Quantum error correction code decoding method, system and terminal based on momentum belief propagation

Abstract

The invention discloses a quantum error correction code decoding method, system and terminal based on momentum belief propagation, and the method comprises the steps: representing a prior message of the occurrence probability of each type of Follicle error of each quantum bit through a log-likelihood ratio, and obtaining an initialization message according to a prior probability vector, and updating messages transmitted to all adjacent variable nodes by the check node according to the initialization message to obtain an updated horizontal message, performing dynamic message updating on the posterior message of each variable node according to the updated horizontal message and the historical message to obtain an updated posterior message, and performing dynamic message updating on the posterior message of each variable node based on the updated horizontal message and the posterior message. And calculating an updated vertical message through a fixed suppression method, obtaining estimation of a real error according to a posterior message, and outputting a result. According to the method, a momentum item is introduced into message updating, a decoding algorithm based on momentum message propagation is obtained, and the decoding precision and the convergence rate of decoding on high-degenerate quantum codes are greatly improved.

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 decoding method, system, terminal and computer-readable storage medium based on momentum belief propagation. Background Art

[0002] The operation of quantum computers is highly sensitive, and even tiny external disturbances may lead to errors in the calculation results. Quantum error correction is a technology developed to enable quantum computers to work normally in the presence of errors. Its basic idea is to encode a logical quantum bit into multiple physical quantum bits to increase its noise resistance. However, since quantum measurement destroys the quantum state, the physical quantum bits cannot be directly detected and corrected. In order to solve this problem, auxiliary quantum bits and error correction algorithms need to be introduced. The belief propagation decoding algorithm is an error correction algorithm based on message updates on the Tanner graph (Tanner graph is a graphical representation method for representing the check matrix of LDPC codes). It can effectively process sparse check matrices and theoretically decode all stable subcodes.

[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. Its accuracy is particularly lacking on highly degenerate quantum codes, and 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 decoding method, system, terminal and computer-readable storage medium based on momentum belief propagation, aiming to solve the problem of low decoding accuracy of 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 decoding method based on momentum belief propagation, and the quantum error correction code decoding method based on momentum belief propagation comprises the following steps: Receive a priori probability vector of each quantum bit, obtain a variable node corresponding to each quantum bit, initialize a message according to the prior probability vector to obtain an initialization message, and transmit the initialization message of each variable node from the corresponding variable node to a check node adjacent to the variable node; Based on the multiple initialization messages, 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; Performing dynamic message updates on the a posteriori message of each variable node according to the updated horizontal message and the historical message to obtain the updated a posteriori message of each variable node; Based on the updated horizontal message and the a posteriori message, a vertical update message of each variable node to each adjacent check node is calculated by a fixed suppression method, and the vertical update message is respectively transmitted from the corresponding variable node to the corresponding check node to obtain an updated vertical message; The Pauli error of each variable node is judged according to the a posteriori message. If the Pauli error meets the decoding condition, the decoding is successful. If the Pauli error does not meet the decoding condition, the horizontal message is updated according to the updated vertical message 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 decoding method based on momentum belief propagation, wherein the message is initialized according to the prior probability vector to obtain multiple initialization messages, 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 messages from the variable nodes to the check nodes are initialized respectively to obtain multiple initialization messages: ; in, Indicates j variable nodes, Indicates i Check nodes, Indicates j The variable node is passed to the first i Initialization message of the check nodes, Represents a scalar message mapping function, represents the log-likelihood ratio vector, represents the calculation process of log-likelihood ratio, represents the log-likelihood ratio vector, containing the prior probability of each Pauli error occurring.

[0008] Optionally, the quantum error correction code decoding method based on momentum belief propagation, wherein the step of updating 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 messages 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 the initialization message sent to the check node by all remaining adjacent variable nodes except the target variable node; The horizontal message sent by the check node to different adjacent variable nodes is calculated according to the initialization message, and all the check nodes are traversed to calculate the horizontal message sent by other check nodes to their respective adjacent variable nodes to obtain the horizontal message sent by each check node to different adjacent variable nodes.

[0009] Optionally, the quantum error correction code decoding method based on momentum belief propagation, wherein the step of dynamically updating the a posteriori message of each variable node according to the updated horizontal message and the historical message to obtain the updated a posteriori message of each variable node, specifically includes: Calculate the momentum term of each variable node according to the accumulated historical update messages and the updated horizontal messages, and use the momentum term to dynamically update the posterior message of each variable node to obtain the updated posterior message of each variable node; Or, according to the accumulated historical update messages, gradient messages and updated level messages, the adaptive step length item of each variable node is calculated, and the posterior message of each variable node is dynamically updated through the adaptive step length item to obtain the updated posterior message of each variable node.

[0010] Optionally, the quantum error correction code decoding method based on momentum belief propagation, wherein the momentum term of each variable node is calculated according to the accumulated historical update messages and the updated horizontal messages, and the posterior message of each variable node is dynamically updated using the momentum term, specifically includes: According to the accumulated historical update messages and the updated level messages, the momentum term of each variable node of the current iteration is calculated: ; in, A variable node representing the current iteration The momentum term, Represents the variable node of the previous iteration in the historical update message The momentum term, represents the momentum decay factor, Represents the energy function The posterior probability The partial derivative of , Indicates the check node in the current iteration To variable node The updated horizontal message sent, Represents the variable node of the previous iteration in the historical update message The a posteriori message, When Pauli is wrong With matrix element When opposing the change, for all nodes with variables that meet the conditions Adjacent check nodes Perform the summation of the updated horizontal messages; The momentum term is used to dynamically update the posterior message of each variable node: ; in, A variable node representing the current iteration The corresponding posterior message after update, Represents the learning rate.

[0011] Optionally, the quantum error correction code decoding method based on momentum belief propagation, wherein the vertical update message of each variable node to each adjacent check node is calculated by a fixed suppression method based on the updated horizontal message and the a posteriori message, specifically includes: Based on the updated horizontal message and the a posteriori message, the vertical update message of each variable node to each adjacent check node is calculated by the fixed suppression method: ; in, Represented by variable nodes Passed to the verification node Vertical update message, Indicates the Pauli error corresponding to the variable node Is it related to the verification node The corresponding stabilizer Easy to use.

[0012] Optionally, the quantum error correction code decoding method based on momentum belief propagation, wherein if the Pauli error meets the decoding condition, the decoding is successful, and if the Pauli error does not meet the decoding condition, the horizontal message is updated according to the updated vertical message to complete a new round of iteration until the number of iterations reaches a maximum value, 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 a posteriori message Smallest Pauli error type: ; in, X, Y and Z They represent the Pauli operators X 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 the stable sub-measurement; Otherwise, the updated vertical message is used to replace the initialization message to update the horizontal message 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 decoding system based on momentum belief propagation, wherein the quantum error correction code decoding system based on momentum belief propagation 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 a message according to the prior probability vector to obtain an initialization message, and transmit the initialization message 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 by a sum-product algorithm based on the multiple initialization messages, to obtain an updated horizontal message; A dynamic message updating module, used to dynamically update the a posteriori message of each variable node according to the updated horizontal message and historical message, to obtain the updated a posteriori message of each variable node; A vertical message update module, used to calculate the vertical update message of each variable node to each adjacent check node through a fixed suppression method based on the updated horizontal message and the posterior message, and transmit the vertical update message from the corresponding variable node to the corresponding check node to obtain an updated vertical message; The hard decision module is used to judge the Pauli error of each variable node according to the a posteriori message. If the Pauli error meets the decoding condition, the decoding is successful. If the Pauli error does not meet the decoding condition, the horizontal message is updated according to the updated vertical message to complete a new round of iterations, until the number of iterations reaches a maximum value, then 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 decoding program based on momentum belief propagation stored in the memory and executable on the processor, wherein the quantum error correction code decoding program based on momentum belief propagation implements the steps of the quantum error correction code decoding method based on momentum belief propagation as described above when the quantum error correction code decoding program based on momentum belief propagation 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 decoding program based on momentum belief propagation, and when the quantum error correction code decoding program based on momentum belief propagation is executed by a processor, the steps of the quantum error correction code decoding method based on momentum belief propagation as described above are implemented.

[0016] In the present invention, the prior message of the probability of each Pauli error of each quantum bit is represented by the log-likelihood ratio, and multiple initialization messages are obtained according to the prior probability vector. The message transmitted by the check node to all adjacent variable nodes is updated according to the initialization message to obtain an updated horizontal message. The posterior message of each variable node is dynamically updated according to the updated horizontal message and the historical message to obtain the updated posterior message of each variable node. Based on the updated horizontal message and the posterior message, the updated vertical message is calculated by the fixed suppression method, and the estimation of the real error is obtained according to the posterior message, and the result is output. The present invention introduces a momentum term in the message update, obtains a decoding algorithm based on momentum message propagation, and greatly improves the decoding accuracy and convergence rate of decoding on highly degenerate quantum codes. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a flow chart of a preferred embodiment of the quantum error correction code decoding method based on momentum belief propagation of the present invention; Figure 2 It is a structural diagram of a preferred embodiment of the quantum error correction code decoding system based on momentum belief propagation 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 decoding method, system and terminal based on momentum belief propagation. 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 herein 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 decoding method based on momentum belief propagation described in the preferred embodiment of the present invention is as follows: Figure 1 and Figure 2 As shown, the quantum error correction code decoding method based on momentum belief propagation 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 message according to the prior probability vector to obtain the initialization message, and respectively transmitting the initialization message 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 expressed 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 qubits. 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, which detects whether a specific type of error occurs in the associated qubit, and each qubit corresponds to a variable node. In this method, each variable node stores the vector message { }, corresponding to the possible locations and types of errors, the check nodes and variable nodes can be represented by a check matrix or a Tanner graph. Tanner In the figure, The check node and The connection of the variable nodes represents the The stabilizer acts on A check matrix represents an error correction code. Belief propagation is to iteratively propagate messages on the Tanner graph to estimate the actual errors. This process 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. According to the prior probability vectors in the form of multiple log-likelihood ratios, the messages from the variable nodes to the check nodes are initialized respectively to obtain multiple initialization messages: ; 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 log-likelihood ratio vector, represents the calculation process of log-likelihood ratio, represents the log-likelihood ratio vector, containing 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 messages, the message transmitted by the check node to all adjacent variable nodes connected to the check node is updated by a 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 the initialization message sent to the check node by all remaining adjacent variable nodes except the target variable node is obtained.

[0029] Furthermore, the horizontal message sent by the check node to different adjacent variable nodes is calculated according to the initialization message, all the check nodes are traversed, the horizontal message sent by other check nodes to their respective adjacent variable nodes is calculated, and the horizontal message 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 this is the first iteration, then Represents the initialization message 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] Step S300: dynamically update the a posteriori message of each variable node according to the updated horizontal message and the historical message to obtain the updated a posteriori message of each variable node.

[0032] In this embodiment, the posterior message of each variable node is dynamically updated according to the updated horizontal message and the historical message, including the message update based on the momentum term and the message update based on the adaptive step length term.

[0033] Specifically, the message based on the momentum term includes: calculating the momentum term of each variable node according to the accumulated historical update messages and the updated horizontal messages, and using the momentum term to dynamically update the posterior message of each variable node to obtain the updated posterior message of each variable node.

[0034] According to the accumulated historical update messages and the updated level messages, the momentum term of each variable node of the current iteration is calculated: ; in, A variable node representing the current iteration The momentum term, Represents the variable node of the previous iteration in the historical update message The momentum term, represents the momentum decay factor, Represents the energy function The posterior probability The partial derivative of , Indicates the check node in the current iteration To variable node The updated horizontal message sent, Represents the variable node of the previous iteration in the historical update message The a posteriori message, When Pauli is wrong With matrix element When opposing the change, for all nodes with variables that meet the conditions Adjacent check nodes Perform the summation of the updated horizontal messages; The momentum term is used to dynamically update the posterior message of each variable node: ; in, A variable node representing the current iteration The corresponding posterior message after update, Represents the learning rate.

[0035] Furthermore, the message update based on the adaptive step length term includes: calculating the adaptive step length term of each variable node according to the accumulated historical update messages, gradient messages and updated horizontal messages, and dynamically updating the posterior messages of each variable node through the adaptive step length term to obtain the updated posterior messages of each variable node. The message update based on the adaptive step length term is similar to the message update calculation process based on the momentum term, which will not be repeated here.

[0036] Step S400: Based on the updated horizontal message and the a posteriori message, a vertical update message of each variable node to each adjacent check node is calculated by a fixed suppression method, and the vertical update message is respectively transmitted from the corresponding variable node to the corresponding check node to obtain an updated vertical message.

[0037] The step of calculating the vertical update message of each variable node to each adjacent check node by a fixed suppression method based on the updated horizontal message and the a posteriori message specifically includes: Based on the updated horizontal message and the a posteriori message, the vertical update message of each variable node to each adjacent check node is calculated by the fixed suppression method: ; in, Represented by variable nodes Passed to the verification node Vertical update message, Indicates the Pauli error corresponding to the variable node Is it related to the verification node The corresponding stabilizer Easy to make.

[0038] Furthermore, after obtaining multiple vertical update messages, the vertical update messages are respectively transmitted from the corresponding variable nodes to the corresponding check nodes to obtain updated vertical messages to achieve the update of the vertical messages. It can be understood that the updated vertical messages will be used as input for the next round of iterative horizontal updates.

[0039] Step S500, judging the Pauli error of each variable node according to the a posteriori message, if the Pauli error meets the decoding condition, the decoding is successful, if the Pauli error does not meet the decoding condition, the horizontal message is updated according to the updated vertical message to complete a new round of iteration, until the number of iterations reaches the maximum value, then the decoding fails.

[0040] Specifically, for each variable node , and each Pauli error , do the following: For the Pauli error of all variable nodes , if there is If holds, the estimated error vector Set to no error, otherwise, the error vector Set so that the a posteriori message Smallest Pauli error type: .

[0041] in, X, Y and Z They represent the Pauli operators X 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 is established, it means that the decoding is successful, and the code returns to convergence and stops checking; Otherwise, the updated vertical message is used to replace the initialization message to update the horizontal message to complete a new round of iterations until the number of iterations reaches the maximum value. When the number of iterations reaches the maximum value, if the decoding condition If it still does not hold, the decoding is considered to have failed, and failure is returned and the algorithm stops.

[0042] in, 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.

[0043] In summary, the quantum error correction code decoding method based on momentum belief propagation provided by the present invention particularly relates to quantum error correction coding and decoding technology in the field of quantum messages, wherein the prior message of the probability of occurrence of each Pauli error of each quantum bit is represented by the log-likelihood ratio, and multiple initialization messages are obtained according to the prior probability vector, and the message transmitted by the check node to all adjacent variable nodes is updated according to the initialization message to obtain an updated horizontal message, and the posterior message of each variable node is dynamically updated according to the updated horizontal message and the historical message to obtain the updated posterior message of each variable node, and the updated vertical message is calculated by the fixed suppression method based on the updated horizontal message and the posterior message, and the estimation of the real error is obtained according to the posterior message, and the result is output. The decoding accuracy and convergence rate of decoding on highly degenerate quantum codes are greatly improved, which is conducive to the engineering realization of fault-tolerant quantum computing, and has broad application prospects and significant social value.

[0044] Furthermore, if Figure 2 As shown, based on the above-mentioned quantum error correction code decoding method based on momentum belief propagation, the present invention also provides a quantum error correction code decoding system based on momentum belief propagation, wherein the quantum error correction code decoding system based on momentum belief propagation 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 a message according to the prior probability vector to obtain an initialization message, and transmit the initialization message 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 by a sum-product algorithm based on the multiple initialization messages, to obtain an updated horizontal message; A dynamic message updating module, used to dynamically update the a posteriori message of each variable node according to the updated horizontal message and historical message, to obtain the updated a posteriori message of each variable node; A vertical message update module, used to calculate the vertical update message of each variable node to each adjacent check node through a fixed suppression method based on the updated horizontal message and the posterior message, and transmit the vertical update message from the corresponding variable node to the corresponding check node to obtain an updated vertical message; The hard decision module is used to judge the Pauli error of each variable node according to the a posteriori message. If the Pauli error meets the decoding condition, the decoding is successful. If the Pauli error does not meet the decoding condition, the horizontal message is updated according to the updated vertical message to complete a new round of iterations, until the number of iterations reaches a maximum value, then the decoding fails.

[0045] Furthermore, if Figure 3 As shown, based on the above-mentioned quantum error correction code decoding method and system based on momentum belief propagation, 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.

[0046] 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 quantum error correction code decoding program 40 based on momentum belief propagation is stored on the memory 20, and the quantum error correction code decoding program 40 based on momentum belief propagation can be executed by the processor 10, thereby realizing the quantum error correction code decoding method based on momentum belief propagation in the present application.

[0047] 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 decoding method based on momentum belief propagation.

[0048] 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 messages on the terminal and to display a visual user interface. The components of the terminal communicate with each other via a system bus.

[0049] In one embodiment, when the processor 10 executes the quantum error correction code decoding program 40 based on momentum belief propagation 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 a message according to the prior probability vector to obtain an initialization message, and transmit the initialization message of each variable node from the corresponding variable node to a check node adjacent to the variable node; Based on the multiple initialization messages, 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; Performing dynamic message updates on the a posteriori message of each variable node according to the updated horizontal message and the historical message to obtain the updated a posteriori message of each variable node; Based on the updated horizontal message and the a posteriori message, a vertical update message of each variable node to each adjacent check node is calculated by a fixed suppression method, and the vertical update message is respectively transmitted from the corresponding variable node to the corresponding check node to obtain an updated vertical message; The Pauli error of each variable node is judged according to the a posteriori message. If the Pauli error meets the decoding condition, the decoding is successful. If the Pauli error does not meet the decoding condition, the horizontal message is updated according to the updated vertical message to complete a new round of iterations until the number of iterations reaches the maximum value, and the decoding fails.

[0050] The initializing the message according to the prior probability vector to obtain the initialization message 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 messages from the variable nodes to the check nodes are initialized respectively to obtain multiple initialization messages: ; in, Indicates j variable nodes, Indicates i Check nodes, Indicates j The variable node is passed to the first i Initialization message of the check nodes, Represents a scalar message mapping function, represents the log-likelihood ratio vector, represents the calculation process of log-likelihood ratio, represents the log-likelihood ratio vector, containing the prior probability of each Pauli error occurring.

[0051] Wherein, based on the multiple initialization messages, 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 the initialization message sent to the check node by all remaining adjacent variable nodes except the target variable node; The horizontal message sent by the check node to different adjacent variable nodes is calculated according to the initialization message, and all the check nodes are traversed to calculate the horizontal message sent by other check nodes to their respective adjacent variable nodes to obtain the horizontal message sent by each check node to different adjacent variable nodes.

[0052] The method of dynamically updating the a posteriori message of each variable node according to the updated horizontal message and the historical message to obtain the updated a posteriori message of each variable node specifically includes: Calculate the momentum term of each variable node according to the accumulated historical update messages and the updated horizontal messages, and use the momentum term to dynamically update the posterior message of each variable node to obtain the updated posterior message of each variable node; Or, according to the accumulated historical update messages, gradient messages and updated level messages, the adaptive step length item of each variable node is calculated, and the posterior message of each variable node is dynamically updated through the adaptive step length item to obtain the updated posterior message of each variable node.

[0053] The step of calculating the momentum term of each variable node according to the accumulated historical update messages and the updated horizontal messages, and using the momentum term to dynamically update the posterior messages of each variable node specifically includes: According to the accumulated historical update messages and the updated level messages, the momentum term of each variable node of the current iteration is calculated: ; in, A variable node representing the current iteration The momentum term, Represents the variable node of the previous iteration in the historical update message The momentum term, represents the momentum decay factor, Represents the energy function The posterior probability The partial derivative of , Indicates the check node in the current iteration To variable node The updated horizontal message sent, Represents the variable node of the previous iteration in the historical update message The a posteriori message, When Pauli is wrong With matrix element When opposing the change, for all nodes with variables that meet the conditions Adjacent check nodes Perform the summation of the updated horizontal messages; The momentum term is used to dynamically update the posterior message of each variable node: ; in, A variable node representing the current iteration The corresponding posterior message after update, Represents the learning rate.

[0054] The method of calculating the vertical update message of each variable node to each adjacent check node by a fixed suppression method based on the updated horizontal message and the a posteriori message specifically includes: Based on the updated horizontal message and the a posteriori message, the vertical update message of each variable node to each adjacent check node is calculated by the fixed suppression method: ; in, Represented by variable nodes Passed to the verification node Vertical update message, Indicates the Pauli error corresponding to the variable node Is it related to the verification node The corresponding stabilizer Easy to use.

[0055] If the Pauli error meets the decoding condition, the decoding is successful; if the Pauli error does not meet the decoding condition, the horizontal message is updated according to the updated vertical message to complete a new round of iteration until the number of iterations reaches a maximum value, specifically including: 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 a posteriori message Smallest Pauli error type: ; in, X, Y and Z They represent the Pauli operators X 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 the stable sub-measurement; Otherwise, the updated vertical message is used to replace the initialization message to update the horizontal message to complete a new round of iteration until the number of iterations reaches a maximum value.

[0056] The present invention also provides a computer-readable storage medium, wherein the computer-readable storage medium stores a quantum error correction code decoding program based on momentum belief propagation, and when the quantum error correction code decoding program based on momentum belief propagation is executed by a processor, the steps of the quantum error correction code decoding method based on momentum belief propagation as described above are implemented.

[0057] In summary, the present invention proposes a quantum error correction code decoding method, system and terminal based on momentum belief propagation, the method comprising: representing the prior message of the probability of each Pauli error of each quantum bit by log-likelihood ratio, obtaining multiple initialization messages according to the prior probability vector, updating the message transmitted by the check node to all adjacent variable nodes according to the initialization message, obtaining an updated horizontal message, dynamically updating the a posteriori message of each variable node according to the updated horizontal message and the historical message, obtaining the updated a posteriori message of each variable node, calculating the updated vertical message based on the updated horizontal message and the a posteriori message by a fixed suppression method, obtaining an estimate of the real error according to the a posteriori message, and outputting the result. The present invention introduces a momentum term in the message update, obtains a decoding algorithm based on momentum message propagation, and greatly improves the decoding accuracy and convergence rate of decoding on highly degenerate quantum codes.

[0058] 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.

[0059] 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).

[0060] 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 decoding method based on momentum belief propagation, characterized in that: The quantum error correction code decoding method based on momentum belief propagation includes: Receive a priori probability vector of each quantum bit, obtain a variable node corresponding to each quantum bit, initialize a message according to the prior probability vector to obtain an initialization message, and transmit the initialization message of each variable node from the corresponding variable node to a check node adjacent to the variable node; Based on the multiple initialization messages, 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; Performing dynamic message updates on the a posteriori message of each variable node according to the updated horizontal message and the historical message to obtain the updated a posteriori message of each variable node; Based on the updated horizontal message and the a posteriori message, a vertical update message of each variable node to each adjacent check node is calculated by a fixed suppression method, and the vertical update message is respectively transmitted from the corresponding variable node to the corresponding check node to obtain an updated vertical message; The Pauli error of each variable node is judged according to the a posteriori message. If the Pauli error meets the decoding condition, the decoding is successful. If the Pauli error does not meet the decoding condition, the horizontal message is updated according to the updated vertical message 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 decoding method based on momentum belief propagation according to claim 1, characterized in that: Initializing the message according to the prior probability vector to obtain the initialization message 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 messages from the variable nodes to the check nodes are initialized respectively to obtain multiple initialization messages: ； in, Indicates j variable nodes, Indicates i Check nodes, Indicates j The variable node is passed to the first i Initialization message of the check nodes, Represents a scalar message mapping function, represents the log-likelihood ratio vector, represents the calculation process of log-likelihood ratio, represents the log-likelihood ratio vector, containing the prior probability of each Pauli error occurring.

3. The quantum error correction code decoding method based on momentum belief propagation according to claim 1 is characterized in that: The method of updating 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 messages 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 the initialization message sent to the check node by all remaining adjacent variable nodes except the target variable node; The horizontal message sent by the check node to different adjacent variable nodes is calculated according to the initialization message, and all the check nodes are traversed to calculate the horizontal message sent by other check nodes to their respective adjacent variable nodes to obtain the horizontal message sent by each check node to different adjacent variable nodes.

4. The quantum error correction code decoding method based on momentum belief propagation according to claim 3 is characterized in that: The step of dynamically updating the a posteriori message of each variable node according to the updated horizontal message and the historical message to obtain the updated a posteriori message of each variable node specifically includes: Calculate the momentum term of each variable node according to the accumulated historical update messages and the updated horizontal messages, and use the momentum term to dynamically update the posterior message of each variable node to obtain the updated posterior message of each variable node; Or, according to the accumulated historical update messages, gradient messages and updated level messages, the adaptive step length item of each variable node is calculated, and the posterior message of each variable node is dynamically updated through the adaptive step length item to obtain the updated posterior message of each variable node.

5. The quantum error correction code decoding method based on momentum belief propagation according to claim 4 is characterized in that: The step of calculating the momentum term of each variable node according to the accumulated historical update messages and the updated horizontal messages, and using the momentum term to dynamically update the posterior messages of each variable node specifically includes: According to the accumulated historical update messages and the updated level messages, the momentum term of each variable node of the current iteration is calculated: ； in, A variable node representing the current iteration The momentum term, Represents the variable node of the previous iteration in the historical update message The momentum term, represents the momentum decay factor, Represents the energy function The posterior probability The partial derivative of , Indicates the check node in the current iteration To variable node The updated horizontal message sent, Represents the variable node of the previous iteration in the historical update message The a posteriori message, When Pauli is wrong With matrix element When opposing the change, for all nodes with variables that meet the conditions Adjacent check nodes Perform the summation of the updated horizontal messages; The momentum term is used to dynamically update the posterior message of each variable node: ； in, A variable node representing the current iteration The corresponding posterior message after update, Represents the learning rate.

6. The quantum error correction code decoding method based on momentum belief propagation according to claim 5, characterized in that: The step of calculating the vertical update message of each variable node to each adjacent check node by a fixed suppression method based on the updated horizontal message and the a posteriori message specifically includes: Based on the updated horizontal message and the a posteriori message, the vertical update message of each variable node to each adjacent check node is calculated by the fixed suppression method: ； in, Represented by variable nodes Passed to the verification node Vertical update message, Indicates the Pauli error corresponding to the variable node Is it related to the verification node The corresponding stabilizer Easy to use.

7. The quantum error correction code decoding method based on momentum belief propagation according to claim 6 is characterized in that: If the Pauli error meets the decoding condition, the decoding is successful; if the Pauli error does not meet the decoding condition, the horizontal message is updated according to the updated vertical message to complete a new round of iteration until the number of iterations reaches a maximum value, specifically including: 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 a posteriori message Smallest Pauli error type: ; in, X, Y and Z They represent the Pauli operators X 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 the stable sub-measurement; Otherwise, the updated vertical message is used to replace the initialization message to update the horizontal message to complete a new round of iteration until the number of iterations reaches a maximum value.

8. A quantum error correction code decoding system based on momentum belief propagation, characterized in that: The quantum error correction code decoding system based on momentum belief propagation 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 a message according to the prior probability vector to obtain an initialization message, and transmit the initialization message 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 by a sum-product algorithm based on the multiple initialization messages, to obtain an updated horizontal message; A dynamic message updating module, used to dynamically update the a posteriori message of each variable node according to the updated horizontal message and historical message, to obtain the updated a posteriori message of each variable node; A vertical message update module, used to calculate the vertical update message of each variable node to each adjacent check node through a fixed suppression method based on the updated horizontal message and the posterior message, and transmit the vertical update message from the corresponding variable node to the corresponding check node to obtain an updated vertical message; The hard decision module is used to judge the Pauli error of each variable node according to the a posteriori message. If the Pauli error meets the decoding condition, the decoding is successful. If the Pauli error does not meet the decoding condition, the horizontal message is updated according to the updated vertical message to complete a new round of iterations, until the number of iterations reaches a maximum value, then the decoding fails.

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

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