Neural network driven asymmetric quantum error correction code decoding method

Abstract

The invention discloses an asymmetric quantum error correction code decoding method driven by a neural network, which comprises the following steps of: firstly, obtaining required quantum asymmetric noise errors # imgabs0 # and # imgabs1 # by using a quantum asymmetric noise model, determining syndromes of the quantum asymmetric noise errors # imgabs2 # and # imgabs3 #, predicting # imgabs4 # errors and # imgabs5 # errors in a quantum system based on a neural network decoder, and decoding the quantum asymmetric noise errors # imgabs0 # and # imgabs1 #. And judging whether the predicted # imgabs6 # error and # imgabs7 # error meet constraint conditions of quantum logic errors or not, if the predicted # imgabs6 # error and # imgabs7 # error meet the constraint conditions, determining that decoding succeeds, and otherwise, determining that decoding fails. According to the scheme of the invention, the asymmetrical noise model is utilized to destroy the symmetry of the HGP structure, so that the decoding performance can be improved by utilizing asymmetrical noise; the performance of the BP algorithm in quantum error correction code decoding is remarkably improved by using the neural network technology, and compared with the existing decoding technology, the decoding method disclosed by the invention shows remarkable performance improvement when asymmetric quantum information is processed.

Description

Technical Field

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

[0002] Quantum systems have great potential in achieving faster computing, more secure communications, and more precise sensing. However, qubits are extremely susceptible to noise, which leads to errors. This problem is one of the main challenges in the development of current quantum systems. In order 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 depolarization noise and assume that various types of errors (such as bit flip (X) errors, phase flip (Z) errors, and Y-type Pauli errors) have equal probability of occurrence. However, in actual quantum systems, qubits often encounter asymmetric noise, in which some types of errors occur more frequently than others. For example, in superconducting qubit systems, phase noise is usually dominant. This asymmetric noise characteristic requires quantum error correction codes to effectively cope with the asymmetry of noise.

[0003] In recent years, quantum error correction codes for asymmetric noise have gradually received widespread attention. Researchers have proposed a variety of schemes, such as XZZX codes and noise-biased lifted product codes, which optimize quantum error correction performance by exploiting the asymmetry of noise. However, existing decoding methods, especially the belief propagation BP algorithm based on sparse graph codes, often do not work well when faced with problems such as quantum short loops and quantum degeneracy. In order to improve the decoding accuracy, researchers have proposed a variety of improvements to the BP algorithm, such as BP with memory effect and BP with posterior probability adjustment, but most of these methods are aimed at symmetric noise environments and fail to effectively solve the decoding challenges under asymmetric noise.

[0004] With the rapid development of machine learning technology, especially the successful application of deep learning and neural networks in many fields, the field of quantum error correction 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 its computational complexity usually increases linearly compared to traditional BP algorithms, trained neural network decoders can often provide decoding performance that is superior to 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] In view of the above problems, the purpose of the present invention is to provide a neural network driven asymmetric quantum error correction code decoding method, and proposes an innovative asymmetric quantum error correction code neural network decoder, which aims to overcome the limitations of existing decoding methods in asymmetric noise environments through the learning ability of neural networks, thereby improving the decoding performance of quantum error correction codes.

[0006] The specific technical solution for achieving the purpose of the present invention is:

[0007] A neural network driven asymmetric quantum error correction code decoding method, comprising the following steps:

[0008] Step 1: Use the quantum asymmetric noise model to obtain the required quantum asymmetric noise error and Error ;

[0009] Step 2: Determine quantum asymmetric noise errors and Error The accompanying type;

[0010] Step 3: Predict the quantum system based on the neural network decoder Errors and mistake;

[0011] 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.

[0012] Compared with the prior art, the present invention has the following beneficial effects:

[0013] The present invention proposes a neural network driven asymmetric quantum error correction code decoder for improving the decoding performance of quantum error correction codes in an asymmetric quantum noise channel;

[0014] The solution of the present invention utilizes an asymmetric noise model to destroy the symmetry of the HGP structure, making it possible to utilize asymmetric noise to improve decoding performance; the performance of the BP algorithm in quantum error correction code decoding is significantly improved by utilizing neural network technology. Compared with existing decoding technologies, the decoding method of the present invention exhibits significant performance improvement when processing asymmetric quantum information.

[0015] The present invention is further described below in conjunction with specific implementation modes. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 This is a schematic flow chart of the neural network driven asymmetric quantum error correction code decoding method of the present invention.

[0017] Figure 2This is a structural diagram of the asymmetric quantum error correction code decoder driven by the neural network of the present invention.

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

[0019] Figure 4 This is a neuron node structure diagram of the neural network decoder of the present invention. DETAILED DESCRIPTION

[0020] Example

[0021] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the accompanying drawings in the embodiments of the present invention. The described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0022] As shown in this application and claims, unless the context clearly indicates an exception, the words "a", "an", "an kind" and / or "the" do not refer to the singular and may also include the plural. Generally speaking, the terms "include" and "comprise" only indicate the inclusion of the steps and elements that have been clearly identified, 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 arrangement, numerical expressions and numerical values ​​of the parts and steps set forth in these embodiments do not limit the scope of the present application. At the same time, it should be understood that, for ease of description, the sizes of the various parts shown in the accompanying drawings are not drawn according to the actual proportional relationship. The technology, method and equipment known to those of ordinary skill in the relevant field may not be discussed in detail, but in appropriate cases, the technology, method and equipment should be considered as a part of the authorization specification. In all examples shown and discussed here, any specific value should be interpreted as being merely exemplary, rather than as a limitation. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters represent similar items in the following drawings, so that once a certain item is defined in an accompanying drawing, it does not need to be further discussed in subsequent drawings.

[0024] Combination Figure 1 , a neural network driven asymmetric quantum error correction code decoding method, comprising the following steps:

[0025] Step 1: Use the quantum asymmetric noise model to obtain the required quantum asymmetric noise error and Error :

[0026] 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 The physical error rates of X, Y and Z errors respectively, and the total physical error rate , under the asymmetric error model, the main consideration is , Unequal situations;

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

[0028] Without loss of generality, the quantum error correction code parameters in this scheme are defined as [[ ]],To illustrate the Hadamard rotation process, the CSS code is first divided into four sub-parts.

[0029]

[0030] Next, a rotation operation is performed.

[0031]

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

[0033] The specific steps include:

[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 a value to the error vector and output the quantum asymmetric noise error and Error ;

[0039] right , use the random function to generate a random number between 0 and 1 ,if ,So , ;if ,So , ;if ,So , .

[0040] Step 2: Determine quantum asymmetric noise errors and Error The companion form:

[0041]

[0042]

[0043] Step 3: Predict the quantum system based on the neural network decoder Errors and mistake:

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

[0045] Neural network decoder Figure 2 As shown in the belief propagation decoder in , the neural network decoder described in this scheme is built 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 Consistent; the number of hidden layer nodes is equal to the check matrix The number of rows multiplied by The maximum row weight of the decoder has 5 sets of weight parameters , representing the t-th iteration of the input layer and the hidden layer respectively (each cycle includes , and 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 follows Figure 4 shown.

[0047] The input of the neural network decoder is: the total channel physical error rate , check matrix or ,mistake or error The companion form of the neural network, the maximum number of iterations ;

[0048] 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;

[0049] 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;

[0050] Specifically include:

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

[0052]

[0053]

[0054] in, Represents the input layer weight;

[0055] 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. :

[0056] Using LLR messages: ,in and ;

[0057] Using the error syndrome: ,in and

[0058] 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 ;

[0059] Step 3-3: Use LLR messages to marginalize variable node information:

[0060]

[0061] in, and , represents the weight of the marginalized variable node in the tth iteration, represents the weight of the output layer.

[0062] Step 3-4: Using marginalized variable node information error X or error , and output the prediction results:

[0063]

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

[0065]

[0066]

[0067]

[0068] in, is the loss function, is the balance coefficient, which is used to control the weight of the two losses. is the loss value of the classic error, is the loss value of logical error, It is used to convert the modulo 2 operation of discrete integers into the modulo 2 operation of continuous values. The first matrix of the logical operator Line Column elements, usually compute logical operators in the form of CSS , should be controlled exist The null space of In the row space of In addition, you need to ensure ;

[0069] In addition, residual connections can also be used to optimize weight updates. Initially, a set of unassigned weights is established In each BP iteration of the hidden layer loop, the information passed to the variable node is taken out and added to the final weighted edge information, which can effectively suppress the propagation of erroneous information in the BP process. The equation of the above residual connection is described as follows:

[0070]

[0071] 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.

[0072] 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.

[0073] In the classical case, successful decoding means an inferred error With real error are exactly the same. However, in the quantum case, successful decoding only requires Belongs to the stable subgroup. The verification equation for successful decoding is:

[0074]

[0075] in, , , yes About Sinnega The orthogonal complement matrix of Include and , that is to say is a 2 A binary matrix.

[0076] The above describes the specific steps of the decoding scheme. Next, the recommended decoder parameter settings 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 set to 30. The decoder should be accelerated by a graphics card, and the graphics card version should be no less than NVIDIA RTX 3060 Laptop GPU. The decoding scheme uses the Adam optimizer based on the TensorFlow architecture to minimize the loss. Recommended training parameters: learning rate 0.0001, total batch size 30000, number of hidden layers 20 represents 10 rounds of BP iterations, number of batches in each epoch is 1000, and batch size 50 represents that each batch can accommodate 50 sets of data input.

[0077] After completing the above steps, a neural network decoder can be successfully trained. The decoder is accurately trained to effectively handle the decoding task of a specific quantum error correction code and provide highly optimized decoding performance for a given quantum error model. The training process enables the neural network decoder to be reused in future applications by learning the characteristics of quantum error correction codes, error patterns, and their corresponding error correction rules. 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, thereby 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. The decoder has high flexibility and adaptability and can be widely used under a variety of quantum error correction codes and different noise models, greatly reducing the workload of frequent parameter adjustment and decoder redesign in traditional decoding methods. Therefore, the neural network decoder not only provides an efficient and reliable decoding solution 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 work closely with specific quantum error correction codes, continue to play a role in different quantum computing and communication tasks, improve the performance of the entire system, and achieve improved fault tolerance.

[0080] In addition, the present invention further provides a computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein 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 error and Error ;

[0082] Step 2: Determine quantum asymmetric noise errors and Error The accompanying type;

[0083] Step 3: Predict the quantum system based on the neural network decoder Errors and mistake;

[0084] 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.

[0085] A computer storable medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the following steps are implemented:

[0086] Step 1: Use the quantum asymmetric noise model to obtain the required quantum asymmetric noise error and Error ;

[0087] Step 2: Determine quantum asymmetric noise errors and Error The accompanying type;

[0088] Step 3: Predict the quantum system based on the neural network decoder Errors and mistake;

[0089] 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.

[0090] The above-mentioned embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, 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 attached 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 ; 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; 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 step 1 is to obtain the desired quantum asymmetric noise error and Error , specifically: 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 .

3. The neural network driven asymmetric quantum error correction code decoding method according to claim 2, 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 , .

4. The neural network driven asymmetric quantum error correction code decoding method according to claim 2, characterized in that: Determining the quantum asymmetric noise error in step 2 and Error The companion form is: ； 。 5. The neural network driven asymmetric quantum error correction code decoding method according to claim 2, characterized in that: The neural network decoder in step 3 predicts errors in quantum systems and Error , specifically: 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.

6. The neural network driven asymmetric quantum error correction code decoding method according to claim 5, characterized in that: Predicting errors in quantum systems and Error The process is: 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 : 。 7. The neural network driven asymmetric quantum error correction code decoding method according to claim 6, 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 matrix consisting of logical operators 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.

8. The neural network driven asymmetric quantum error correction code decoding method according to claim 6, 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 .

9. 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 8 are implemented.

10. 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 8 are implemented.

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