Surface code Pauli-Y error decoding method and device, terminal and storage medium

Abstract

The invention provides a surface code Pauli-Y error decoding method and device, a terminal and a storage medium, and the method comprises the steps: directly decoding the obtained error symptom points of the Pauli-Y error to obtain an intermediate decoding result, and during the direct decoding process, when the error symptoms of all the error symptom points can be eliminated, the error symptom points of the Pauli-Y error can be directly decoded, the error symptom points of the Pauli-Y error can be directly decoded, and the error symptom points of the Pauli-Y error can be directly decoded. An intermediate decoding result is used as a final target decoding result, and for a mark error symptom point of which an error symptom cannot be eliminated through direct decoding, the mark error symptom point is decomposed, and then a decomposed mark error symptom point obtained through decomposition is decoded through an original Union-find decoding algorithm; therefore, the final target decoding result is formed by the intermediate decoding result obtained by directly decoding the Pauli-Y error and the decoding result obtained by using the original Union-find decoding algorithm, the decoding of the surface code Pauli-Y error is realized, and the codeword capacity threshold of the Pauli-Y error can be improved.

Description

Technical Field

[0001] The present invention relates to the field of quantum error correction technology, and in particular to a surface code Pauli-Y error decoding method, device, terminal and storage medium. Background Art

[0002] Surface codes are a type of code developed based on toric codes. They have a simple topological structure, resulting in efficient and fast decoding algorithms. Currently, the Union-find decoding algorithm (union-find decoding algorithm) among surface code decoding algorithms has the advantages of a time complexity close to that of BP (Belief Propagation) decoding algorithms and a decoding accuracy close to that of MWPM (Minim Weight Perfect Match) decoding algorithms. This makes it capable of meeting the decoding speed and accuracy requirements of fault-tolerant quantum computing in the NISQ (Noisy Intermediate-Scale Quantum) era.

[0003] However, because the coupling between Pauli-X errors and Pauli-Z errors introduced by Pauli-Y errors in the codeword capacity noise model is not considered, the Union-find decoding algorithm has poor error correction performance under pure Pauli-Y errors. The decoding codeword capacity threshold is only around 10%, far lower than the decoding threshold of around 25% of the fully decoupled BP decoding algorithm. Furthermore, current improved Union-find decoding algorithms, such as the weighted Union-find decoding algorithm and the Belief-find algorithm that combines BP and Union-find, have also failed to improve the codeword capacity threshold. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a surface code Pauli-Y error decoding method, device, terminal and storage medium to address the above-mentioned defects of the prior art, which can improve the codeword capacity threshold of Pauli-Y errors.

[0005] The technical solutions adopted by the present invention to solve the technical problems are as follows: A surface code Pauli-Y error decoding method, wherein the method comprises: S1. Obtain the error symptom point corresponding to the Pauli-Y error of the target surface code; S2. generating a corresponding error symptom chain based on the error symptom point, and determining a target rectangular area with the minimum cost when performing a padding decoding operation based on the error symptom chain; S3. Determine whether the error symptom point is a flag error symptom point that cannot be directly decoded based on the target rectangular area and the error symptom chain; S4, if the error symptom point is not the flag error symptom point that cannot be directly decoded, performing a padding decoding operation on the target rectangular area to obtain an intermediate decoding result; S5. Determine whether there are any remaining error symptom points whose error symptoms have not been eliminated; S6. When there are currently remaining error symptom points, re-execute steps S2 to S3 based on the current remaining error symptom points, and when the current remaining error symptom point is the flag error symptom point that cannot be directly decoded, decompose the flag error symptom point to obtain a corresponding decomposed error symptom point, and use the original Union-find decoding algorithm to decode the decomposed error symptom point to obtain a decoding result, until there are currently no remaining error symptom points, determine the target decoding result based on the intermediate decoding result and the decoding result.

[0006] In one implementation, generating a corresponding error symptom chain based on the error symptom point, and determining a target rectangular area with the minimum cost when performing a padding decoding operation based on the error symptom chain includes: A pairwise matching operation is performed on the error symptom points to obtain a corresponding error symptom chain, and the error symptom points on the error symptom chain are traversed to determine a target rectangular area with the minimum cost when performing a padding decoding operation.

[0007] In one implementation, performing pairwise matching operations on the error symptom points to obtain corresponding error symptom chains includes: Using a modified Union-find decoding algorithm, performing a pairwise matching operation on the error symptom points to obtain a corresponding error symptom chain; The modified Union-find decoding algorithm is obtained by modifying the growth direction of the cluster in the original Union-find decoding algorithm, and is used to perform pairwise matching on the error symptom points to divide the error symptom points into multiple error symptom chains.

[0008] In one implementation, determining whether the error symptom point is a flag error symptom point that cannot be directly decoded based on the target rectangular area and the error symptom chain includes: Determine a row match on the error symptom chain that completely overlaps with any edge on the target rectangular area, and determine whether two endpoints of the row match constitute a column match to obtain a corresponding determination result; determining, based on the judgment result, whether the error symptom point is a flag error symptom point that cannot be directly decoded; The step of determining whether the error symptom point is a flag error symptom point that cannot be directly decoded based on the judgment result includes: When the judgment result indicates that the two endpoints of the row match do not constitute the column match, determining that the error symptom point is not the flag error symptom point that cannot be directly decoded; When the judgment result indicates that the two endpoints of the row match constitute the column match, the error symptom point is determined to be the flag error symptom point that cannot be directly decoded.

[0009] In one implementation, performing a padding decoding operation on the target rectangular area to obtain an intermediate decoding result includes: Applying a Pauli-Y operator to all data qubits within the target rectangular region to flip the error symptoms of four vertices on the target rectangular region to obtain an intermediate decoding result.

[0010] In one implementation, determining whether there are any remaining error symptom points whose error symptoms have not been eliminated includes: determining the number of error symptom points on all the error symptom chains currently, and judging whether there are any remaining error symptom points whose error symptoms have not been eliminated based on the number of error symptom points; The determining, based on the number of error symptom points, whether there are currently any remaining error symptom points whose error symptoms have not been eliminated includes: When the number of error symptom points is zero, it is determined that there are no remaining error symptom points; When the number of error symptom points is not zero, it is determined that there are currently remaining error symptom points.

[0011] In one implementation, decomposing the flag error symptom point to obtain a corresponding decomposed error symptom point, and decoding the decomposed error symptom point using an original Union-find decoding algorithm to obtain a decoding result, includes: The flag error syndrome point is decomposed to obtain an error syndrome point of an X error and an error syndrome point of an Z error, and the error syndrome point of the X error and the error syndrome point of the Z error are respectively decoded using an original Union-find decoding algorithm to obtain a first decoding result and a second decoding result.

[0012] The present invention also discloses a surface code Pauli-Y error decoding device, wherein the device comprises: An error symptom point acquisition module is used to obtain error symptom points corresponding to Pauli-Y errors of the target surface code; An error symptom chain generating module, configured to generate a corresponding error symptom chain based on the error symptom point; A rectangular area determination module, configured to determine a target rectangular area with the minimum cost when performing a padding decoding operation based on the error symptom chain; A first judgment module determines whether the error symptom point is a flag error symptom point that cannot be directly decoded based on the target rectangular area and the error symptom chain; a first decoding module configured to, if the error symptom point is not the flag error symptom point that cannot be directly decoded, perform a padding decoding operation on the target rectangular area to obtain an intermediate decoding result; The second judgment module is used to judge whether there are any remaining error symptom points whose error symptoms have not been eliminated; The second decoding module is used to, when there are currently remaining error symptom points, re-execute the step of generating a corresponding error symptom chain based on the error symptom points, and determine the target rectangular area with the minimum cost when performing the filling decoding operation based on the error symptom chain, and the step of determining whether the error symptom point is a flag error symptom point that cannot be directly decoded based on the target rectangular area and the error symptom chain, and when the current remaining error symptom point is the flag error symptom point that cannot be directly decoded, decompose the flag error symptom point to obtain a corresponding decomposed error symptom point, and use the original Union-find decoding algorithm to decode the decomposed error symptom point to obtain a decoding result, until there are currently no remaining error symptom points, and determine the target decoding result based on the intermediate decoding result and the decoding result.

[0013] The present invention also discloses a terminal, which includes: a memory, a processor, and a surface code Pauli-Y error decoding program stored in the memory and executable on the processor. When the surface code Pauli-Y error decoding program is executed by the processor, the steps of the surface code Pauli-Y error decoding method described above are implemented.

[0014] The present invention also discloses a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and the computer program can be executed to implement the steps of the surface code Pauli-Y error decoding method as described above.

[0015] The present invention provides a surface code Pauli-Y error decoding method, device, terminal and storage medium. The surface code Pauli-Y error decoding method includes: S1, obtaining an error symptom point corresponding to a Pauli-Y error of a target surface code; S2, generating a corresponding error symptom chain based on the error symptom point, and determining a target rectangular area with the minimum cost when performing a padding decoding operation based on the error symptom chain; S3, determining whether the error symptom point is a flag error symptom point that cannot be directly decoded based on the target rectangular area and the error symptom chain; S4, if the error symptom point is not the flag error symptom point that cannot be directly decoded, performing a padding decoding operation on the target rectangular area. Perform a filling decoding operation on the shaped area to obtain an intermediate decoding result; S5, determine whether there are residual error symptom points whose error symptoms have not been eliminated; S6, when there are residual error symptom points, re-execute steps S2 to S3 based on the current residual error symptom points, and when the current residual error symptom point is the flag error symptom point that cannot be directly decoded, decompose the flag error symptom point to obtain a corresponding decomposed error symptom point, and use the original Union-find decoding algorithm to decode the decomposed error symptom point to obtain a decoding result, until there are no residual error symptom points, determine the target decoding result based on the intermediate decoding result and the decoding result. It can be seen from this that the present invention obtains an intermediate decoding result by directly decoding the error symptom points of the Pauli-Y error. In the process of direct decoding, for the error symptom points whose error symptoms cannot be eliminated by direct decoding, that is, the flag error symptom points that cannot be directly decoded, they are decomposed and then decoded by the original Union-find decoding algorithm. The intermediate decoding result obtained by directly decoding the Pauli-Y error and the decoding result obtained by decoding the decomposed error symptom points using the original Union-find decoding algorithm constitute the final target decoding result. The above-mentioned technical solution of the present application is used to realize the decoding of the surface code Pauli-Y error, which can improve the codeword capacity threshold of the Pauli-Y error. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 This is a flow chart of a standard Union-find decoding algorithm disclosed in the present invention; Figure 2 This is a flow chart of a preferred embodiment of a surface code Pauli-Y error decoding method disclosed in the present invention; Figure 3 It is a schematic diagram of establishing a coordinate system for points in a surface code disclosed in the present invention; Figure 4 This is a schematic diagram of error symptom points of a Pauli-Y error disclosed in the present invention; Figure 5This is a schematic diagram of pairwise matching of error symptom points in the x-direction and the y-direction disclosed by the present invention; Figure 6 This invention discloses a Schematic diagram of the type chain; Figure 7 This is a specific schematic diagram of the change of error symptom points when eliminating symptoms in a target rectangular area disclosed by the present invention; Figure 8 This is a specific schematic diagram of a target rectangular area disclosed in the present invention; Figure 9 This is another specific schematic diagram of the change of error symptom points and the target rectangular area when eliminating symptoms in the target rectangular area disclosed by the present invention; Figure 10 This is a specific diagram of the decoding performance simulation experiment results of a 2D-toric code decoded in a pure Pauli-Y noise environment using the improved decoding algorithm of the present application disclosed in the present invention; Figure 11 This is a specific decoding performance simulation experiment result diagram of 2D-toric code decoding using the original Union-find decoding algorithm in a pure Pauli-Y noise environment disclosed by the present invention; Figure 12 This is a flowchart of a specific multiple Union-find algorithm disclosed in the present invention for decoding Pauli-Y errors of surface codes; Figure 13 This is a functional principle block diagram of a preferred embodiment of the surface code Pauli-Y error decoding device of the present invention; Figure 14 It is a functional principle block diagram of a preferred embodiment of the terminal in the present invention. DETAILED DESCRIPTION

[0017] In order to make the purpose, technical solutions and advantages of the present invention more clear and distinct, the present invention is further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0018] It should be noted that the time complexity bottleneck of the standard Union-Find decoding algorithm lies in the asymptotic time complexity of the classic Union-Find algorithm itself. When the Pauli-Y noise bias is high, the decoding performance will be significantly affected by the non-correlated decoding characteristics of the decoding algorithm itself. Figure 1As shown in the figure, in the specific process of the standard Union-find decoding algorithm for decoding 2D-toric codes and Planar surface codes, the distribution information of the actual Pauli errors that can be obtained by the decoding algorithm is implicit in the error symptom S (Syndrome) obtained by measuring all stable sub-elements, including the correlation information between Pauli-X errors and Pauli-Z errors introduced by Pauli-Y errors.

[0019] The decoding process of the standard UF decoding algorithm will cause the loss of correlation information in the following algorithm steps: (1) Segmentation step: S X With S Z Separating the S and decoding them independently, each independent decoding sub-process can only utilize partial error symptom information. When the distribution of Pauli-Y errors is dense, the UF decoding algorithm will not have sufficient error information in the local decoding process, thus reducing decoding performance.

[0020] (2) Union-Find growth step: During the UF growth process, edges outside the valid cluster will be removed from the perfect matching edge set corresponding to the final decoding result, which may lead to the loss of correlation information.

[0021] (3) Random forest generation step: Edges in the subgraph corresponding to valid clusters are randomly removed, rather than being pruned based on a specific strategy, resulting in a large loss of error distribution information. Due to the characteristics of the Peeling decoding process, when the random forest is determined, the output of the decoding algorithm is also uniquely determined.

[0022] To this end, the present application proposes a surface code Pauli-Y error decoding method, which maximizes the correlation information between Pauli-X errors and Pauli-Z errors introduced by Pauli-Y errors, thereby improving the codeword capacity threshold of Pauli-Y errors.

[0023] See Figure 2 , Figure 2 FIG. 1 is a flow chart of the surface code Pauli-Y error decoding method of the present invention. Figure 1 As shown, the surface code Pauli-Y error decoding method according to the embodiment of the present invention includes: Step S1: Obtain error symptom points corresponding to Pauli-Y errors of a target surface code.

[0024] In this embodiment, the target surface code can be a 2D-toric code or a Planar surface code, and the error symptom point is a symptom point corresponding to the error symptom that can be obtained by measuring the stabilizer in the quantum stabilizer code. Therefore, when decoding the Pauli-Y error of the surface code, the error symptom point corresponding to the Pauli-Y error is obtained to eliminate the error symptom of the error symptom point corresponding to the Pauli-Y error in subsequent steps.

[0025] Among them, the Pauli-Y error is a compound error in which the quantum bit simultaneously experiences bit flip and phase flip. The symptoms of the Pauli-Y error are manifested as the superposition of the X error symptoms and the Z error symptoms. That is, in stabilizer encoding, such as surface codes, the Y error will simultaneously trigger the symptoms of the X-type stabilizer and the Z-type stabilizer.

[0026] Step S2: Based on the error symptom point, a corresponding error symptom chain is generated, and based on the error symptom chain, a target rectangular area with the minimum cost when performing a padding decoding operation is determined.

[0027] In this embodiment, after obtaining the complete error symptom points of the Pauli-Y error, corresponding error symptom chains are generated based on these error symptom points, and then the target rectangular area with the lowest cost when performing the filling decoding operation is determined based on the error symptom chain, so that when the filling decoding operation is subsequently performed, the error symptoms are eliminated in one rectangular area each time to continuously reduce the number of error symptom points until the error symptoms of all error symptom points are eliminated.

[0028] Specifically, a pairwise matching operation is performed on the error symptom points to obtain a corresponding error symptom chain. The error symptom points in the error symptom chain are then traversed to determine the target rectangular area with the lowest cost when performing the padding decoding operation. A function value linearly related to the area of the rectangular area can be used as a comparison measure for the padding decoding operation cost.

[0029] In a specific embodiment, performing pairwise matching operations on the error symptom points to obtain corresponding error symptom chains may specifically include: using a modified Union-find decoding algorithm to perform pairwise matching operations on the error symptom points to obtain corresponding error symptom chains; wherein the modified Union-find decoding algorithm is a decoding algorithm obtained by modifying the growth direction of the cluster in the original Union-find decoding algorithm, and is used to perform pairwise matching on the error symptom points to divide the error symptom points into multiple error symptom chains.

[0030] Among them, the MWPM decoding algorithm or the exhaustive method can also be used to perform pairwise matching operations on error symptom points. The reason why the exhaustive method is applicable is that there are only two optional matching points for each error symptom point in the direction parallel to the x-axis or y-axis. Therefore, there are only two solutions to the problem of pairwise matching between even points, namely the minimum match and its complementary match. It is determined whether the sum of the matching side lengths is greater than the code length L. If not, it indicates that the complementary match of the current match is the minimum match. Otherwise, the current match is the minimum match.

[0031] It should be noted that during direct decoding of Pauli-X errors, the corresponding syndrome is no longer segmented but treated as a whole. Furthermore, under pure Pauli-Y noise, the syndrome points corresponding to Pauli-Y errors exhibit certain distribution characteristics.

[0032] See also Figure 3 and Figure 4 As shown in the Figure 3 Each small square vertex represents a data qubit (quantum bit), and each face represents a stabilizer, where the blue one is an X-type stabilizer and the yellow one is a Z-type stabilizer. Figure 3 To simplify the representation, periodic boundary features or boundary stabilizers are omitted. Figure 4 Part (a) shows that the error symptom points are connected by matching edges to form a rectangular polygon. Figure 4 Part (b) shows that a single qubit has a Pauli-Y error, which triggers the flip of the measurement error symptoms of the four surrounding stable sub-qubits. Figure 4 Parts (c) and (d) in the figure represent the error symptoms when Pauli-Y errors occur in two adjacent qubits.

[0033] See also Figure 3 and Figure 4 As shown in the figure, it can be seen that the Pauli-Y error of a single qubit will cause the error symptoms of the surrounding four stabilizers to flip. The error symptoms formed by the Pauli-Y errors of multiple qubits are always an even number, and the number of error symptoms on each line parallel to the x-axis or y-axis is always an even number. Therefore, the modified Union-finddecoder algorithm can be applied independently on each line parallel to the x-axis or y-axis to match these error symptoms in pairs, see Figure 5As shown, these points are matched in pairs parallel to the x-axis and in pairs parallel to the y-axis. Therefore, in the undirected graph consisting of all matching and error symptom points, each vertex (error symptom point) has a degree of 2, resulting from the matching in the x-axis and y-axis directions, respectively. According to graph theory, since all vertices in the graph have a degree of 2, the undirected graph can be divided into many subgraphs, each consisting of error symptom points and their matchings, forming an error symptom chain. The term "chain" is used because, in 2D-toric codes, the modified Union-find decoder algorithm forms a cycle in graph theory, but in planar surface codes, it forms a cycle, or a path that starts and ends at the boundary.

[0034] Step S3: Determine whether the error symptom point is a flag error symptom point that cannot be directly decoded based on the target rectangular area and the error symptom chain.

[0035] In this embodiment, after performing a pairwise matching operation on the error symptom points to obtain multiple error symptom chains, the error symptom points on all chains are traversed to find the target rectangular area with the minimum cost when performing the padding decoding operation. Then, based on the target rectangular area and the error symptom chain, it is determined whether the error symptom point of the Pauli-Y error is a flag error symptom point that cannot be directly decoded. Specifically, a row match on the error symptom chain that completely coincides with any edge on the target rectangular area is determined, and it is judged whether the two endpoints of the row match constitute a column match to obtain a corresponding judgment result; based on the judgment result, it is determined whether the error symptom point is a flag error symptom point that cannot be directly decoded; when the judgment result shows that the two endpoints of the row match do not constitute a column match, the error symptom point is determined not to be a flag error symptom point that cannot be directly decoded; when the judgment result shows that the two endpoints of the row match constitute a column match, the error symptom point is determined to be a flag error symptom point that cannot be directly decoded, and the two endpoints of the row match on the error symptom chain that completely coincide with any edge on the target rectangular area can constitute a column match, and when it is determined that the error symptom point corresponding to the Pauli-Y error is a flag error symptom point that cannot be directly decoded, the flag error symptom point is directly decomposed to obtain the corresponding decomposed error symptom point, and the decomposed error symptom point is decoded using the original Union-find decoding algorithm to obtain a decoding result, at which time the decoding result is the final decoding result, the decoding is completed, and the subsequent steps are not executed.

[0036] It can be understood that after finding the target rectangular area with the minimum cost (minimum area) when performing the padding decoding operation, a row match on the error symptom chain that completely overlaps with a certain edge of the target rectangular area can be determined. For 2D-toriccode decoding, it is possible to determine whether the error symptom point is a flag error symptom point that cannot be directly decoded by judging whether the two endpoints of this row match also form a column match. If the error symptom point is a flag error symptom point that cannot be directly decoded, it is decomposed and then the decomposed flag error symptom point obtained by the decomposition is decoded using the original Union-find decoding algorithm.

[0037] It should be noted that when the characteristic error symptoms appear, all the chains in the decoding undirected graph are Type chain, see Figure 6 As shown, where L represents the side length of the codeword, for 2d-toriccode, The physical qubit encodes two logical qubits, so the two endpoints of a row match on the error symptom chain that completely coincide with an edge of the target rectangular area can also form a column match, which means that the row and column match lengths are both L, and the row match chain is a The corresponding rectangular area of the chain is the smallest, so all chains in the undirected graph are Type chain.

[0038] It should also be noted that for planar surface codes, since their boundaries are open, after the coordinate system is established, the coordinates of the corresponding points of the stabilizer measurement qubit and the physical qubit grow and change linearly, and have fixed boundaries, so there will be no Type chain, its corresponding error symptom point is not a flag error symptom point that cannot be directly decoded, and there is no need to call the original Union-find decoding algorithm for decoding. That is, for the error symptom point corresponding to the Pauli-Y error of the planar surface code, when the two endpoints of the row match that completely coincide with any edge of the target rectangular area on the error symptom chain do not constitute a column match, the error symptom point corresponding to the Pauli-Y error of the planar surface code can be directly decoded, and each time in the process of eliminating the symptom by taking the target rectangular area with the minimum cost when performing the padding decoding operation as the direct decoding object, no flag error symptom point that cannot be directly decoded will be generated, until all error symptoms are completely eliminated, and the intermediate decoding result is the final target decoding result.

[0039] Step S4: If the error symptom point is not the flag error symptom point that cannot be directly decoded, a padding decoding operation is performed on the target rectangular area to obtain an intermediate decoding result.

[0040] In this embodiment, if the error symptom point is not a flag error symptom point that cannot be directly decoded, a fill decoding operation is performed on the target rectangular area to obtain an intermediate decoding result. Specifically, the Pauli-Y operator is applied to all data qubits in the target rectangular area to flip the error symptoms of the four vertices on the target rectangular area to obtain the intermediate decoding result. It can be understood that the symptom elimination is performed within a rectangular area each time to continuously reduce the number of error symptom points. For example, if the error symptoms of three vertices in the target rectangular area are -1, performing a fill decoding operation on the target rectangular area will eliminate the error symptoms at the original three vertices and add a new error symptom point at the fourth vertex.

[0041] See also Figure 7 As shown in the figure, it is assumed that the shaded part is the target rectangular area with the minimum cost found, and the area of the area is equal to the product of the row matching and column matching lengths of the vertex in the lower left corner of the area. Then, if the error symptom point is not a mark error symptom point that cannot be directly decoded, the target rectangular area is filled with decoding operations to eliminate the symptoms. Figure 7 Each inflection point in the chain represents an error symptom point. After eliminating the symptoms in the rectangular area, the original chain becomes a straight line after re-matching the error symptom points on the two straight lines. Type chain.

[0042] Step S5: Determine whether there are any remaining error symptom points whose error symptoms have not been eliminated.

[0043] In this embodiment, each time after the filling decoding operation is performed on the target rectangular area with the minimum cost as the current decoding object, it can be determined whether there are any remaining error symptom points whose error symptoms have not been eliminated. Specifically, the number of error symptom points on all current error symptom chains is determined, and based on the number of error symptom points, it is determined whether there are any remaining error symptom points whose error symptoms have not been eliminated. When the number of error symptom points is zero, it is determined that there are no remaining error symptom points. When the number of error symptom points is not zero, it is determined that there are remaining error symptom points.

[0044] Step S6: When there are currently remaining error symptom points, re-execute steps S2 to S3 based on the current remaining error symptom points, and when the current remaining error symptom point is the flag error symptom point that cannot be directly decoded, decompose the flag error symptom point to obtain a corresponding decomposed error symptom point, and use the original Union-find decoding algorithm to decode the decomposed error symptom point to obtain a decoding result, until there are currently no remaining error symptom points, determine the target decoding result based on the intermediate decoding result and the decoding result.

[0045] In this embodiment, the filling decoding of the target rectangular area with the minimum cost is completed. If there are currently remaining error symptom points, the corresponding error symptom chain is regenerated based on the current remaining error symptom points to find the target rectangular area with the minimum cost when the filling decoding operation is performed next time. The current remaining error symptom points are further judged to determine whether they are flag error symptom points that cannot be directly decoded. Then, if the current remaining error symptom points are flag error symptom points that cannot be directly decoded, the flag error symptom points are decomposed to obtain corresponding decomposed error symptom points, and the decomposed error symptom points are decoded using the original Union-find decoding algorithm to obtain a decoding result. When there are currently no remaining error symptom points, the target decoding result is determined based on the intermediate decoding result obtained by direct decoding and the decoding result obtained by decoding the decomposed error symptom points using the original Union-find decoding algorithm. The two decoding results are aggregated to obtain the final target decoding result.

[0046] For example, see Figure 8 and Figure 9 As shown in the figure, by traversing all chains, the rectangular area with the lowest cost when performing the symptom elimination operation is found. After performing the filling decoding operation on the rectangular area, the modified Union-find decoding algorithm is called to perform pairwise matching in two directions (x direction and y direction) to obtain the minimum match of the error symptom point, ensuring that the decoding result of each symptom elimination corresponds to the smallest rectangular area, thereby ensuring that the final decoding result is close to the maximum likelihood decoding result.

[0047] It should be pointed out that after the filling decoding operation is performed on the target rectangular area, new error symptom points are generated, and the current remaining error symptom points include the error symptom points on the two sides of the target rectangular area that do not overlap with the error symptom chain, the new error symptom points, and the error symptom points on the non-target rectangular area that are in the same row or column as the error symptom points on the two sides or the new error symptom points; after the filling decoding operation is performed on the target rectangular area, no new error symptom points are generated, and the current remaining error symptom points include the error symptom points on the two sides of the target rectangular area that do not overlap with the error symptom chain, and the error symptom points on the non-target rectangular area that are in the same row or column as the error symptom points on the two sides.

[0048] In this embodiment, decomposing the flag error syndrome point to obtain corresponding decomposed error syndrome points, and decoding the decomposed error syndrome points using the original Union-find decoding algorithm to obtain decoding results may specifically include: decomposing the flag error syndrome point to obtain an error syndrome point of an X error and an error syndrome point of an Z error, and respectively decoding the error syndrome point of the X error and the error syndrome point of the Z error using the original Union-find decoding algorithm to obtain a first decoding result and a second decoding result.

[0049] For example, if the error symptom is a sign error symptom, the error symptom can be decomposed into two categories according to the coordinates, that is, the error symptom is divided into S X With S Z , and then decode S according to the standard UF decoding algorithm X With S Z Decode them separately, where, due to the measurement qubit vertex coordinates of the x-type stabilizer and the z-type stabilizer, according to the above Figure 3 After the coordinate system is established, it can be distinguished, so the error symptom point can be decomposed into S according to the coordinates X With S Z .

[0050] Among them, the original Union-find decoding algorithm used in this application serves as both a sub-process in the entire decoding process and a supplementary decoding means in the direct decoding process to complete the entire decoding process.

[0051] It can be seen that in the embodiment of the present invention, an intermediate decoding result is obtained by directly decoding the error symptom points of the obtained Pauli-Y error. When the error symptoms of all error symptom points can be eliminated during the direct decoding process, the intermediate decoding result is used as the final target decoding result. For the error symptom points whose error symptoms cannot be eliminated by direct decoding, that is, the flag error symptom points that cannot be directly decoded, they are decomposed and then decoded by the original Union-find decoding algorithm. The intermediate decoding result obtained by directly decoding the Pauli-Y error and the decoding result obtained by decoding the decomposed error symptom points using the original Union-find decoding algorithm constitute the final target decoding result. The above-mentioned technical solution of the present application is used to realize the decoding of the surface code Pauli-Y error, which can improve the codeword capacity threshold of the Pauli-Y error.

[0052] For example, the surface code Pauli-Y error decoding method of the present application and the original Union-find decoding algorithm, the decoding performance simulation results of 2D-toric code in a pure Pauli-Y environment are as follows: Figure 10 and Figure 11 As shown, the codeword capacity threshold of the surface code Pauli-Y error decoding method of the present application is increased from the original 10% to more than 20%, and the decoding error rate of the surface code Pauli-Y error decoding method of the present application does not exceed 50%.

[0053] For example, see Figure 12As shown, the Syndrome corresponding to the Pauli-Y error is used as input, and then the modified Union-find decoding algorithm is called to perform pairwise matching operations on the error symptom points to obtain the corresponding error symptom chain. The error symptom points on all error symptom chains are traversed to find the target rectangular area with the minimum cost when performing the filling decoding operation. When there are multiple target rectangular areas, any one of the target rectangular boxes is selected to perform the step of judging whether the error symptom is a mark error symptom, that is, to determine the row match that completely overlaps with any edge on the target rectangular area on the error symptom chain, and judge the row match. Whether the two endpoints of the row match constitute a column match, thereby determining whether the error symptom point is a flag error symptom point that cannot be directly decoded. When the two endpoints of the row match constitute a column match, the error symptom point is determined to be a flag error symptom point that cannot be directly decoded. After decomposing it, the decomposed flag error symptom point is decoded by the original Union-find decoding algorithm to obtain a decoding result. At this time, the decoding result is the final decoding result, and the decoding is completed. When the two endpoints of the row match do not constitute a column match, the error symptom point is determined not to be a flag error symptom point that cannot be directly decoded, and the target rectangular area is filled. The filling decoding operation obtains the intermediate decoding result. After completing the current filling decoding operation, it is judged whether the error symptom is completely eliminated, that is, whether there are residual error symptom points that have not been eliminated. If there are still residual error symptom points, the modified Union-find decoding algorithm is called locally to perform a pairwise matching operation, that is, the modified Union-find decoding algorithm is called to perform a pairwise matching operation on the current remaining error symptom points, and the corresponding error symptom chain is regenerated to find the target rectangular area with the minimum cost when the filling decoding operation is performed next time, and continue to judge whether the error symptom is completely eliminated. Determine whether the current remaining error symptom point is a flag error symptom point that cannot be directly decoded, and execute the above process in a loop. After the error symptom is completely eliminated, the decoding is completed, and the intermediate decoding results obtained by direct decoding and the decoding results obtained using the original Union-find decoding algorithm are summarized to obtain the final target decoding result. If, during this decoding process, until the error symptom is completely eliminated, there are no flag error symptom points that cannot be directly decoded, that is, there is no need to use the original Union-find decoding algorithm for decoding, then the intermediate decoding results are directly used as the final target decoding result to complete the decoding.

[0054] In one embodiment, if Figure 13 As shown, based on the above-mentioned surface code Pauli-Y error decoding method, the present invention also provides a surface code Pauli-Y error decoding device, including: An error symptom point acquisition module 11 is used to acquire error symptom points corresponding to Pauli-Y errors of the target surface code; An error symptom chain generating module 12 is configured to generate a corresponding error symptom chain based on the error symptom point; A rectangular region determining module 13 is configured to determine a target rectangular region with the minimum cost when performing a padding decoding operation based on the error symptom chain; The first judgment module 14 determines whether the error symptom point is a flag error symptom point that cannot be directly decoded based on the target rectangular area and the error symptom chain; A first decoding module 15 is configured to perform a padding decoding operation on the target rectangular area to obtain an intermediate decoding result if the error symptom point is not the flag error symptom point that cannot be directly decoded; The second judgment module 16 is used to judge whether there are any remaining error symptom points whose error symptoms have not been eliminated; The second decoding module 17 is used to, when there are currently remaining error symptom points, re-execute the step of generating a corresponding error symptom chain based on the error symptom points, and determine the target rectangular area with the minimum cost when performing the filling decoding operation based on the error symptom chain, and the step of determining whether the error symptom point is a flag error symptom point that cannot be directly decoded based on the target rectangular area and the error symptom chain, and when the current remaining error symptom point is the flag error symptom point that cannot be directly decoded, decompose the flag error symptom point to obtain a corresponding decomposed error symptom point, and use the original Union-find decoding algorithm to decode the decomposed error symptom point to obtain a decoding result, until there are currently no remaining error symptom points, and determine the target decoding result based on the intermediate decoding result and the decoding result.

[0055] Figure 14 This is a schematic diagram of the structure of a terminal provided in an embodiment of the present application. The terminal may include: Memory 501 , processor 502 , and computer programs stored in the memory 501 and executable on the processor 502 .

[0056] When the processor 502 executes the program, the surface code Pauli-Y error decoding method provided in the above embodiment is implemented.

[0057] Furthermore, the terminal further includes: The communication interface 503 is used for communication between the memory 501 and the processor 502 .

[0058] The memory 501 is used to store computer programs that can be run on the processor 502 .

[0059] The memory 501 may include a high-speed RAM memory, and may also include a non-volatile memory (non-volatile memory), such as at least one disk memory.

[0060] If memory 501, processor 502, and communication interface 503 are implemented independently, communication interface 503, memory 501, and processor 502 can be interconnected via a bus to facilitate communication. The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus. Buses can be categorized as address buses, data buses, and control buses. For ease of illustration, the figure uses only one line, but this does not imply that there is only one bus or only one type of bus.

[0061] Optionally, in a specific implementation, if the memory 501, the processor 502 and the communication interface 503 are integrated on a chip, the memory 501, the processor 502 and the communication interface 503 can communicate with each other through an internal interface.

[0062] The processor 502 may be a central processing unit (CPU), an application specific integrated circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of the present application.

[0063] This embodiment further provides a computer-readable storage medium having a computer program stored thereon. When the program is executed by a processor, the above-mentioned surface code Pauli-Y error decoding method is implemented.

[0064] Other embodiments of the present invention will readily occur to those skilled in the art after considering the specification and practicing the invention disclosed herein. The present invention is intended to cover any variations, uses, or adaptations of the present invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein. The description and examples are to be considered as exemplary only, with the true scope and spirit of the invention being indicated by the claims.

[0065] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example" or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or N embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine different embodiments or examples described in this specification and features of different embodiments or examples without contradiction.

[0066] The logic and / or steps represented in the flowchart or otherwise described herein may be considered, for example, as a sequenced list of executable instructions for implementing the logical functions, and may be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a system including a processor, or other system that can read and execute instructions from an instruction execution system, apparatus, or device).

[0067] It should be understood that various parts of this application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiment, the N steps or methods can be implemented using software or firmware stored in a memory and executed by a suitable instruction execution system. If implemented using hardware, as in another embodiment, any one of the following technologies known in the art or a combination thereof can be used: a discrete logic circuit having logic gate circuits for implementing logical functions on data signals, an application-specific integrated circuit having suitable combinational logic gate circuits, a programmable gate array (PGA), a field-programmable gate array (FPGA), etc.

[0068] It should be understood that the application of the present invention is not limited to the above examples. For those skilled in the art, improvements or changes can be made based on the above description. All these improvements and changes should fall within the scope of protection of the claims attached to the present invention.

Claims

1. A surface code Pauli-Y error decoding method, characterized in that: The method comprises: S1. Obtain the error symptom point corresponding to the Pauli-Y error of the target surface code; S2. generating a corresponding error symptom chain based on the error symptom point, and determining a target rectangular area with the minimum cost when performing a padding decoding operation based on the error symptom chain; S3. Determine whether the error symptom point is a flag error symptom point that cannot be directly decoded based on the target rectangular area and the error symptom chain; S4, if the error symptom point is not the flag error symptom point that cannot be directly decoded, performing a padding decoding operation on the target rectangular area to obtain an intermediate decoding result; S5. Determine whether there are any remaining error symptom points whose error symptoms have not been eliminated; S6. When there are currently remaining error symptom points, re-execute steps S2 to S3 based on the current remaining error symptom points, and when the current remaining error symptom point is the flag error symptom point that cannot be directly decoded, decompose the flag error symptom point to obtain a corresponding decomposed error symptom point, and use the original Union-find decoding algorithm to decode the decomposed error symptom point to obtain a decoding result, until there are currently no remaining error symptom points, determine the target decoding result based on the intermediate decoding result and the decoding result.

2. The surface code Pauli-Y error decoding method according to claim 1, characterized in that: The step of generating a corresponding error symptom chain based on the error symptom point, and determining a target rectangular area with the minimum cost when performing a padding decoding operation based on the error symptom chain, comprises: A pairwise matching operation is performed on the error symptom points to obtain a corresponding error symptom chain, and the error symptom points on the error symptom chain are traversed to determine a target rectangular area with the minimum cost when performing a padding decoding operation.

3. The surface code Pauli-Y error decoding method according to claim 2, characterized in that: The performing pairwise matching operations on the error symptom points to obtain corresponding error symptom chains includes: Using a modified Union-find decoding algorithm, performing a pairwise matching operation on the error symptom points to obtain a corresponding error symptom chain; The modified Union-find decoding algorithm is obtained by modifying the growth direction of the cluster in the original Union-find decoding algorithm, and is used to perform pairwise matching on the error symptom points to divide the error symptom points into multiple error symptom chains.

4. The surface code Pauli-Y error decoding method according to claim 3, characterized in that: The determining, based on the target rectangular area and the error symptom chain, whether the error symptom point is a flag error symptom point that cannot be directly decoded includes: Determine a row match on the error symptom chain that completely overlaps with any edge on the target rectangular area, and determine whether two endpoints of the row match constitute a column match to obtain a corresponding determination result; determining, based on the judgment result, whether the error symptom point is a flag error symptom point that cannot be directly decoded; The step of determining whether the error symptom point is a flag error symptom point that cannot be directly decoded based on the judgment result includes: When the judgment result indicates that the two endpoints of the row match do not constitute the column match, determining that the error symptom point is not the flag error symptom point that cannot be directly decoded; When the judgment result indicates that the two endpoints of the row match constitute the column match, the error symptom point is determined to be the flag error symptom point that cannot be directly decoded.

5. The surface code Pauli-Y error decoding method according to claim 1, characterized in that: The performing the padding decoding operation on the target rectangular area to obtain an intermediate decoding result includes: Applying a Pauli-Y operator to all data qubits within the target rectangular region to flip the error symptoms of four vertices on the target rectangular region to obtain an intermediate decoding result.

6. The surface code Pauli-Y error decoding method according to claim 1, characterized in that: The determining whether there are any remaining error symptom points whose error symptoms have not been eliminated includes: determining the number of error symptom points on all the error symptom chains currently, and judging whether there are any remaining error symptom points whose error symptoms have not been eliminated based on the number of error symptom points; The determining, based on the number of error symptom points, whether there are currently any remaining error symptom points whose error symptoms have not been eliminated includes: When the number of error symptom points is zero, it is determined that there are no remaining error symptom points; When the number of error symptom points is not zero, it is determined that there are currently remaining error symptom points.

7. The surface code Pauli-Y error decoding method according to any one of claims 1 to 6, characterized in that: Decomposing the flag error symptom point to obtain a corresponding decomposed error symptom point, and decoding the decomposed error symptom point using an original Union-find decoding algorithm to obtain a decoding result, includes: The flag error syndrome point is decomposed to obtain an error syndrome point of an X error and an error syndrome point of an Z error, and the error syndrome point of the X error and the error syndrome point of the Z error are respectively decoded using an original Union-find decoding algorithm to obtain a first decoding result and a second decoding result.

8. A surface code Pauli-Y error decoding device, characterized in that: The device comprises: An error symptom point acquisition module is used to obtain error symptom points corresponding to Pauli-Y errors of the target surface code; An error symptom chain generating module, configured to generate a corresponding error symptom chain based on the error symptom point; A rectangular area determination module, configured to determine a target rectangular area with the minimum cost when performing a padding decoding operation based on the error symptom chain; A first judgment module determines whether the error symptom point is a flag error symptom point that cannot be directly decoded based on the target rectangular area and the error symptom chain; a first decoding module configured to, if the error symptom point is not the flag error symptom point that cannot be directly decoded, perform a padding decoding operation on the target rectangular area to obtain an intermediate decoding result; The second judgment module is used to judge whether there are any remaining error symptom points whose error symptoms have not been eliminated; The second decoding module is used to, when there are currently remaining error symptom points, re-execute the step of generating a corresponding error symptom chain based on the error symptom points, and determine the target rectangular area with the minimum cost when performing the filling decoding operation based on the error symptom chain, and the step of determining whether the error symptom point is a flag error symptom point that cannot be directly decoded based on the target rectangular area and the error symptom chain, and when the current remaining error symptom point is the flag error symptom point that cannot be directly decoded, decompose the flag error symptom point to obtain a corresponding decomposed error symptom point, and use the original Union-find decoding algorithm to decode the decomposed error symptom point to obtain a decoding result, until there are currently no remaining error symptom points, and determine the target decoding result based on the intermediate decoding result and the decoding result.

9. A terminal, characterized in that: include: A memory, a processor, and a surface code Pauli-Y error decoding program stored in the memory and executable on the processor, wherein the surface code Pauli-Y error decoding program, when executed by the processor, implements the steps of the surface code Pauli-Y error decoding method according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, and the computer program can be executed to implement the steps of the surface code Pauli-Y error decoding method according to any one of claims 1 to 7.

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