Quantum error correction, a technique that relies on the principle of redundancy to encode logical information into additional qubits to better protect the system from noise, is necessary to design a viable quantum computer. For this new topological stabilizer code-XYZ 2 code defined on the cellular lattice, it is implemented on a hexagonal lattice of qubits and it encodes the logical qubits with the help of stabilizer measurements of weight six and weight two. However topological stabilizer codes in cellular lattice quantum systems suffer from the detrimental effects of noise due to interaction with the environment. Several decoding approaches have been proposed to address this problem. Here, we propose the use of a state-attention based reinforcement learning decoder to decode XYZ 2 codes, which enables the decoder to more accurately focus on the information related to the current decoding position, and the error correction accuracy of our reinforcement learning decoder model under the optimisation conditions can reach 83.27% under the depolarizing noise model, and we have measured thresholds of 0.18856 and 0.19043 for XYZ 2 codes at code spacing of 3–7 and 7–11, respectively. our study provides directions and ideas for applications of decoding schemes combining reinforcement learning attention mechanisms to other topological quantum error-correcting codes.
Quantum error correction, a technique that relies on the principle of redundancy to encode logical information into additional qubits to better protect the system from noise, is necessary to design a viable quantum computer. For this new topological stabilizer code-XYZ 2 code defined on the cellular lattice, it is implemented on a hexagonal lattice of qubits and it encodes the logical qubits with the help of stabilizer measurements of weight six and weight two. However topological stabilizer codes in cellular lattice quantum systems suffer from the detrimental effects of noise due to interaction with the environment. Several decoding approaches have been proposed to address this problem. Here, we propose the use of a state-attention based reinforcement learning decoder to decode XYZ 2 codes, which enables the decoder to more accurately focus on the information related to the current decoding position, and the error correction accuracy of our reinforcement learning decoder model under the optimisation conditions can reach 83.27% under the depolarizing noise model, and we have measured thresholds of 0.18856 and 0.19043 for XYZ 2 codes at code spacing of 3–7 and 7–11, respectively. our study provides directions and ideas for applications of decoding schemes combining reinforcement learning attention mechanisms to other topological quantum error-correcting codes.
Quantum error correction technology is a vital method to eliminate noise during the operation of quantum computers. To solve the problem caused by noise, in this paper, reinforcement learning is used to encode defects of Semion codes, and the experience replay technique is used to realize the design of decoder. Semion codes are quantum topological error correction codes with the same symmetry group Z 2 as Kitaev toric codes, we used the topological characteristics of error correction codes to map qubits to multi-dimensional space, and error correction accuracy of the decoder is calculated to be 77.5%. Calculate the threshold of topological quantum Semion code, depending on the code distance, resulting in different thresholds, p threshold = 0.081574 when the code distance is d = 3, 5, 7 and threshold p threshold = 0.09542 when the code distance is d = 5, 7, 9. And we design the Q -network to optimize the cost of quantum circuit gates and compare the size of the cost reduction under different thresholds. Reinforcement learning is an important method for designing Semion code decoders and optimizing numerical values, providing more general error models and error correction codes for future machine engineering decoders.
Quantum information transfer is an information processing technology with high speed and high entanglement with the help of quantum mechanics principles. To solve the problem of quantum information getting easily lost during transmission, we choose topological quantum error correction codes as the best candidate codes to improve the fidelity of quantum information. The stability of topological error correction codes brings great convenience to error correction. The quantum error correction codes represented by surface codes have produced very good effects in the error correction mechanism. In order to solve the problem of strong spatial correlation and optimal decoding of surface codes, we introduced a reinforcement learning decoder that can effectively characterize the spatial correlation of error correction codes. At the same time, we use a double-layer convolutional neural network model in the confrontation network to find a better error correction chain, and the generation network can approach the best correction model, to ensure that the discriminant network corrects more nontrivial errors. To improve the efficiency of error correction, we introduced a double-Q algorithm and ResNet network to increase the error correction success rate and training speed of the surface code. Compared with the previous MWPM 0.005 decoder threshold, the success rate has slightly improved, which can reach up to 0.0068 decoder threshold. By using the residual neural network architecture, we saved one-third of the training time and increased the training accuracy to about 96.6%. Using a better training model, we have successfully increased the decoder threshold from 0.0068 to 0.0085, and the depolarized noise model being used does not require a priori basic noise, so that the error correction efficiency of the entire model has slightly improved. Finally, the fidelity of the quantum information has successfully improved from 0.2423 to 0.7423 by using the error correction protection schemes.
Sequential decoding of the XYZ2 hexagonal stabilizer code
Quantum error correction requires accurate and efficient decoding to optimally suppress errors in the encoded information. For concatenated codes, where one code is embedded within another, optimal decoding can be achieved using a message-passing algorithm that sends conditional error probabilities from the lower-level code to a higher-level decoder. In this work, we study the XYZ2 topological stabilizer code, defined on a honeycomb lattice, and use the fact that it can be viewed as a concatenation of a [[2, 1, 1]] phase-flip parity check code and the surface code with YZZY stabilizers, to decode the syndrome information in two steps. We use this sequential decoding scheme to correct errors on data qubits, as well as measurement errors, under various biased error models using both a maximum-likelihood decoder (MLD) and more efficient matching-based decoders. For depolarizing noise we find that the sequential matching decoder gives a threshold of 18.3%, close to optimal, as a consequence of a favorable, effectively biased, error model on the upper-level YZZY code. For phase-biased noise on data qubits, at a bias η=px+pypz=10, we find that a belief-matching-based decoder reaches thresholds of 24.1%, compared to 28.6% for the MLD. With measurement errors the thresholds are reduced to 3.4% and 4.3%, for depolarizing and biased noise respectively, using the belief-matching decoder. This demonstrates that the XYZ2 code has thresholds that are competitive with other codes tailored to biased noise. The results also showcase two approaches to taking advantage of concatenated codes: 1) tailoring the upper-level code to the effective noise profile of the decoded lower-level code, and 2) making use of an upper-level decoder that can utilize the local information from the lower-level code.
The advent of promising quantum error correction (QEC) codes with efficient resource utilization and high-performance fault-tolerant quantum memories signifies a critical step towards realizing practical quantum computation. While surface codes have been a dominant approach, their limitations have spurred the development of more advanced QEC architectures. These advanced codes often present increased complexity, demanding innovative decoding methodologies. This work investigates the application of reinforcement learning (RL) techniques, including hybrid and multi-agent approaches, to enhance the decoding of various advanced QEC architectures. By leveraging the ability of RL to learn optimal strategies from noisy syndrome measurements, we explore the potential for achieving improved logical error rates and scalability compared to traditional decoding methods. Our approach examines the adaptation of reinforcement learning to exploit the structural properties of these modern QEC models. We also explore the benefits of combining different RL algorithms to address the multifaceted nature of the decoding problem, considering factors such as code degeneracy and real-world noise characteristics. With our proposed method, we are able to demonstrate that an autonomously trained agent can derive decoding schemes for the complex decoding requirement of advanced QEC architectures.
Quantum error correction technology is an important method to eliminate errors during the operation of quantum computers. In order to solve the problem of influence of errors on physical qubits, we propose an approximate error correction scheme that performs dimension mapping operations on surface codes. This error correction scheme utilizes the topological properties of error correction codes to map the surface code dimension to three dimensions. Compared to previous error correction schemes, the present three-dimensional surface code exhibits good scalability due to its higher redundancy and more efficient error correction capabilities. By reducing the number of ancilla qubits required for error correction, this approach achieves savings in measurement space and reduces resource consumption costs. In order to improve the decoding efficiency and solve the problem of the correlation between the surface code stabilizer and the 3D space after dimension mapping, we employ a reinforcement learning (RL) decoder based on deep Q-learning, which enables faster identification of the optimal syndrome and achieves better thresholds through conditional optimization. Compared to the minimum weight perfect matching decoding, the threshold of the RL trained model reaches 0.78%, which is 56% higher and enables large-scale fault-tolerant quantum computation.
Decoding is an essential component of quantum error correction (QEC), translating stabilizer measurement outcomes into corrective actions that suppress logical errors and preserve logical quantum information. Building fault-tolerant architectures requires increasing the code distance, which in turn places growing demands on decoding accuracy, scalability, and practical deployability. While a wide range of decoding algorithms have been proposed and demonstrated, achieving reliable, scalable, and real-time decoding remains a significant challenge. Machine-learning (ML) approaches are particularly well suited to this setting, as quantum error decoding is fundamentally a problem of processing large volumes of classical data with complex spatiotemporal correlations. This chapter surveys ML-based methods for quantum error decoding, with a focus on topological codes and an emphasis on architectural principles, practical performance, and real-time considerations. We first frame decoding as a learning problem and outline key paradigms, including discriminative, generative, and reinforcement-learning formulations. We then introduce the neural network building blocks that underpin most contemporary neural decoders and discuss how these components can be integrated to balance expressivity, scalability, and latency. Building on this architectural perspective, we review recent progress and benchmarks in neural decoding for memory experiments, and discuss real-time decoding, open challenges, and future directions toward scalable fault-tolerant quantum computing.