized by offline satisfiability modulo theory, the transformation matrix and permutation matrix are solved to transform the original check matrix into a diagonal block matrix and an arbitrary sparse matrix. Through an online hierarchical greedy decoding algorithm, the error pattern is decomposed into a left error corresponding to a diagonal block matrix and a right error corresponding to an arbitrary sparse matrix. The error bits of the right error are first guessed, and then the error symptom corresponding to the left error is calculated based on an arbitrary sparse matrix. The error symptom is then divided according to the diagonal block matrix for parallel decoding, and the decoding results of all the block matrices are merged to form the left error. Finally, the left error and the right error are spliced ​​to obtain the complete error pattern.

2. The high-performance decoding method for quantum low-density parity-check codes according to claim 1, characterized in that: The matrix decoupling strategy optimized by offline satisfiability modulo theory solves the transformation matrix and the permutation matrix to equivalently transform the original check matrix into a diagonal block matrix and an arbitrary sparse matrix, including: The matrix decoupling strategy of offline satisfiability modulo theory optimization first solves the specific transformation matrix by using the satisfiability modulo theory solver under the constraints. and permutation matrix And maximize the sparsity of the decoupled check matrix, and then convert the check matrix of the original quantum low-density parity check code into By left-multiplying the transformation matrix and right-multiply the permutation matrix Perform equivalent transformation to obtain a diagonal block matrix and any sparse matrix The decoupled check matrix ,in Indicates the A block matrix, Represents the total number of block matrices.

3. The high-performance decoding method for quantum low-density parity-check codes according to claim 2, characterized in that: The specific transformation matrix and permutation matrix are solved by using the satisfiability module theory solver under the constraint conditions, including: The transformation matrix and permutation matrix Set as a Boolean variable and used to represent the decoupled check matrix Elements, set the constraints during the decoupling process as follows: (1) Transformation matrix It is a full-rank matrix, that is, no subset of rows can be XORed to the zero vector; (2) Permutation matrix Each row and column must contain only one non-zero element; (3) Decoupling check matrix Satisfy the specific shape defined, The constraints are as follows: i, each block in the decoupled parity check matrix must have the same shape; ii, except for sparse matrices Besides, all elements outside the block must be zero; iii. Each block in the decoupled check matrix must contain an identity matrix; The objective function is set to seek to minimize the decoupled check matrix The total number of non-zero elements in , and then the specific transformation matrix is ​​obtained by the satisfiability module theory solver based on the constraints and objective function. and permutation matrix .

4. The high-performance decoding method for quantum low-density parity-check codes according to claim 2 or 3, characterized in that: The decomposition of the error pattern into a left error corresponding to a diagonal block matrix and a right error corresponding to an arbitrary sparse matrix comprises: Error Mode Split into left error and right error Two-part vector, Corresponding to the diagonal block matrix , Corresponding to a sparse matrix , expressed as: ， ， in, is the error pattern after substitution, is the original error pattern, is the error symptom after transformation, is the original error symptom, It is an exclusive OR operation.

5. The high-performance decoding method for quantum low-density parity-check codes according to claim 4, characterized in that: The method of first guessing the error bit of the right error and then calculating the error symptom corresponding to the left error based on an arbitrary sparse matrix includes: According to the divided left error and right error, Defined as right error symptoms and moving it to the right side of the equation, we get the left error symptom ,Right now: ， First enter the original error symptoms , through the transformation matrix After the transformation, the error symptoms after the transformation are obtained , by successively guessing the right error The error bit and multiplying the sparse matrix Get the right error symptoms ,pass Calculate the left error symptoms for each time .

6. The high-performance decoding method for quantum low-density parity-check codes according to claim 5, characterized in that: The error symptom is divided into diagonal block matrices for parallel decoding and the decoding results of all the block matrices are combined to form a left error, including: Based on the left error symptoms obtained for each calculation Decompose the matrix into smaller components based on the block , thus transforming into a set of smaller independent decoding problems Then parallel decoding is performed, and the decoding results corresponding to all block matrices are obtained through iterative greedy guessing function decoding and then merged into the current calculation Left error.

7. The high-performance decoding method for quantum low-density parity-check codes according to claim 6, characterized in that: Finally, the left error and the right error are concatenated to obtain a complete error pattern, including: Concatenate all the left errors and right errors to get the permuted error pattern ,pass Permutation to obtain the complete error pattern .

8. The high-performance decoding method for quantum low-density parity-check codes according to claim 6, characterized in that: Decoding is performed through a greedy guessing function, including: Using the structure of the decoupled check matrix ,in, represents the identity matrix, Represents an arbitrary matrix, and the left error Re-divided into and Two parts, Corresponding to the identity matrix , For any matrix ,according to Reset the decoding constraints to: ， The goal of decoding is to minimize the objective function as the likelihood , that is, minimize The number of non-zero values ​​in The number of non-zero values ​​in the quantifier is guessed, starting from the minimum number and gradually increasing until the current target is less than the existing minimum. Then stop the iteration.

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