A neural network-driven decoding method for asymmetric quantum error correction codes

Abstract

The present invention discloses a neural network-driven decoding method for asymmetric quantum error correction codes. First, using the quantum asymmetric noise model, the required quantum asymmetric noise errors and mistakes are obtained, and the syndromes of the quantum asymmetric noise errors and mistakes are determined. Based on the neural network decoder, the errors and mistakes in the quantum system are predicted, and it is judged whether the predicted errors and mistakes satisfy the constraint conditions of quantum logic errors. If all satisfy the constraint conditions, the decoding is successful; otherwise, the decoding fails. The solution of the present invention uses the asymmetric noise model to break the symmetry of the HGP structure, making it possible to use asymmetric noise to improve the decoding performance; the use of neural network technology significantly improves the performance of the BP algorithm in the decoding of quantum error correction codes. Compared with the existing decoding technologies, the decoding method of the present invention shows a significant performance improvement when dealing with asymmetric quantum information.

Description

Technical Field

[0001] The present invention belongs to the field of neural network decoding of quantum error correction codes, and particularly relates to a decoding method for an asymmetric quantum error correction code driven by a neural network. Background Art

[0002] Quantum systems have great potential in achieving faster computing, more secure communication, and more precise sensing. However, qubits are extremely vulnerable to noise, leading to errors, which is one of the main challenges in the current development of quantum systems. To ensure the fault tolerance of quantum computing, the introduction of quantum error correction codes has become a crucial solution. Traditional quantum error correction codes usually assume that qubits are affected by depolarizing noise and consider that the probabilities of various types of errors (such as bit-flip (X) errors, phase-flip (Z) errors, and Y-type Pauli errors) are equal. However, in actual quantum systems, qubits often encounter asymmetric noise, where certain types of errors occur more frequently than others. For example, in the superconducting qubit system, phase noise usually dominates, and this asymmetric noise characteristic requires quantum error correction codes to be able to effectively cope with the asymmetry of the noise.

[0003] In recent years, quantum error correction codes for asymmetric noise have gradually received extensive attention. Researchers have proposed various schemes, such as the XZZX code and the noise-biased lifted product code, etc. These schemes optimize the quantum error correction performance by utilizing the asymmetry of the noise. However, existing decoding methods, especially the belief propagation (BP) algorithm based on sparse graph codes, often perform poorly in the face of problems such as quantum short cycles and quantum degeneracy. To improve the decoding accuracy, researchers have proposed various improvements to the BP algorithm, such as BP with memory effect and BP with posterior probability adjustment, but most of these methods are for symmetric noise environments and fail to effectively solve the decoding challenges under asymmetric noise.

[0004] With the rapid development of machine learning technologies, especially the successful application of deep learning and neural networks in multiple fields, the quantum error correction field has gradually explored the introduction of machine learning methods into the decoding process. Although the training process of neural network decoders is complex and time-consuming, and compared with traditional BP algorithms, their computational complexity usually grows linearly, the trained neural network decoders often provide better decoding performance than traditional methods, especially when dealing with asymmetric noise and complex noise patterns, neural networks have significant advantages. Therefore, machine learning, especially neural network technology, has become an important direction for solving the problem of asymmetric noise decoding in quantum error correction. Summary of the Invention

[0005] To address the above problems, the objective of the present invention is to provide a neural network-driven decoding method for asymmetric quantum error-correcting codes, and an innovative neural network decoder for asymmetric quantum error-correcting codes is proposed. The aim is to overcome the limitations of existing decoding methods in an asymmetric noise environment through the learning ability of the neural network, thereby improving the decoding performance of quantum error-correcting codes.

[0006] The specific technical solution for achieving the objective of the present invention is as follows:

[0007] A neural network-driven decoding method for asymmetric quantum error-correcting codes includes the following steps:

[0008] Step 1: Utilize the quantum asymmetric noise model to obtain the required quantum asymmetric noise errors and errors ;

[0009] Step 2: Determine the syndromes of the quantum asymmetric noise errors and errors ;

[0010] Step 3: Based on the neural network decoder, predict the errors and errors in the quantum system;

[0011] Step 4: Determine whether the predicted errors and errors satisfy the constraint conditions of quantum logic errors. If both satisfy the constraint conditions, the decoding is successful; otherwise, the decoding fails.

[0012] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0013] The present invention proposes a neural network-driven decoder for asymmetric quantum error-correcting codes to improve the decoding performance of quantum error-correcting codes in an asymmetric quantum noise channel;

[0014] The solution of the present invention uses the asymmetric noise model to break the symmetry of the HGP structure, making it possible to use asymmetric noise to improve the decoding performance; the use of neural network technology significantly improves the performance of the BP algorithm in the decoding of quantum error-correcting codes. Compared with existing decoding technologies, the decoding method of the present invention shows a significant performance improvement in processing asymmetric quantum information.

[0015] The following further describes the present invention in conjunction with specific embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 It is a schematic flowchart of the neural network-driven decoding method for asymmetric quantum error-correcting codes of the present invention.

[0017] Figure 2Structural diagram of the neural network-driven asymmetric quantum error correction code decoder of the present invention.

[0018] Figure 3 Underlying Tanner graph of the quantum error correction code of the present invention.

[0019] Figure 4 Structural diagram of the neuron nodes of the neural network decoder of the present invention. Detailed implementation manners

[0020] Embodiment

[0021] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. The described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0022] As shown in this application and the claims, unless the context clearly indicates an exception, the words "a", "an", "one" and / or "the" are not specifically singular and may also include the plural. Generally speaking, the terms "comprising" and "including" only indicate the inclusion of the clearly identified steps and elements, and these steps and elements do not constitute an exclusive list. The method or device may also include other steps or elements.

[0023] Unless otherwise specifically stated, the relative arrangements, numerical expressions and values of the components and steps described in these embodiments do not limit the scope of this application. At the same time, it should be understood that for the convenience of description, the dimensions of the various parts shown in the drawings are not drawn according to the actual proportional relationship. Technologies, methods and devices known to those of ordinary skill in the relevant art may not be discussed in detail, but where appropriate, the said technologies, methods and devices should be regarded as part of the authorization specification. In all the examples shown and discussed here, any specific value should be interpreted as merely exemplary and not as a limitation. Therefore, other examples of the exemplary embodiments may have different values. It should be noted that: similar reference numerals and letters indicate similar items in the following drawings. Therefore, once an item is defined in one drawing, it does not need to be further discussed in subsequent drawings.

[0024] In combination with Figure 1 , a neural network-driven asymmetric quantum error correction code decoding method includes the following steps:

[0025] Step 1: Using the quantum asymmetric noise model, obtain the required quantum asymmetric noise errors and errors :

[0026] Using the quantum asymmetric noise model, input the parity-check matrix of the quantum error-correcting code and , the code length of the quantum error-correcting code corresponding to the parity-check matrix , components of the number of columns of , the quantum Pauli error rate , where , and are the physical error rates of X, Y, and Z errors respectively, and the total physical error rate . In the asymmetric error model, mainly consider , the case where they are not equal;

[0027] Perform a Hadamard rotation operation on the input data to generate asymmetric noise errors and error ;

[0028] Without loss of generality, in this scheme, the parameters of the quantum error-correcting code are defined as , in order to illustrate the Hadamard rotation process, first divide the CSS code into four sub-parts.

[0029]

[0030] Next, perform the rotation operation.

[0031]

[0032] So far, a quantum error-correcting code with an XZZX structure has been obtained. Observing the HGP code in the CSS code family, this quantum error-correcting code has four sub-parts. The Hadamard rotation operation reasonably destroys the symmetry of the HGP structure, making it possible to improve the decoding performance using asymmetric noise.

[0033] Specifically, it includes the following steps:

[0034] Step 1-1: Initialize the error vector , , and initialize the probability vector: , ;

[0035] Step 1-2: Assign values to the probability vector:

[0036] , ,

[0037] , ,

[0038] Step 1-3: Assign values to the error vectors and output the quantum asymmetric noise errors and errors ;

[0039] For , use the random function to generate a random number between 0 and 1 , if , then , ; If , then , ; If , then , .

[0040] Step 2: Determine the syndrome of the quantum asymmetric noise error and error :

[0041]

[0042]

[0043] Step 3: Based on the neural network decoder, predict the errors and errors in the quantum system:

[0044] The neural network decoder generates the network structure according to the underlying Tanner graph of the quantum error correction code parity-check matrix, as Figure 3 shown. The main input data is the log-likelihood ratio (LLR) information of the channel and the syndrome. The decoder independently solves for X and Z, and their implementation details are the same.

[0045] The neural network decoder is as Figure 2 the belief propagation decoder in . The neural network decoder described in this scheme is constructed based on the BP neural network, including an input layer, 2T hidden layers representing T rounds of BP iterations, and an output layer; the dimensions of its input and output are the same as the code length of the quantum error correction code; the number of hidden layer nodes is equal to the number of rows of the parity-check matrix multiplied by the maximum row weight of , and updates) and the weights of the output layer; in addition, the weight update strategy is optimized through the loss function and residual connection.

[0046] The neuron node structure diagram of the neural network decoder in this embodiment is as Figure 4 shown.

[0047] The input of the neural network decoder is: the total channel physical error rate , the parity-check matrix or , the error or the syndrome of the error , and the maximum number of iterations of the neural network;

[0048] Iterate based on the input data to update the information of each node in the BP neural network. When the maximum number of iterations is reached, output the predicted error or error in the quantum system;

[0049] Update the weight parameters of the neural network decoder , where represents the weight of the input layer, the weight of the hidden layer, represents the weight of the output layer;

[0050] Specifically, it includes:

[0051] Step 3-1, initialize the information transmitted to the variable node (using the LLR message ):

[0052]

[0053]

[0054] Among them, represents the weight of the input layer;

[0055] Step 3-2, update the variable node information based on the iteration number t, and repeat this step until the maximum number of iterations is reached:

[0056] Use the LLR message: , where and ;

[0057] Use the error syndrome: , where and

[0058] Among them, respectively represent the weights in node transmission during the t-th iteration; represents the information transmitted from a variable node to a check node during the -th iteration, and the information transmitted from a check node to a variable node during the = ; represents the set of all neighbor nodes of v, and represents the set of all neighbor nodes of c; or error represents the syndrome of error or

[0059] Step 3-3. Marginalize the variable node information using the LLR message:

[0060]

[0061] where and ; represents the weight of the marginalized variable node during the t-th iteration, and

[0062] Step 3-4. Use the marginalized variable node information to error X or error and output the prediction result:

[0063]

[0064] Furthermore, during the iterative training process, the neural network decoder updates each weight value through a loss function:

[0065]

[0066]

[0067]

[0068] where is the loss function, is the balance coefficient used to control the weights of the two losses, is the loss value of the classical error, is the loss value of the logical error, is used to convert the modulo-2 operation of discrete integers into the modulo-2 operation of continuous values, represents the The element in the row and column, usually calculates the logical operator in the form of CSS and should control such that the null space of is not in the row space of . In addition, it is also necessary to ensure ;

[0069] In addition, residual connections can also be used to optimize the update of weights. Initially, a set of unassigned weights is established. In each round of BP iteration in the hidden layer loop, the information passed to the variable nodes is added to the final weighted edge information, which can effectively suppress the propagation of error information during the BP process. The equation description of the above residual connection is as follows:

[0070]

[0071] When making a prediction of error X or error , the loss value of the classical error and the loss value of the logical error are calculated respectively according to the error type of error X or error , and the final loss function value is obtained for updating each weight value.

[0072] Step 4, determine whether the predicted error and error satisfy the constraint conditions of the quantum logic error. If both satisfy the constraint conditions, the decoding is successful; otherwise, the decoding fails;

[0073] In the classical case, successful decoding means that the inferred error is exactly the same as the true error . However, in the quantum case, successful decoding only requires to belong to the stabilizer subgroup. The verification equation for successful decoding is:

[0074]

[0075] where , , is the orthogonal complement matrix with respect to the symplectic inner product , contains and , that is to say is a 2 binary matrix.

[0076] The specific steps of the decoding scheme are described above. Next, the parameter settings of the proposed decoder are given. It should be understood that the parameters of the decoder can be adjusted according to specific circumstances. Generally, the number of BP iterations is set to 10, and the neural network training cycle is 30. The decoder should use GPU acceleration, and the GPU version should not be lower than NVIDIA RTX 3060 Laptop GPU. The decoding scheme is based on the TensorFlow architecture and uses the Adam optimizer to minimize the loss. The proposed training parameters are: learning rate 0.0001, total batch size 30000, number of hidden layers 20 representing 10 rounds of BP iterations, number of batches per epoch 1000, and batch size 50 representing that each batch can accommodate 50 groups of data inputs.

[0077] After completing the above steps, a neural network decoder can be successfully trained. This decoder is precisely trained to effectively handle the decoding tasks of specific quantum error correction codes and provide highly optimized decoding performance for a given quantum error model. The training process enables the neural network decoder to learn the characteristics of the quantum error correction code, the error patterns, and their corresponding error correction rules, so that it can be reused in future applications. This reusability means that under the same or similar quantum error correction codes and noise conditions, the trained neural network decoder can decode quickly and accurately, thus significantly improving the fault tolerance and error correction efficiency of the quantum system.

[0078] In addition, since the training process of the neural network decoder can be optimized according to the noise characteristics in the actual quantum system, it can not only achieve good decoding results under specific quantum error correction codes, but also adapt to the performance of quantum error correction codes in different noise environments. This decoder has high flexibility and adaptability and can be widely applied under various quantum error correction codes and different noise models, greatly reducing the workload of frequently adjusting parameters and redesigning the decoder in traditional decoding methods. Therefore, this neural network decoder not only provides an efficient and reliable decoding scheme for the field of quantum error correction, but also provides a solid foundation for the practical application of future quantum information processing systems.

[0079] Through the above process, the trained neural network decoder can closely cooperate with specific quantum error correction codes, continuously play a role in different quantum computing and communication tasks, improve the performance of the entire system, and achieve an improvement in the fault tolerance function.

[0080] In addition, the present invention also provides a computer device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the computer program, the following steps are implemented:

[0081] Step 1: Use the quantum asymmetric noise model to obtain the required quantum asymmetric noise errors and errors ;

[0082] Step 2, determine the quantum asymmetric noise error and errors syndrome;

[0083] Step 3, based on the neural network decoder, predict the errors and errors in the quantum system;

[0084] Step 4, determine whether the predicted errors and errors meet the constraint conditions of the quantum logic error. If both meet the constraint conditions, the decoding is successful; otherwise, the decoding fails.

[0085] A computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the following steps are implemented:

[0086] Step 1, using the quantum asymmetric noise model, obtain the required quantum asymmetric noise error and errors ;

[0087] Step 2, determine the quantum asymmetric noise error and errors syndrome;

[0088] Step 3, based on the neural network decoder, predict the errors and errors in the quantum system;

[0089] Step 4, determine whether the predicted errors and errors meet the constraint conditions of the quantum logic error. If both meet the constraint conditions, the decoding is successful; otherwise, the decoding fails.

[0090] The above embodiments only represent several implementation manners of the present application. The description is relatively specific and detailed, but it should not be construed as a limitation on the scope of the invention patent. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present application, several modifications and improvements can still be made, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application shall be subject to the appended claims.

Claims

1. A neural network driven asymmetric quantum error correction code decoding method, characterized in that: The following steps are involved: Step 1: Use the quantum asymmetric noise model to obtain the required quantum asymmetric noise error and Error ; Using the quantum asymmetric noise model, input the quantum error correction code check matrix and , the quantum error correction code length corresponding to the check matrix is , The amount Number of columns , quantum Pauli error rate ,in, , and are the physical error rates of X, Y, and Z errors, respectively, and the data is Hadamard rotated to generate asymmetric noise errors and Error ; Step 2: Determine quantum asymmetric noise errors and Error The accompanying type; Step 3: Predict the quantum system based on the neural network decoder Errors and mistake: The neural network decoder is constructed based on the BP neural network and includes an input layer, a hidden layer and an output layer; The input of the neural network decoder is: channel physical error rate , check matrix or ,mistake or error The accompanying type; Iterate based on the input data and update the information of each node in the BP neural network. When the maximum number of iterations is reached, the output is the predicted quantum system. Error or mistake; Update the weight parameters of the neural network decoder ,in represents the input layer weight, The weights of the hidden layers, represents the weight of the output layer; Step 3-1, Initialize the information transmitted to the variable node: ； ； in, Represents the input layer weight; Step 3-2: Update the variable node information based on the number of iterations t, and repeat this step until the maximum number of iterations is reached. : ,in and ; ,in and ; in, They represent the weights of node transmission in the tth iteration respectively; Indicates The information transmitted from the variable node to the check node in the round iteration, No. The information transmitted from the check node to the variable node in the round iteration, in the first iteration, = ; represents the set of all neighbor nodes of v, Represents the set of all neighbor nodes of c; Indicates an error or error The accompanying type, In addition to outside, The set of all neighbor nodes of Step 3-3, marginalization variable node information: ； in, and , represents the weight of the marginalized variable node in the tth iteration, represents the weight of the output layer; Step 3-4: Using marginalized variable node information error X or error , and output the prediction results : ； Step 4: Determine the predicted Errors and Whether the error satisfies the constraint conditions of quantum logic error. If so, the decoding is successful, otherwise the decoding fails.

2. The neural network driven asymmetric quantum error correction code decoding method according to claim 1, characterized in that: The process of generating a biased error vector is: Step 1-1, Initialize the error vector , , and initialize the probability vector: , ; Step 1-2: Assign values ​​to the probability vector: ， ， ； ， ， ； Step 1-3: Assign a value to the error vector and output the quantum asymmetric noise error and Error ; right , use the random function to generate a random number between 0 and 1 ,if ,So , ;if ,So , ;if ,So , .

3. The neural network driven asymmetric quantum error correction code decoding method according to claim 1, characterized in that: Determining the quantum asymmetric noise error in step 2 and Error The companion form is: ； 。 4. The neural network driven asymmetric quantum error correction code decoding method according to claim 1, characterized in that: The neural network decoder updates each weight value through the loss function during the iterative training process: ； ； ； in, is the loss function, is the balance coefficient, is the loss value of the classic error, is the loss value of logical error, , The first matrix of the logical operator Line Column elements, K represents the number of information bits of the quantum error correction code; When making an error X or error When predicting, according to the error X or error The error types are used to calculate the loss values ​​of classic errors and logical errors respectively, and the final loss function value is obtained to update the weight values.

5. The neural network driven asymmetric quantum error correction code decoding method according to claim 1, characterized in that: The judgment prediction in step 4 Errors and Whether the error satisfies the constraint conditions of quantum logic error, specifically: The verification equation for successful decoding is: ； in, , , yes About Sinnega The orthogonal complement matrix of Include and .

6. A computer device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 5 are implemented.

7. A computer storable medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 5 are implemented.

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