A quantum toric code decoder and method

Abstract

The application discloses a kind of quantum torus code decoder and method, using the self-attention U-net quantum error correction decoder obtained by training to decode torus code.SU‑NetQD is composed of two parts of low-level decoder and high-level decoder.The low-level decoder uses the extracted error syndrome as input and predicts recovery chain operation, and the high-level decoder uses the recovery chain predicted by the low-level decoder and the original error syndrome as input and predicts the logical error introduced by the low-level decoder.The decoder decodes successfully when and only when the recovery chain predicted by the low-level decoder can completely eliminate the error syndrome, and the logical error predicted by the high-level decoder conforms to the combined effect of the recovery chain and the original error.The application can efficiently and quickly implement the denoising function for torus code under complex noise, maintain the original information of quantum bits without interference, and perform better than the traditional MWPM decoder in various situations.

Description

Technical Field

[0001] The present invention belongs to the field of quantum computing technology, and in particular relates to a quantum torus code decoder and method. Background Art

[0002] Quantum computing, due to its theoretically superior computing power, has become one of the most hotly debated topics in the scientific community. For certain complex problems, researchers have proposed numerous efficient quantum algorithms that can provide quadratic or even exponential speedups compared to classical computing. However, due to the presence of quantum noise, existing quantum computers still exhibit high error rates, which limits the scale and complexity of viable quantum algorithms. Therefore, quantum error correction, which aims to detect and correct qubit errors in quantum systems, remains an extremely important and active area of ​​research. Quantum error correction is a necessary step towards achieving reliable, large-scale quantum computing.

[0003] Surface codes are one of the most popular and hardware-friendly error-correcting codes. Traditional surface code decoding methods, such as minimum weight perfect matching (MWPM) and union find (UF), face problems with decoding accuracy and scalability. Therefore, designing a new low-latency, high-precision, and scalable decoder has become a scientific problem that needs to be solved urgently. Recently, machine learning technology based on neural networks has attracted widespread attention due to some good properties. However, existing solutions, such as MLP, CNN, RNN, etc., do not take into account the structural characteristics of surface codes, and their decoding accuracy and scalability need to be improved. At the same time, some complex network architectures, such as Transformer, still have high requirements on the size of the training data set, which is difficult to meet for scarce quantum error correction data.

[0004] In summary, the problems and defects of the existing technical solutions can be summarized as follows:

[0005] 1. Scale limitation: The minimum weight perfect matching algorithm, currently the most popular traditional surface code decoding method, is limited by the algorithm's time complexity and is unable to perform error correction tasks in large-scale quantum systems.

[0006] 2. Accuracy limitations: Although the minimum weight perfect matching algorithm has very high error correction capabilities at low error rates, it performs poorly in complex correlated noise and high error rate scenarios, which can easily lead to logical errors and low decoding accuracy.

[0007] 3. High computational overhead: Many neural network decoder-based models, such as multi-layer perceptrons, have fixed input and output sizes. Therefore, changes in the surface code distance will require retraining a completely new model, resulting in considerable overhead.

[0008] 4. High data requirements: Neural network models based on the Transformer structure often require more training data to achieve better decoding results due to the lack of certain translation invariance and local perception.

[0009] 5. Model structure design flaws: When the existing neural network decoder model unfolds the surface code into a two-dimensional plane graphic, it does not consider the toroidal structural characteristics of the surface code itself and the relationship between the error chain and the original lattice and the dual lattice. This results in low accuracy in the model's prediction of edge errors.

[0010] 6. Poor decoder scalability: Existing decoders mostly focus on low-level decoders that detect the exact location of errors in data qubits, while ignoring the role of high-level decoders that correct logical errors. A systematic, scalable decoder has yet to be proposed. Summary of the Invention

[0011] In order to overcome the shortcomings of the prior art, the present invention provides a quantum torus code decoder and method, which uses a trained self-attention U-net quantum error correction decoder (SU-NetQD) to decode the torus code. SU-NetQD consists of two parts: a low-level decoder and a high-level decoder. The low-level decoder uses the extracted error syndrome as input and predicts the recovery chain operation, while the high-level decoder uses the recovery chain predicted by the low-level decoder and the original error syndrome as input and predicts the logical error introduced by the low-level decoder. The decoder decodes successfully if and only if the recovery chain predicted by the low-level decoder can completely eliminate the error syndrome, and the logical error predicted by the high-level decoder is consistent with the combined effect of the recovery chain and the original error. The present invention can efficiently and quickly implement denoising functions for torus codes under complex noise, keep the original information of the quantum bits undisturbed, and outperform traditional MWPM decoders in various situations.

[0012] The technical solutions adopted by the present invention to solve the technical problems are as follows:

[0013] A quantum torus code decoder, comprising a low-level decoder and a high-level decoder;

[0014] The low-level decoder adopts the Self-attention U-Net (SU-Net) model, which consists of a two-dimensional U-Net structure that extracts information within the lattice, a three-dimensional self-attention block that extracts the dependency relationship of different types of error syndromes between lattices, and a residual block;

[0015] The advanced decoder reuses three SU-Net models. First, two SU-Net models are used to extract the original error syndrome and the contextual information of the recovery chain respectively. Then, the intermediate features are added together to fuse the information and input into another SU-Net model for final feature extraction. Finally, a global average pooling layer is used to average all elements in each channel and directly use them for classification.

[0016] The low-level decoder uses the error syndrome as input and predicts the recovery chain operation; the high-level decoder uses the recovery chain predicted by the low-level decoder and the original error syndrome as input and predicts the logical errors introduced by the low-level decoder.

[0017] A quantum torus code decoding method comprises the following steps:

[0018] Step 1: Use the MWPM algorithm to decode the error syndrome generated by the collected torus code and the recovery operation that needs to be performed in a noisy environment, and correct the recovery operation predicted by MWPM by detecting the logical quantum state of the torus code;

[0019] Step 2: Build low-level decoder and high-level decoder;

[0020] The SU-Net used in low-level decoding consists of a 2D U-Net structure that extracts information within the lattice, and a 3D self-attention block and residual block that extract the dependencies between different types of error syndromes between lattices;

[0021] The advanced decoder reuses three SU-Net models. First, two SU-Nets are used to extract the original error syndrome and the contextual information of the recovery chain respectively. Then, the intermediate features are added together to fuse the information and input into another SU-Net for final feature extraction. Finally, a global average pooling layer is used to average all elements in each channel and directly use them for classification.

[0022] Step 3: Use the error syndrome in step 1 as the training dataset feature vector and the recovery chain operation as the dataset label. Train the low-level decoder built in step 2 until it converges. Record the recovery chain operation predicted by the low-level decoder and the introduced logical error.

[0023] Step 4: Use the error syndrome and the recovery chain operation predicted by the low-level decoder in step 3 as the feature vector of the training dataset, and the logical errors occurring on the torus code as the dataset labels. Train the high-level decoder constructed in step 2 until it converges.

[0024] Step 5: For new errors generated on the torus code under the same noise condition, the low-level decoder uses the extracted error syndrome as input and iteratively predicts the recovery chain operation. The high-level decoder uses the recovery chain predicted by the low-level decoder and the original error syndrome as input and predicts the logical errors introduced by the low-level decoder.

[0025] The final decoding is successful if and only if the recovery chain predicted by the low-level decoder can make the error syndrome completely disappear, and the logical error predicted by the high-level decoder is consistent with the joint effect of the recovery chain and the original error.

[0026] Furthermore, the recovery chain predicted by the low-level decoder once cannot completely eliminate the original error syndrome; an iterative decoding strategy is used to first use the currently predicted recovery chain to eliminate part of the error syndrome, and then the remaining error syndrome is input into the low-level decoder again for prediction, and this operation is repeated until the error syndrome disappears or the pre-set maximum number of predictions is reached.

[0027] A computer program enables a computer to execute the quantum torus code decoding method.

[0028] An electronic device comprises: a processor and a memory; the memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory, so that the electronic device performs the above-mentioned quantum torus code decoding method.

[0029] A computer-readable storage medium stores a computer program, which implements the quantum torus code decoding method when executed by a processor.

[0030] A chip includes: a processor for calling and running a computer program from a memory, so that a device equipped with the chip executes the above-mentioned quantum torus code decoding method.

[0031] A computer program product includes a computer storage medium storing a computer program, wherein the computer program includes instructions executable by at least one processor, and when the instructions are executed by the at least one processor, the above-mentioned quantum torus code decoding method is implemented.

[0032] The beneficial effects of the present invention are as follows:

[0033] First, the number of downsampling and upsampling layers in the SU-Net network structure of the present invention can be automatically adjusted based on specific accuracy requirements and computational complexity. SU-NetQD achieves significantly higher decoding accuracy than the MWPM decoder under varying physical error rates and code lengths, while significantly reducing average decoding time, regardless of torus code size. The measured threshold value has been improved from 0.095 to 0.231. Furthermore, the advanced decoder of the present invention significantly improves the performance of the MWPM decoder.

[0034] Second, the present invention can efficiently and quickly implement the denoising function for torus codes under complex noise, keeping the original information of the quantum bits undisturbed, and outperforming the traditional MWPM decoder in various situations.

[0035] Third, the present invention is universal and practical, applicable to a variety of quantum hardware platforms in the NIST era, including superconducting quantum, ion trap, optical quantum, and topological quantum. This invention addresses quantum error correction, a key aspect of quantum information processing, and can be integrated into quantum computing software packages to improve the decoding accuracy of torus codes, thereby enhancing their practicality.

[0036] Fourth, the technical solution of the present invention fills the technical gap in the industry at home and abroad:

[0037] Existing torus code decoding schemes have certain drawbacks in decoding accuracy, decoding time, and scalability. The torus code decoding scheme proposed in this invention has the advantages of high accuracy, portability, and easy scalability, and is suitable for decoding near-term quantum torus codes. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 Schematic diagram of the torus code structure and logical operations thereon provided by an embodiment of the present invention;

[0039] Figure 2 This is a circuit diagram for measuring an error syndrome provided by an embodiment of the present invention;

[0040] Figure 3 This is a schematic diagram of quantum error correction provided by an embodiment of the present invention;

[0041] Figure 4 SU-NetQD overall decoding process diagram provided by an embodiment of the present invention;

[0042] Figure 5 2 is a schematic diagram of an iterative decoding process of a low-level decoder provided by an embodiment of the present invention;

[0043] Figure 6 Schematic diagram of the mapping relationship between quantum bits and classical data on a torus code provided by an embodiment of the present invention;

[0044] Figure 71 is a schematic diagram of the structure of a low-level decoder provided by an embodiment of the present invention;

[0045] Figure 8 1 is a schematic diagram of the structure of an advanced decoder provided by an embodiment of the present invention;

[0046] Figure 9 FIG1 is a schematic diagram showing the decoding performance comparison between SU-NetQD and MWPM under different noise and error rates provided by an embodiment of the present invention;

[0047] Figure 10 is the threshold error rate p provided in the embodiment of the present invention c Schematic diagram of the relationship with deviation η. DETAILED DESCRIPTION

[0048] The present invention will be further described below with reference to the accompanying drawings and examples.

[0049] The purpose of this invention is to provide a high-precision, scalable, and compatible method for designing an efficient quantum torus code decoder. Based on the U-Net structure and a multi-head self-attention mechanism, it adopts the idea of ​​hierarchical design and gradual refinement, effectively solving the problems existing in the prior art.

[0050] The technical solution adopted by the present invention is to decode torus codes using a trained SU-NetQD. SU-NetQD consists of two parts: a low-level decoder and a high-level decoder. The low-level decoder uses the extracted error syndrome as input and predicts the recovery chain operation, while the high-level decoder uses the recovery chain predicted by the low-level decoder and the original error syndrome as input and predicts the logical errors introduced by the low-level decoder. The decoder successfully decodes if and only if the recovery chain predicted by the low-level decoder completely eliminates the error syndrome and the logical error predicted by the high-level decoder matches the combined effect of the recovery chain and the original error.

[0051] Rearranging the data based on the position of the qubits in the lattice facilitates the extraction of potential features. Furthermore, to fully utilize the torus structure of the torus code, the traditional zero-padding scheme is abandoned in favor of a torus-padding method, which effectively improves the ability to correct edge errors.

[0052] The low-level decoder employs an iterative decoding strategy, predicting results in stages and gradually refining the decoding results. Each iteration of the low-level decoder predicts the recovery chain based on the remaining syndromes after the previous decoding round, further eliminating these syndromes. Furthermore, based on the number of error syndromes before and after the iteration, the low-level decoder trained at different error rates allows for targeted decoding.

[0053] The low-level decoder adopts a novel SU-Net structure, which not only effectively utilizes the inductive bias properties of convolution, but also captures the long-range dependencies in surface codes, achieving a good balance between computational complexity and decoding accuracy, and requiring less training data.

[0054] The advanced decoder reuses three SU-Net structures, analogous to multi-label classification problems, recovering from the high-level decoder input syndrome and the low-level decoder prediction chain, predicting logical errors. The advanced decoder can be easily combined with the traditional decoder and significantly improves the decoding accuracy of the traditional decoder.

[0055] SU-NetQD adopts a transfer learning strategy and can perform transfer learning on toroidal codes of different code distances. This not only avoids the overhead caused by repeated training, but also significantly enhances the performance of the model on toroidal codes with small code distances.

[0056] The torus code decoding solution provided by the embodiment of the present invention generally includes the following steps:

[0057] 1. The designed low-level decoder and high-level decoder networks are trained using existing torus code error correction data under specific noise and error rates, so that the low-level decoder can accept the input of error syndrome and output the predicted recovery chain operation. At the same time, the high-level decoder can simultaneously accept the recovery chain predicted by the low-level decoder and the original error syndrome and output the predicted logical error.

[0058] 2. For new errors generated on the toroidal code in a noise-like environment, the low-level decoder is first used to iteratively decode the errors to obtain the initial recovery chain operation. Then, the high-level decoder is used to predict the logical errors that may be introduced during the decoding process. The corresponding logical operations are used to correct them to obtain the final recovery chain required for the toroidal code.

[0059] like Figure 1 This is a schematic diagram of the torus code structure and the logical operations on it, provided by an embodiment of the present invention. A torus code is a square lattice with periodic boundary conditions, with a quantum bit (represented by a circle) on each edge. The solid line represents the original lattice, and the dashed line represents the dual lattice. Operations on the torus code are divided into trivial and nontrivial loops. Trivial loops are typically local and can be reduced to a single vertex through local operations, without affecting the system. Nontrivial loops, on the other hand, surround the entire lattice and cannot be reduced to a single point through continuous deformation, causing logical changes in the system.

[0060] like Figure 3This is a schematic diagram of quantum error correction provided by an embodiment of the present invention. The left figure shows an X-type error occurring on a torus code under bit-flip noise. The middle subgraph represents a correct recovery operation because it forms a trivial ring with the error chain. The right figure represents an incorrect recovery operation because it forms a non-trivial ring with the error chain, which will cause a logical error in the system.

[0061] Specifically include:

[0062] Step 1: Collect the error syndromes generated by the torus code and the recovery operations that need to be performed in a specific noise environment. The MWPM algorithm can be used to decode and collect the error syndromes, and the recovery operations predicted by the MWPM can be corrected by detecting the logical quantum state of the torus code. Figure 2 Shown are error syndrome measurement circuit diagrams; the left diagram shows a Z-type error detection circuit; the right diagram shows an X-type error detection circuit.

[0063] Step 2: Follow the Figure 7 、 Figure 8 The model structure shown builds a low-level decoder and a high-level decoder. The SU-Net used in the low-level decoder consists of a two-dimensional U-Net structure that extracts information within the lattice, and a three-dimensional self-attention block and residual block that extract the dependencies between different types of error syndromes between lattices. The high-level decoder reuses three SU-Net models. It first uses two SU-Nets to extract the original error syndrome and the context information of the recovery chain respectively. Then, the intermediate features are added together to fuse the information of the two and input into another SU-Net for final feature extraction. Finally, a global average pooling layer is used to average all elements in each channel and directly use them for classification.

[0064] In step 3, the error syndrome in step 1 is used as the feature vector of the training dataset and the recovery chain operation is used as the dataset label. The low-level decoder built in step 2 is trained to converge. The recovery chain operation obtained by the last prediction of the low-level decoder and the introduced logical errors are recorded.

[0065] In step 4, the error syndrome and the recovery chain operation predicted by the low-level decoder in step 3 are used as the feature vector of the training dataset, and the logical errors occurring on the torus code are used as the dataset labels. The high-level decoder built in step 2 is trained to achieve convergence.

[0066] Step five, such as Figure 4As shown in the figure, for new errors generated on a torus code under similar noise, the low-level decoder uses the extracted error syndrome as input and iteratively predicts the recovery chain operation. The high-level decoder then uses the recovery chain predicted by the low-level decoder and the original error syndrome as input and predicts the logical error introduced by the low-level decoder. The decoder successfully decodes the code if and only if the recovery chain predicted by the low-level decoder completely eliminates the error syndrome and the logical error predicted by the high-level decoder matches the combined effect of the recovery chain and the original error.

[0067] Due to the complexity of the errors, the recovery chain predicted by the low-level decoder once may not completely eliminate the original error syndrome. In this case, an iterative decoding strategy can be used. First, the currently predicted recovery chain is used to eliminate part of the error syndrome. Then the remaining error syndrome is input into the low-level decoder again for prediction. This operation is repeated until the error syndrome disappears or the maximum number of predictions set in advance is reached. In view of this feature, the present invention recommends training multiple low-level decoders to learn the potential noise distribution under different error rates. For example, after the low-level decoder eliminates part of the error syndrome, the remaining error distribution is similar to the error distribution under low noise. Therefore, a decoder trained under low noise can be used to perform more accurate decoding. If the error syndrome disappears completely, the final recovery chain operation is obtained by XORing the recovery chains predicted at each stage. Figure 5 Schematic diagram of the iterative decoding process of the low-level decoder provided by an embodiment of the present invention; the low-level decoder receives the original error syndrome as input, and in each iteration predicts the recovery chain based on the error syndrome remaining after the previous round of decoding, and further eliminates the error syndrome; the final output of the low-level decoder is the XOR of the recovery chains predicted at each stage.

[0068] Even under the same noise model, toroidal codes of different code lengths exhibit different anti-interference capabilities. Traditional methods typically require retraining at a significant computational cost to decode toroidal codes of new code lengths. SU-NetQD, however, employs a transfer learning strategy. This strategy leverages the similarity in potential error distributions between toroidal codes of different code lengths at the same physical error rate to fine-tune a pre-trained model on surface codes at new distances, effectively reducing training time. Furthermore, using transfer learning to fine-tune a model learned at a larger code length on a smaller code length often yields superior results.

[0069] Example 1:

[0070] The embodiment of the present invention takes the performance of torus codes with different code distances under various types of noise as an example to illustrate the feasibility and effect of the present invention. To this end, the present invention selects torus codes with code distances of 5, 7, and 9, and considers bit-phase flip noise, symmetric and asymmetric depolarization noise models. Bit flip and phase flip noise are not considered separately here, because the MWPM algorithm is considered to be close to optimal in correcting such noise. Under each noise model, errors are randomly introduced into each data qubit with different probabilities, and then the corresponding error syndrome is extracted as a data set. As Figure 6 This is a schematic diagram of the mapping relationship between quantum bits on the torus code provided by an embodiment of the present invention and classical data; the measurement results on the measurement quantum bits constitute the training data set of the low-level decoder (upper right corner), and the recovery operations on the data quantum bits constitute the data set labels of the low-level decoder (lower right corner).

[0071] Specifically, a Pauli error channel can be represented by an array (1-p, p x , p y , p z ), where each value corresponds to the probability of a Pauli error I (no error), X, Y, and Z. Therefore, the physical error rate on each data qubit is p = p x +p y +p z , this embodiment always considers the independent and identically distributed case. The deviation η is defined as the ratio of the probability of Pauli Y error to the total probability of non-Y Pauli error, that is, At the same time, for the sake of simplicity, this embodiment only considers the special case p x =p z Then when the physical error rate is p, the probability of Y error occurring is The probability of X and Z errors occurring is Note that when η = 0.5, the probability of each Pauli error is p / 3, corresponding to a symmetric depolarization channel; when η → ∞, the probability of a Y error is p, corresponding to a bit-phase flip channel. For the error syndrome in the training dataset, when the MWPM decoder decodes successfully and the number of bits affected by the recovery operation is less than the number of bits in error, its label is set to the recovery chain predicted by the MWPM decoder; otherwise, it is set to the set of original errors (which can also be regarded as a recovery chain operation).

[0072] The experimental results of this embodiment are as follows Figure 9As shown, the horizontal axis is the physical error rate and the vertical axis is the decoding accuracy. Different curves represent the decoding performance of each decoder on torus codes of different sizes. It can be seen that the performance of the two-stage decoder SU-NetQD of the present invention is always better than that of the MWPM decoder under different physical error rates and code distances. As the error rate increases, the decoding accuracy of both SQ-UNetQD and MWPM decreases. However, the rate of decrease in the decoding accuracy of the SU-NetQD of the present invention is much smaller than that of the MWPM, which reflects the stability of the SU-NetQD performance. Under the conditions of the same error rate and noise type, the decoding accuracy of the SU-NetQD of the present invention is much higher than that of the MWPM. This is mainly because the neural network can learn the correlation between X and Z errors, and takes into account the error distribution under different physical error rates, and thus can provide more accurate decoding results.

[0073] The curves of different distances under the same decoder intersect at a point. When the physical error rate is less than this threshold, a larger code distance will reduce the logical error rate. However, when p is greater than the threshold, a larger code distance will lead to a higher logical error rate. This trend can be attributed to the increase in the number of errors introduced by the larger system size at high error rates, which masks the benefits of using more quantum bits to bring greater redundancy. Figure 10 A comparative chart comparing the threshold values ​​measured by the SU-NetQD and MWPM of the present invention as a function of the deviation coefficient η is presented. The horizontal axis represents the ratio of the Y-type error rate to the X and Z-type error rates, while the vertical axis represents the error threshold of the torus code measured by the decoder. The intersection of the quantum error correction decoding curves for different code lengths measures the threshold of the torus code's inherent noise immunity. Generally speaking, as the deviation coefficient η increases, the threshold measured by the SU-NetQD increases. When η → ∞, i.e., in a bit-phase-flipped channel, the threshold measured by the decoder of the present invention improves from 0.095 to 0.231 compared to the result obtained by the MWPM.

[0074] Example 2:

[0075] This embodiment of the present invention uses the performance of an advanced decoder post-processing MWPM decoding results as an example to illustrate the scalability and effectiveness of the advanced decoder in this invention. Several advanced decoders were trained using the MWPM as a low-level decoder under different noise conditions. This advanced decoder can determine which logical errors the MWPM introduces during the decoding process, thereby improving decoding accuracy. Specifically, for bit-flip noise, this embodiment trains an advanced decoder based on the MWPM decoding results and the corresponding logical errors at an error rate of p = 0.13. The advanced decoder receives the recovery chain generated by the MWPM and the original error syndrome and predicts the probability of each logical error. During testing, if the probability of a particular logical error exceeds a preset threshold, the error is considered to have occurred and the corresponding logical operation must be performed; otherwise, it is considered to have not occurred. The final recovery chain operation is the exclusive-or operation of the recovery chain operation provided by the MWPM and the corresponding logical operation. For depolarization noise and bit-phase flip noise, training is performed at an error rate of p = 0.17, with other operations similar to those for bit-flip noise.

[0076] The final experimental results are shown in Table 1, where better_MWPM refers to the result obtained after post-processing the decoding result of MWPM using an advanced decoder. It can be seen that after post-processing by the advanced decoder, the decoding accuracy of MWPM is often greatly improved. Even under the bit flip noise model, the advanced decoder can also produce a certain improvement in the decoding accuracy of MWPM. This also further illustrates that the MWPM decoder is only close to the optimal under bit flip noise, rather than the theoretical optimal. These findings highlight the effectiveness of integrating advanced neural network strategies (such as the advanced decoder of the present invention) into traditional quantum error correction schemes, especially in complex noise environments, where traditional methods (such as MWPM) may be insufficient.

[0077] Table 1

[0078]

Claims

1. A quantum torus code decoder, characterized in that: Includes low-level decoder and high-level decoder; The low-level decoder adopts a self-attention U-net model, which consists of a two-dimensional U-net structure that extracts information within the lattice, a three-dimensional self-attention block that extracts the dependency relationship of different types of error syndromes between lattices, and a residual block; The advanced decoder reuses three SU-Net models. First, two SU-Net models are used to extract the original error syndrome and the contextual information of the recovery chain respectively. Then, the intermediate features are added together to fuse the information and input into another SU-Net model for final feature extraction. Finally, a global average pooling layer is used to average all elements in each channel and directly use them for classification. The low-level decoder uses the error syndrome as input and predicts the recovery chain operation; the high-level decoder uses the recovery chain predicted by the low-level decoder and the original error syndrome as input and predicts the logical errors introduced by the low-level decoder.

2. A quantum torus code decoding method using the decoder according to claim 1, characterized in that: The steps include: Step 1: Use the MWPM algorithm to decode the error syndrome generated by the collected torus code and the recovery operation that needs to be performed in a noisy environment, and correct the recovery operation predicted by MWPM by detecting the logical quantum state of the torus code; Step 2: Build low-level decoder and high-level decoder; The SU-Net used in low-level decoding consists of a 2D U-Net structure that extracts information within the lattice, and a 3D self-attention block and residual block that extract the dependencies between different types of error syndromes between lattices; The advanced decoder reuses three SU-Net models. First, two SU-Nets are used to extract the original error syndrome and the contextual information of the recovery chain respectively. Then, the intermediate features are added together to fuse the information and input into another SU-Net for final feature extraction. Finally, a global average pooling layer is used to average all elements in each channel and directly use them for classification. Step 3: Use the error syndrome in step 1 as the training dataset feature vector and the recovery chain operation as the dataset label. Train the low-level decoder built in step 2 until it converges. Record the recovery chain operation predicted by the low-level decoder and the introduced logical error. Step 4: Use the error syndrome and the recovery chain operation predicted by the low-level decoder in step 3 as the feature vector of the training dataset, and the logical errors occurring on the torus code as the dataset labels. Train the high-level decoder constructed in step 2 until it converges. Step 5: For new errors generated on the torus code under the same noise condition, the low-level decoder uses the extracted error syndrome as input and iteratively predicts the recovery chain operation. The high-level decoder uses the recovery chain predicted by the low-level decoder and the original error syndrome as input and predicts the logical errors introduced by the low-level decoder. The final decoding is successful if and only if the recovery chain predicted by the low-level decoder can make the error syndrome completely disappear, and the logical error predicted by the high-level decoder is consistent with the joint effect of the recovery chain and the original error.

3. A quantum torus code decoding method according to claim 2, characterized in that: The recovery chain predicted by the low-level decoder once cannot completely eliminate the original error syndrome; an iterative decoding strategy is used to first use the currently predicted recovery chain to eliminate part of the error syndrome, and then the remaining error syndrome is input into the low-level decoder again for prediction, and this operation is repeated until the error syndrome disappears or the pre-set maximum number of predictions is reached.

4. An electronic device, characterized in that: include: processor and memory; The memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory, so that the electronic device performs the method according to any one of claims 2 to 3.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method according to any one of claims 2 to 3 is implemented.

6. A chip, characterized in that: include: A processor, configured to call and run a computer program from a memory, so that a device equipped with the chip executes the method according to any one of claims 2 to 3.

7. A computer program product, characterized in that The computer program product comprises a computer storage medium storing a computer program, wherein the computer program comprises instructions executable by at least one processor, and when the instructions are executed by the at least one processor, the method according to any one of claims 2 to 3 is implemented.

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