Quantum error correction code belief propagation decoding method, system and terminal based on adaptive prior probability

Abstract

The invention discloses a quantum error correction code belief propagation decoding method, system and terminal based on an adaptive prior probability, and the method comprises the steps: carrying out the adaptive updating of the prior probability of the occurrence of each Follicle error of a quantum bit through an exponential weighted average method, so as to carry out the dynamic initialization of each iteration; according to a sum-product algorithm, updating messages transmitted by a check node to all adjacent variable nodes connected with the check node to obtain updated horizontal messages; according to a sum-product algorithm, updating messages transmitted by the variable nodes to all adjacent check nodes connected with the variable nodes, and obtaining updated vertical messages; based on the priori information, the updated horizontal message, and the updated vertical message, posterior information is calculated to obtain an estimate of the true error. According to the method, the priori information is adaptively adjusted, the decoding precision and the convergence rate of the high-degenerate quantum code are improved, meanwhile, the calculation complexity is kept unchanged, and engineering implementation of fault-tolerant quantum calculation is facilitated.

Description

Technical Field

[0001] The present invention relates to the field of quantum error correction in quantum computer technology, and in particular to a quantum error correction code belief propagation decoding method, system, terminal and computer-readable storage medium based on adaptive prior probability. Background Art

[0002] The information in quantum computing devices is highly sensitive to noise, and even tiny external disturbances may lead to errors in the calculation results. To solve this problem, quantum error correction introduces redundant physical quantum bits to encode information into a larger space for protection. At present, quantum error correction is the only way to achieve universal fault-tolerant quantum computing, but it requires a high-precision and low-latency decoding algorithm. Among the existing decoding algorithms, the belief propagation algorithm has attracted much attention due to its linear time complexity and its versatility for low-density parity-check codes.

[0003] However, the current belief propagation decoding algorithm still cannot meet the accuracy requirements of quantum error correction without relying on high-overhead post-processing algorithms. In particular, it will fall into a trap set and fail to converge on highly degenerate quantum codes. Relevant technologies are urgently needed to improve the decoding accuracy.

[0004] Therefore, the prior art still needs to be improved and developed. Summary of the invention

[0005] The main purpose of the present invention is to provide a quantum error correction code belief propagation decoding method, system, terminal and computer-readable storage medium based on adaptive prior probability, aiming to solve the problem of low decoding accuracy of the belief propagation decoding algorithm on highly degenerate quantum codes in the prior art.

[0006] To achieve the above object, the present invention provides a quantum error correction code belief propagation decoding method based on adaptive prior probability, and the quantum error correction code belief propagation decoding method based on adaptive prior probability comprises the following steps: Receive a priori probability vector of each quantum bit, obtain a variable node corresponding to each quantum bit, initialize information according to the prior probability vector to obtain initialization information, and transmit the initialization information of each variable node from the corresponding variable node to a check node adjacent to the variable node; Based on the multiple initialization information, updating the message transmitted by the check node to all adjacent variable nodes connected to the check node by a sum-product algorithm to obtain an updated horizontal message; Calculating posterior information based on the prior probability vector and the updated horizontal message; The Pauli error of each variable node is judged according to the posterior information. If the Pauli error meets the decoding conditions, the decoding is successful. If the Pauli error does not meet the decoding conditions, the prior probability vector of each quantum bit is adaptively updated to complete a new round of iterations until the number of iterations reaches the maximum value, and the decoding fails.

[0007] Optionally, the quantum error correction code belief propagation decoding method based on adaptive prior probability, wherein the information is initialized according to the prior probability vector to obtain the initialization information, specifically includes: The log-likelihood ratio is used to represent the prior probability vector of each Pauli error occurring at each variable node. Based on multiple prior probability vectors in the form of log-likelihood ratios, the information from the variable node to the check node is initialized respectively to obtain multiple initialization information: ; in, Indicates variable nodes, Indicates Check nodes, Indicates The variable node is passed to the first Initialization message of the check nodes, Represents a scalar message mapping function, represents the prior probability vector in the form of log-likelihood ratio, represents the calculation process of log-likelihood ratio, represents the initial prior probability, which contains the prior probability of each Pauli error occurring.

[0008] Optionally, the quantum error correction code belief propagation decoding method based on adaptive prior probability, wherein the message transmitted by the check node to all adjacent variable nodes connected to the check node is updated by a sum-product algorithm based on the multiple initialization information to obtain an updated horizontal message, specifically includes: Obtain all adjacent variable nodes of a check node, traverse each adjacent variable node in turn, use the traversed adjacent variable node as the target variable node, and obtain initialization information sent to the check node by all remaining adjacent variable nodes except the target variable node; The level information sent by the check node to different adjacent variable nodes is calculated according to the initialization information, all the check nodes are traversed, the level information sent by other check nodes to their respective adjacent variable nodes is calculated, and the level information sent by each check node to different adjacent variable nodes is obtained.

[0009] Optionally, the quantum error correction code belief propagation decoding method based on adaptive prior probability, wherein the step of obtaining the updated horizontal message further comprises: Get and remove the check node All variable nodes Adjacent check nodes Send to variable node News ; According to the message Update variable node Passed to the node with the variable All adjacent check nodes connected News , and obtain an updated vertical message, which is used for calculating the next round of horizontal messages.

[0010] Optionally, the quantum error correction code belief propagation decoding method based on adaptive prior probability, wherein the a posteriori information is calculated based on the prior probability vector and the updated horizontal message, specifically comprising: For each variable node , according to the prior probability vector of each Pauli error in this iteration and variable nodes Updated level message received , calculate the posterior information of this round of iteration : ; in, Scalar message mapping functions, Error Operator With matrix element Oppose Yi.

[0011] Optionally, the quantum error correction code belief propagation decoding method based on adaptive prior probability, wherein if the Pauli error meets the decoding condition, the decoding is successful, specifically includes: Pauli Error for all variable nodes , if there is If holds, the estimated error vector Set to no error, otherwise, the error vector Set so that the posterior information Smallest Pauli error type: ; in, X, Y and Z They represent the Pauli operators Errors and Pauli operators acting on the system state Errors and Pauli operators acting on the system state Errors caused by acting on the system state; Error vector for all variable nodes Check if the decoding condition If it holds, it means the decoding is successful, returns convergence and stops checking, where, represents the product operation of matrix and vector, The check matrix represents the connection relationship between the check nodes and the variable nodes. Represents the error symptom vector obtained by stable sub-measurement.

[0012] Optionally, the quantum error correction code belief propagation decoding method based on adaptive prior probability, wherein if the Pauli error does not meet the decoding condition, the prior probability vector of each quantum bit is adaptively updated to complete a new round of iteration until the number of iterations reaches a maximum value, specifically includes: If the decoding condition If it is not true, then the dynamic adaptive prior probability vector of the next iteration is calculated based on the prior probability vector of each quantum bit and the a posteriori information in the previous iteration: ; in, Indicated in Variable nodes in iterations The corresponding Pauli error The dynamic adaptive prior probability vector that occurs, Represents the variable node at the initial moment The corresponding Pauli error The prior probability vector of occurrence, Indicates the variable node after this round of iteration The corresponding Pauli error The posterior information that occurs, is a discount factor used to balance the weight between the prior probability vector and the posterior information updated in this iteration; The dynamic adaptive prior probability vector is used to replace the prior probability vector to calculate the horizontal message, the vertical message and the posterior information and make a hard decision to complete a new round of iteration until the number of iterations reaches a maximum value.

[0013] In addition, to achieve the above-mentioned purpose, the present invention also provides a quantum error correction code belief propagation decoding system based on adaptive prior probability, wherein the quantum error correction code belief propagation decoding system based on adaptive prior probability comprises: An initialization module, used to receive a priori probability vector of each quantum bit, obtain a variable node corresponding to each quantum bit, initialize information according to the prior probability vector to obtain initialization information, and respectively transmit the initialization information of each variable node from the corresponding variable node to a check node adjacent to the variable node; A horizontal message updating module, configured to update the message transmitted by the check node to all adjacent variable nodes connected to the check node through a sum-product algorithm based on the multiple initialization information, to obtain an updated horizontal message; A posterior information calculation module, used to calculate the posterior information based on the prior probability vector and the updated horizontal message; The hard decision module is used to judge the Pauli error of each variable node according to the posterior information. If the Pauli error meets the decoding conditions, the decoding is successful. If the Pauli error does not meet the decoding conditions, the prior probability vector of each quantum bit is adaptively updated to complete a new round of iterations until the number of iterations reaches a maximum value, and the decoding fails.

[0014] In addition, to achieve the above-mentioned purpose, the present invention also provides a terminal, wherein the terminal includes: a memory, a processor, and a quantum error correction code belief propagation decoding program based on adaptive prior probability stored in the memory and executable on the processor, wherein the quantum error correction code belief propagation decoding program based on adaptive prior probability implements the steps of the quantum error correction code belief propagation decoding method based on adaptive prior probability as described above when the quantum error correction code belief propagation decoding program based on adaptive prior probability is executed by the processor.

[0015] In addition, to achieve the above-mentioned purpose, the present invention also provides a computer-readable storage medium, wherein the computer-readable storage medium stores a quantum error correction code belief propagation decoding program based on adaptive prior probability, and when the quantum error correction code belief propagation decoding program based on adaptive prior probability is executed by a processor, the steps of the quantum error correction code belief propagation decoding method based on adaptive prior probability as described above are implemented.

[0016] In the present invention, the prior probability of each Pauli error of the quantum bit is adaptively updated by the exponential weighted average method to perform dynamic initialization for each round of iteration; the message transmitted by the check node to all adjacent variable nodes connected to the check node is updated according to the sum-product algorithm to obtain an updated horizontal message; the message transmitted by the variable node to all adjacent check nodes connected to the variable node is updated according to the sum-product algorithm to obtain an updated vertical message; based on the prior information, the updated horizontal message and the updated vertical message, the posterior information is calculated to obtain an estimate of the real error. The present invention significantly improves the decoding accuracy and convergence rate of highly degenerate quantum codes by adaptively adjusting the prior information, while maintaining the computational complexity unchanged, which is conducive to the engineering realization of fault-tolerant quantum computing. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a flow chart of a preferred embodiment of the quantum error correction code belief propagation decoding method based on adaptive prior probability of the present invention; Figure 2 It is a structural diagram of a preferred embodiment of the quantum error correction code belief propagation decoding system based on adaptive prior probability of the present invention; Figure 3 Schematic diagram of the operating environment of a preferred embodiment of the terminal of the present invention. DETAILED DESCRIPTION

[0018] The present application provides a quantum error correction code belief propagation decoding method, system and terminal based on adaptive prior probability. In order to make the purpose, technical solution and effect of the present application clearer and more specific, the present application is further described in detail with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described here are only used to explain the present application and are not used to limit the present application.

[0019] It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as those generally understood by those skilled in the art to which this application belongs. It should also be understood that terms such as those defined in general dictionaries should be understood to have meanings consistent with those in the context of the prior art, and will not be interpreted with idealized or overly formal meanings unless specifically defined as here.

[0020] In addition, if there are descriptions involving "first", "second", etc. in the embodiments of the present invention, the descriptions of "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or suggesting their relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of the features. In addition, the technical solutions between the various embodiments can be combined with each other, but they must be based on the ability of ordinary technicians in the field to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such a combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0021] The quantum error correction code belief propagation decoding method based on adaptive prior probability described in the preferred embodiment of the present invention is as follows: Figure 1 As shown, the quantum error correction code belief propagation decoding method based on adaptive prior probability includes the following steps: Step S100, receiving the prior probability vector of each quantum bit, obtaining the variable node corresponding to each quantum bit, initializing the information according to the prior probability vector to obtain initialization information, and respectively transmitting the initialization information of each variable node from the corresponding variable node to the check node adjacent to the variable node.

[0022] In this embodiment, the prior information of the probability of each Pauli error of each qubit is represented by the log-likelihood ratio, and the message from the variable node to the check node is initialized. X , Y , Z Errors that occur on the system state, where X It is a bit flip, flipping the |0> state to the |1> state; Z For phase flipping, the |1> state is introduced with a phase factor of -1; Y It can be understood that bit and phase flipping act simultaneously.

[0023] It can be understood that Pauli error is the basic error type for evaluating the environmental interference of a quantum system. Any quantum error generated in the system can be expressed as a linear combination of Pauli errors. Therefore, correcting Pauli error is equivalent to correcting any quantum error.

[0024] Specifically, we receive a priori probability vectors describing the various Pauli error types on each qubit ,in, Represents a variable node Pauli X The probability of error, Represents a variable node Pauli The probability of error, Represents a variable node Pauli The probability of error, Indicates the number of variable nodes; and obtains multiple variable nodes and multiple check nodes corresponding to each of the quantum bits. It should be noted that the present invention can link the problem of quantum error correction with classical error correction with the help of the stabilizer framework: each stabilizer corresponds to a check node to detect whether a specific type of error occurs in the associated quantum bit, and each quantum bit corresponds to a variable node. In this method, each variable node stores vector information { }, corresponding to the location and type of error that may occur, the check nodes and variable nodes can be represented by the check matrix, or by Tanner The figure shows ( Tanner A graph is a way to represent LDPC The graphical representation of the check matrix of the code Tanner In the figure, The check node and The connection of the variable nodes represents the The stabilizer acts on qubits. A check matrix represents an error correction code. Belief propagation is Tanner The process of iteratively propagating messages on the graph to estimate the actual error is called decoding.

[0025] Furthermore, the log-likelihood ratio is used to represent the prior probability vector of each Pauli error occurring at each variable node. Based on multiple prior probability vectors in the form of log-likelihood ratios, the information from the variable node to the check node is initialized respectively to obtain multiple initialization information: ; in, Indicates variable nodes, Indicates Check nodes, Indicates The variable node is passed to the first Initialization message of the check nodes, Represents a scalar message mapping function, The role of is to map the log-likelihood ratio vector into a scalar value, represents the prior probability vector in the form of log-likelihood ratio, represents the calculation process of log-likelihood ratio, represents the initial prior probability, which contains the prior probability of each Pauli error occurring.

[0026] Furthermore, the scalar message mapping function Defined as: ; in, Pauli error Whether it is with the stabilizer The commutative log-likelihood ratio, represents a natural constant, 、 、 Pauli The probability of error, the occurrence of Pauli The probability of error and the occurrence of Pauli The probability of error, represents the probability of a certain Pauli error, The type of Pauli error is X , Y , Z One of the The function is to calculate the The variable node is given to The scalar message transmitted by the check nodes depends on the calculation of the check matrix elements. type).

[0027] Step S200: Based on the multiple initialization information, the message transmitted by the check node to all adjacent variable nodes connected to the check node is updated by the sum-product algorithm to obtain an updated horizontal message.

[0028] Specifically, all adjacent variable nodes of a check node are obtained, each adjacent variable node is traversed in turn, the traversed adjacent variable node is used as the target variable node, and initialization information sent to the check node by all remaining adjacent variable nodes except the target variable node is obtained.

[0029] Furthermore, the level information sent by the check node to different adjacent variable nodes is calculated according to the initialization information, all the check nodes are traversed, the level information sent by other check nodes to their respective adjacent variable nodes is calculated, and the level information sent by each check node to different adjacent variable nodes is obtained.

[0030] The message transmitted by the check node to all adjacent variable nodes connected to the check node is updated by the sum-product algorithm to obtain an updated horizontal message: ; in, Indicates the updated horizontal message, Indicates that the message sent takes into account all The variable nodes adjacent to the first check node, but at the same time exclude the first target variable nodes; if the current iteration is the first round, then Represents the initialization information sent by the remaining adjacent variable nodes to the check node. If the current iteration is not the first round, then Indicates the number of The variable node The vertical message sent by the verification node, Indicates The verification result of the verification node, that is, The measurement results of the stabilizer.

[0031] Furthermore, the step of obtaining the updated horizontal message further includes: Get and remove the check node All variable nodes Adjacent check nodes Send to variable node News ; According to the message Update variable node Passed to the node with the variable All adjacent check nodes connected News , and obtain an updated vertical message, which is used for calculating the next round of horizontal messages.

[0032] In this embodiment, the process of calculating the updated vertical message is: ; in, Indicates the updated vertical message, represents the prior probability vector in the form of log-likelihood ratio, Indicates when the error operator With matrix element When opposing the change, remove the verification nodes that meet the conditions All variable nodes Adjacent check nodes Send to variable node News Perform the summation.

[0033] It is understandable that the prior probability vector will change dynamically with the iteration process. In the first iteration, the prior probability vector , in the subsequent iterations, the prior probability vector will be dynamically adapted to the prior probability vector replace.

[0034] Step S300: Calculate the posterior information based on the prior probability vector and the updated horizontal message.

[0035] Specifically, for each variable node , according to the prior probability vector of each Pauli error in this iteration and variable nodes Updated level message received , calculate the posterior information of this round of iteration : ; in, Represents a scalar message mapping function, Error Operator With matrix element Oppose Yi.

[0036] Step S400, judging the Pauli error of each variable node according to the posterior information, if the Pauli error meets the decoding condition, the decoding is successful, if the Pauli error does not meet the decoding condition, the prior probability vector of each quantum bit is adaptively updated to complete a new round of iteration, until the number of iterations reaches the maximum value, then the decoding fails.

[0037] If the Pauli error meets the decoding condition, the decoding is successful, which specifically includes: Pauli Error for all variable nodes , if there is If holds, the estimated error vector Set to no error, otherwise, the error vector Set so that the posterior information Smallest Pauli error type: ; in, X, Y and Z They represent the Pauli operators Errors and Pauli operators acting on the system state Errors and Pauli operators acting on the system state Errors caused by acting on the system state; Error vector for all variable nodes Check if the decoding condition If it holds, it means the decoding is successful, returns convergence and stops checking, where, represents the product operation of matrix and vector, The check matrix represents the connection relationship between the check nodes and the variable nodes. Represents the error symptom vector obtained by stable sub-measurement.

[0038] Understandably, The check matrix that represents the connection relationship between the check nodes and the variable nodes can also represent an error correction code. Each row of the matrix corresponds to a check node, and each column corresponds to a variable node. The error symptom vector obtained by measuring the stabilizer is also called the error symptom, and its dimension is equal to the number of stabilizers, that is, the rows of the check matrix. Represents the product operation of matrix and vector, which is used to check whether the error estimate output by the decoding algorithm is correct. The same is equivalent to successfully inferring the cause of the error symptom.

[0039] Furthermore, if the Pauli error does not meet the decoding condition, the prior probability vector of each quantum bit is adaptively updated to complete a new round of iteration until the number of iterations reaches a maximum value, specifically including: If the decoding condition If it is not true, then the dynamic adaptive prior probability vector of the next iteration is calculated based on the prior probability vector of each quantum bit and the a posteriori information in the previous iteration: ; in, Indicated in Variable nodes in iterations The corresponding Pauli error The dynamic adaptive prior probability vector that occurs, Represents the variable node at the initial moment The corresponding Pauli error The prior probability vector of occurrence, Indicates that the variable node after this round of iteration The corresponding Pauli error The posterior information that occurs, is a discount factor used to balance the weight between the prior probability vector and the posterior information updated in this iteration; The dynamic adaptive prior probability vector is used to replace the prior probability vector to calculate the horizontal message, the vertical message and the posterior information and make a hard decision to complete a new round of iteration until the number of iterations reaches a maximum value.

[0040] It is understandable that, except for the first round of iteration, the present invention updates the prior probability vector of the Pauli error type of each quantum bit in each round of iteration. ,Will As a dynamic and adaptive prior probability vector, the information is initialized instead of the prior probability vector, which can effectively improve the decoding accuracy.

[0041] In summary, the quantum error correction code belief propagation decoding method, system and terminal based on adaptive prior probability provided by the present invention particularly relate to quantum error correction coding and decoding technology in the field of quantum information. First, the prior probability of each Pauli error of the quantum bit is adaptively updated by the exponential weighted average method to perform dynamic initialization of each round of iteration; the message transmitted by the check node to all adjacent variable nodes connected to the check node is updated according to the sum-product algorithm to obtain an updated horizontal message; the message transmitted by the variable node to all adjacent check nodes connected to the variable node is updated according to the sum-product algorithm to obtain an updated vertical message; based on the prior information and the updated horizontal message, the posterior information is calculated to obtain an estimate of the real error. The present invention significantly improves the decoding accuracy and convergence rate of highly degenerate quantum codes by adaptively adjusting the prior information, while maintaining the unchanged computational complexity, which is conducive to the engineering realization of fault-tolerant quantum computing.

[0042] Furthermore, if Figure 2 As shown, based on the above quantum error correction code belief propagation decoding method based on adaptive prior probability, the present invention also provides a quantum error correction code belief propagation decoding system based on adaptive prior probability, wherein the quantum error correction code belief propagation decoding system based on adaptive prior probability includes: An initialization module 51 is used to receive a priori probability vector of each quantum bit, obtain a variable node corresponding to each quantum bit, initialize information according to the priori probability vector to obtain initialization information, and transmit the initialization information of each variable node from the corresponding variable node to a check node adjacent to the variable node; A horizontal message updating module 52, configured to update the message transmitted by the check node to all adjacent variable nodes connected to the check node by a sum-product algorithm based on the multiple initialization information, to obtain an updated horizontal message; A posterior information calculation module 53, used to calculate the posterior information based on the prior probability vector and the updated horizontal message; The hard decision module 54 is used to judge the Pauli error of each variable node according to the a posteriori information. If the Pauli error meets the decoding conditions, the decoding is successful. If the Pauli error does not meet the decoding conditions, the prior probability vector of each quantum bit is adaptively updated to complete a new round of iterations until the number of iterations reaches a maximum value, and the decoding fails.

[0043] Furthermore, if Figure 3As shown, based on the above-mentioned quantum error correction code belief propagation decoding method and system based on adaptive prior probability, the present invention also provides a terminal accordingly, and the terminal includes a processor 10, a memory 20 and a display 30. Figure 3 Only some components of the terminal are shown, but it should be understood that it is not required to implement all of the components shown, and more or fewer components may be implemented instead.

[0044] In some embodiments, the memory 20 may be an internal storage unit of the terminal, such as a hard disk or memory of the terminal. In other embodiments, the memory 20 may also be an external storage device of the terminal, such as a plug-in hard disk, a smart memory card (Smart Media Card, SMC), a secure digital (SecureDigital, SD) card, a flash card (Flash Card), etc. equipped on the terminal. Further, the memory 20 may also include both an internal storage unit of the terminal and an external storage device. The memory 20 is used to store application software and various types of data installed on the terminal, such as the program code of the installation terminal. The memory 20 may also be used to temporarily store data that has been output or is to be output. In one embodiment, a belief propagation decoding program 40 based on adaptive prior probability is stored on the memory 20, and the quantum error correction code belief propagation decoding program 40 based on adaptive prior probability can be executed by the processor 10, thereby realizing the quantum error correction code belief propagation decoding method based on adaptive prior probability in the present application.

[0045] In some embodiments, the processor 10 may be a central processing unit (CPU), a microprocessor or other data processing chip, used to run the program code or process data stored in the memory 20, such as executing the quantum error correction code belief propagation decoding method based on adaptive prior probability.

[0046] In some embodiments, the display 30 may be an LED display, a liquid crystal display, a touch-sensitive liquid crystal display, an OLED (Organic Light-Emitting Diode) touch device, etc. The display 30 is used to display information on the terminal and to display a visual user interface. The components of the terminal communicate with each other via a system bus.

[0047] In one embodiment, when the processor 10 executes the quantum error correction code belief propagation decoding program 40 based on adaptive prior probability in the memory 20, the following steps are implemented: Receive a priori probability vector of each quantum bit, obtain a variable node corresponding to each quantum bit, initialize information according to the prior probability vector to obtain initialization information, and transmit the initialization information of each variable node from the corresponding variable node to a check node adjacent to the variable node; Based on the multiple initialization information, updating the message transmitted by the check node to all adjacent variable nodes connected to the check node by a sum-product algorithm to obtain an updated horizontal message; Calculating posterior information based on the prior probability vector and the updated horizontal message; The Pauli error of each variable node is judged according to the posterior information. If the Pauli error meets the decoding conditions, the decoding is successful. If the Pauli error does not meet the decoding conditions, the prior probability vector of each quantum bit is adaptively updated to complete a new round of iterations until the number of iterations reaches the maximum value, and the decoding fails.

[0048] The initializing the information according to the prior probability vector to obtain the initialization information specifically includes: The log-likelihood ratio is used to represent the prior probability vector of each Pauli error occurring at each variable node. Based on multiple prior probability vectors in the form of log-likelihood ratios, the information from the variable node to the check node is initialized respectively to obtain multiple initialization information: ; in, Indicates variable nodes, Indicates Check nodes, Indicates The variable node is passed to the first Initialization message of the check nodes, Represents a scalar message mapping function, represents the prior probability vector in the form of log-likelihood ratio, represents the calculation process of log-likelihood ratio, represents the initial prior probability, which contains the prior probability of each Pauli error occurring.

[0049] Wherein, based on the multiple initialization information, updating the message transmitted by the check node to all adjacent variable nodes connected to the check node by the sum-product algorithm to obtain the updated horizontal message specifically includes: Obtain all adjacent variable nodes of a check node, traverse each adjacent variable node in turn, use the traversed adjacent variable node as the target variable node, and obtain initialization information sent to the check node by all remaining adjacent variable nodes except the target variable node; The level information sent by the check node to different adjacent variable nodes is calculated according to the initialization information, all the check nodes are traversed, the level information sent by other check nodes to their respective adjacent variable nodes is calculated, and the level information sent by each check node to different adjacent variable nodes is obtained.

[0050] The step of obtaining the updated horizontal message further includes: Get and remove the check node All variable nodes Adjacent check nodes Send to variable node News ; According to the message Update variable node Passed to the node with the variable All adjacent check nodes connected News , and obtain an updated vertical message, which is used for calculating the next round of horizontal messages.

[0051] The step of calculating the posterior information based on the prior probability vector and the updated horizontal message specifically includes: For each variable node , according to the prior probability vector of each Pauli error in this iteration and variable nodes Updated level message received , calculate the posterior information of this round of iteration : ; in, Represents a scalar message mapping function, Error Operator With matrix element Oppose Yi.

[0052] Wherein, if the Pauli error meets the decoding condition, the decoding is successful, which specifically includes: Pauli Error for all variable nodes , if there is If holds, the estimated error vector Set to no error, otherwise, the error vector Set so that the posterior information Smallest Pauli error type: ; in, X, Y and Z They represent the Pauli operatorsX Errors and Pauli operators acting on the system state Errors and Pauli operators acting on the system state Errors caused by acting on the system state; Error vector for all variable nodes Check if the decoding condition If it holds, it means the decoding is successful, returns convergence and stops checking, where, represents the product operation of matrix and vector, The check matrix represents the connection relationship between the check nodes and the variable nodes. Represents the error symptom vector obtained by stable sub-measurement.

[0053] If the Pauli error does not meet the decoding condition, the prior probability vector of each quantum bit is adaptively updated to complete a new round of iteration until the number of iterations reaches a maximum value, specifically including: If the decoding condition If it is not true, then the dynamic adaptive prior probability vector of the next iteration is calculated based on the prior probability vector of each quantum bit and the a posteriori information in the previous iteration: ; in, Indicated in Variable nodes in iterations The corresponding Pauli error The dynamic adaptive prior probability vector that occurs, Represents the variable node at the initial moment The corresponding Pauli error The prior probability vector of occurrence, Indicates the variable node after this round of iteration The corresponding Pauli error The posterior information that occurs, is a discount factor used to balance the weight between the prior probability vector and the posterior information updated in this iteration; The dynamic adaptive prior probability vector is used to replace the prior probability vector to calculate the horizontal message, the vertical message and the posterior information and make a hard decision to complete a new round of iteration until the number of iterations reaches a maximum value.

[0054] The present invention also provides a computer-readable storage medium, wherein the computer-readable storage medium stores a quantum error correction code belief propagation decoding program based on adaptive prior probability, and when the quantum error correction code belief propagation decoding program based on adaptive prior probability is executed by a processor, the steps of the quantum error correction code belief propagation decoding method based on adaptive prior probability as described above are implemented.

[0055] In summary, the present invention proposes a quantum error correction code belief propagation decoding method, system and terminal based on adaptive prior probability, the method comprising: adaptively updating the prior probability of each Pauli error of the quantum bit by exponential weighted average method to perform dynamic initialization of each round of iteration; updating the message transmitted by the check node to all adjacent variable nodes connected to the check node according to the sum-product algorithm to obtain an updated horizontal message; updating the message transmitted by the variable node to all adjacent check nodes connected to the variable node according to the sum-product algorithm to obtain an updated vertical message; based on the prior information, the updated horizontal message and the updated vertical message, calculating the posterior information to obtain an estimate of the real error. The present invention significantly improves the decoding accuracy and convergence rate of highly degenerate quantum codes by adaptively adjusting the prior information, while maintaining the unchanged computational complexity, which is conducive to the engineering realization of fault-tolerant quantum computing.

[0056] It should be noted that, in this article, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or terminal including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or terminal. In the absence of further restrictions, an element defined by the sentence "comprises a ..." does not exclude the presence of other identical elements in the process, method, article or terminal including the element.

[0057] Of course, those skilled in the art can understand that all or part of the processes in the above-mentioned embodiments can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided by the present invention can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. As an illustration and not limitation, RAM is available in many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).

[0058] It should be understood that the application of the present invention is not limited to the above examples. For ordinary technicians in this field, 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 quantum error correction code belief propagation decoding method based on adaptive prior probability, characterized in that: The quantum error correction code belief propagation decoding method based on adaptive prior probability includes: Receive a priori probability vector of each quantum bit, obtain a variable node corresponding to each quantum bit, initialize information according to the prior probability vector to obtain initialization information, and transmit the initialization information of each variable node from the corresponding variable node to a check node adjacent to the variable node; Based on the multiple initialization information, updating the message transmitted by the check node to all adjacent variable nodes connected to the check node by a sum-product algorithm to obtain an updated horizontal message; Calculating posterior information based on the prior probability vector and the updated horizontal message; The Pauli error of each variable node is judged according to the posterior information. If the Pauli error meets the decoding conditions, the decoding is successful. If the Pauli error does not meet the decoding conditions, the prior probability vector of each quantum bit is adaptively updated to complete a new round of iterations until the number of iterations reaches the maximum value, and the decoding fails.

2. The quantum error correction code belief propagation decoding method based on adaptive prior probability according to claim 1 is characterized in that: Initializing the information according to the prior probability vector to obtain the initialization information specifically includes: The log-likelihood ratio is used to represent the prior probability vector of each Pauli error occurring at each variable node. Based on multiple prior probability vectors in the form of log-likelihood ratios, the information from the variable node to the check node is initialized respectively to obtain multiple initialization information: ； in, Indicates variable nodes, Indicates Check nodes, Indicates The variable node is passed to the first Initialization message of the check nodes, Represents a scalar message mapping function, represents the prior probability vector in the form of log-likelihood ratio, represents the calculation process of log-likelihood ratio, represents the initial prior probability, which contains the prior probability of each Pauli error occurring.

3. The quantum error correction code belief propagation decoding method based on adaptive prior probability according to claim 1 is characterized in that: The updating of the message transmitted by the check node to all adjacent variable nodes connected to the check node by the sum-product algorithm based on the multiple initialization information to obtain the updated horizontal message specifically includes: Obtain all adjacent variable nodes of a check node, traverse each adjacent variable node in turn, use the traversed adjacent variable node as the target variable node, and obtain initialization information sent to the check node by all remaining adjacent variable nodes except the target variable node; The level information sent by the check node to different adjacent variable nodes is calculated according to the initialization information, all the check nodes are traversed, the level information sent by other check nodes to their respective adjacent variable nodes is calculated, and the level information sent by each check node to different adjacent variable nodes is obtained.

4. The quantum error correction code belief propagation decoding method based on adaptive prior probability according to claim 3 is characterized in that: The updated horizontal message further includes: Get and remove the check node All variable nodes Adjacent check nodes Send to variable node News ; According to the message Update variable node Passed to the node with the variable All adjacent check nodes connected News , and obtain an updated vertical message, which is used for calculating the next round of horizontal messages.

5. The quantum error correction code belief propagation decoding method based on adaptive prior probability according to claim 4 is characterized in that: The calculating the posterior information based on the prior probability vector and the updated horizontal message specifically includes: For each variable node , according to the prior probability vector of each Pauli error in this iteration and variable nodes Updated level message received , calculate the posterior information of this round of iteration : ； in, Represents a scalar message mapping function, Error Operator With matrix element Oppose Yi.

6. The quantum error correction code belief propagation decoding method based on adaptive prior probability according to claim 5 is characterized in that: If the Pauli error meets the decoding condition, the decoding is successful, which specifically includes: Pauli Error for all variable nodes , if there is If holds, the estimated error vector Set to no error, otherwise, the error vector Set so that the posterior information Smallest Pauli error type: ; in, X, Y and Z They represent the Pauli operators Errors and Pauli operators acting on the system state Errors and Pauli operators acting on the system state Errors caused by acting on the system state; Error vector for all variable nodes Check if the decoding condition If it holds, it means the decoding is successful, returns convergence and stops checking, where, represents the product operation of matrix and vector, The check matrix represents the connection relationship between the check nodes and the variable nodes. Represents the error symptom vector obtained by stable sub-measurement.

7. The quantum error correction code belief propagation decoding method based on adaptive prior probability according to claim 6 is characterized in that: If the Pauli error does not meet the decoding condition, the prior probability vector of each quantum bit is adaptively updated to complete a new round of iteration until the number of iterations reaches a maximum value, specifically including: If the decoding condition If it is not true, then the dynamic adaptive prior probability vector of the next iteration is calculated based on the prior probability vector of each quantum bit and the a posteriori information in the previous iteration: ； in, Indicated in Variable nodes in iterations The corresponding Pauli error The dynamic adaptive prior probability vector that occurs, Represents the variable node at the initial moment The corresponding Pauli error The prior probability vector of occurrence, Indicates that the variable node after this round of iteration The corresponding Pauli error The posterior information that occurs, is a discount factor used to balance the weight between the prior probability vector and the posterior information updated in this iteration; The dynamic adaptive prior probability vector is used to replace the prior probability vector to calculate the horizontal message, the vertical message and the posterior information and make a hard decision to complete a new round of iteration until the number of iterations reaches a maximum value.

8. A belief propagation decoding system based on adaptive prior probability, characterized in that: The quantum error correction code belief propagation decoding system based on adaptive prior probability includes: An initialization module, used to receive a priori probability vector of each quantum bit, obtain a variable node corresponding to each quantum bit, initialize information according to the prior probability vector to obtain initialization information, and respectively transmit the initialization information of each variable node from the corresponding variable node to a check node adjacent to the variable node; A horizontal message updating module, configured to update the message transmitted by the check node to all adjacent variable nodes connected to the check node through a sum-product algorithm based on the multiple initialization information, to obtain an updated horizontal message; A posterior information calculation module, used to calculate the posterior information based on the prior probability vector and the updated horizontal message; The hard decision module is used to judge the Pauli error of each variable node according to the posterior information. If the Pauli error meets the decoding conditions, the decoding is successful. If the Pauli error does not meet the decoding conditions, the prior probability vector of each quantum bit is adaptively updated to complete a new round of iterations until the number of iterations reaches a maximum value, and the decoding fails.

9. A terminal, characterized in that: The terminal comprises: a memory, a processor, and a quantum error correction code belief propagation decoding program based on adaptive prior probability stored in the memory and executable on the processor. When the quantum error correction code belief propagation decoding program based on adaptive prior probability is executed by the processor, the steps of the quantum error correction code belief propagation decoding method based on adaptive prior probability as claimed in any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a quantum error correction code belief propagation decoding program based on adaptive prior probability, and when the quantum error correction code belief propagation decoding program based on adaptive prior probability is executed by a processor, the steps of the quantum error correction code belief propagation decoding method based on adaptive prior probability as described in any one of claims 1 to 7 are implemented.

Images