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Scientia Sinica Informationis

量子生成对抗网络抗噪优化的容错量子隐形传态系统

Jiaxin Li, Shangshang Shi, Ruimin Shang, Yanan Li, Zhimin Wang, Yongjian Gu

Published Feb 1, 2024• 0 citations
Publisher

Abstract

Quantum generative adversarial networks (QGANs) have demonstrated superior performance when applied to image processing, financial analysis, and other fields. This paper proposes a quantum topological code decoder based on QGANs, which is applied to optimize fault-tolerant quantum teleportation systems. In this study, we first construct and test the quantum circuit of a QGAN algorithm, establishing a topological code decoder training model. Subsequently, algorithms are designed for the input and output of the topological code eigenvalue dataset, and an efficient decoder is trained. Finally, a topological-code-optimized quantum teleportation system with a QGAN decoder is constructed, exhibiting better fault-tolerance performance compared to the original system. Decoding experiments with a code distance d=3 and d=5 show that the error correction success rate of this model reaches 99.887%. The QGAN decoder demonstrates a fidelity threshold of P=0.1706, significantly higher than the classical decoder threshold, which is approximately P=0.1099. Furthermore, the quantum teleportation system, optimized for noise resistance under a topological code with d=3, shows a noticeable fidelity improvement within the non-polarized noise threshold range of P<0.0607, while under a topological code optimization with d=5, there is a significant fidelity improvement within the non-polarized noise threshold range of P<0.0778. The proposed QGAN decoding model, combined with quantum teleportation methods, provides a novel approach for the application of quantum deep learning, whose principles can be applied to other areas of non-uniform noise processing.

DOI
10.1360/ssi-2024-0015

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Quantum generative adversarial networks (QGANs) have demonstrated superior performance when applied to image processing, financial analysis, and other fields. This paper proposes a quantum topological code decoder based on QGANs, which is applied to optimize fault-tolerant quantum teleportation systems. In this study, we first construct and test the quantum circuit of a QGAN algorithm, establishing a topological code decoder training model. Subsequently, algorithms are designed for the input and output of the topological code eigenvalue dataset, and an efficient decoder is trained. Finally, a topological-code-optimized quantum teleportation system with a QGAN decoder is constructed, exhibiting better fault-tolerance performance compared to the original system. Decoding experiments with a code distance d=3 and d=5 show that the error correction success rate of this model reaches 99.887%. The QGAN decoder demonstrates a fidelity threshold of P=0.1706, significantly higher than the classical decoder threshold, which is approximately P=0.1099. Furthermore, the quantum teleportation system, optimized for noise resistance under a topological code with d=3, shows a noticeable fidelity improvement within the non-polarized noise threshold range of P<0.0607, while under a topological code optimization with d=5, there is a significant fidelity improvement within the non-polarized noise threshold range of P<0.0778. The proposed QGAN decoding model, combined with quantum teleportation methods, provides a novel approach for the application of quantum deep learning, whose principles can be applied to other areas of non-uniform noise processing.
Abstract A generative adversarial network (GAN)‐based decoder is proposed for quantum topological codes and applied it to enhance a quantum teleportation protocol under depolarizing noise. By constructing and training the GAN's generator and discriminator networks using eigenvalue datasets from the code, a decoder is obtained with a significantly improved decoding pseudo‐threshold. Simulation results show that the GAN decoder achieves a pseudo‐threshold of approximately , estimated from the crossing point of logical error rate curves for code distances and , nearly double that of a classical decoder under the same conditions (). Moreover, at the same target logical error rate, the GAN decoder consistently achieves higher logical fidelity compared to the classical decoder. When applied to quantum teleportation, the protocol optimized using the decoder demonstrates enhanced fidelity across noise regimes. Specifically, for code distance , fidelity improves within the depolarizing noise threshold range ; for , the range extends to . Moreover, with appropriate training, our GAN decoder can generalize to other error models. This work positions GANs as powerful tools for decoding in topological quantum error correction, offering a flexible and noise‐resilient framework for fault‐tolerant quantum information processing.
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.
Abstract To address qubits' high environmental sensitivity and reduce the significant error rates in current quantum devices, quantum error correction stands as one of the most dependable approaches. The topological surface code, renowned for its unique qubit lattice structure, is widely considered a pivotal tool for enabling fault-tolerant quantum computation. Through redundancy introduced across multiple qubits, the surface code safeguards quantum information and identifies errors via state changes captured by syndrome qubits. However, simultaneous errors in data and syndrome qubits substantially escalate decoding complexity. Quantum Generative Adversarial Networks (QGANs) have emerged as promising deep learning frameworks, effectively harnessing quantum advantages for practical tasks such as image processing and data optimization. Consequently, a topological code trainer for quantum-classical hybrid GANs is proposed as an auxiliary model to enhance error correction in machine learning-based decoders, demonstrating significantly improved training accuracy compared to the traditional Minimum Weight Perfect Matching (MWPM) algorithm, which achieves an accuracy of 65 % . Numerical experiments reveal that the decoder achieves a fidelity threshold of P=0.1978, substantially surpassing the traditional algorithm's threshold of P=0.1024. To enhance decoding efficiency, a Transformer decoder is integrated, incorporating syndrome error outputs trained via QGANs into its framework. By leveraging its self-attention mechanism, the Transformer effectively captures long-range qubit dependencies at a global scale, enabling high-fidelity error correction over larger dimensions. Numerical validation of the surface code error threshold demonstrates an 8.5% threshold with a correction success rate exceeding 94%, whereas the local MWPM decoder achieves only 55% and fails to support large-scale computation at a 4% threshold.
Quantum error correction (QEC) is a key technique for building scalable quantum computers that can be used to mitigate the effects of errors on physical quantum bits. Since quantum states are more or less affected by noise, errors are inevitable. Traditional QEC codes face huge challenges. Therefore, designing an error suppression algorithm based on neural networks (NN) and quantum topological error correction (QTEC) codes is particularly important for quantum teleportation. In this paper, QTEC codes: semion codes—a greater than 2 dimensional (2D) error correction code based on the double semion model—are used to suppress errors during quantum teleportation, using a NN to build a decoder based on semion codes and to simulate the quantum information error suppression process and the suppression effect. The proposed convolutional neural network (CNN) decoder is suitable for small distance topological semion codes. The aim is to optimize the NN for better decoder performance while deriving the relationship between decoder performance and slope and pseudothreshold during training and calculate the thresholds for different noise areas when the code distances are the same, P t h r e s h o l d = 0.082 for A r e a < 0.007 d B and P t h r e s h o l d = 0.096 for A r e a < 0.01 d B . This paper demonstrates the ability of CNNs to suppress errors in quantum transmission information and the great potential of NNs in the field of quantum computing.
Topological quantum error-correcting codes are an important tool for realizing fault-tolerant quantum computers. Heavy hexagonal coding is a new class of quantum error-correcting coding that assigns physical and auxiliary qubits to the vertices and edges of a low-degree graph. The layout of heavy hexagonal codes is particularly suitable for superconducting qubit architectures to reduce frequency conflicts and crosstalk. Although various topological code decoders have been proposed, constructing the optimal decoder remains challenging. Machine learning is an effective decoding scheme for topological codes, and in this paper, we propose a machine learning heavy hexagonal decoder based on a convolutional neural network (CNN) to obtain the decoding threshold. We test our method on heavy hexagonal codes with code distance of three, five, and seven, and increase it to five, seven, and nine by optimizing the RestNet network architecture. Our results show that the decoder thresholding accuracies are about 0.57% and 0.65%, respectively, which are about 25% higher than the conventional decoding scheme under the depolarizing noise model. The proposed decoding architecture is also applicable to other topological code families.
Solving for quantum error correction remains one of the key challenges of quantum computing. Traditional decoding methods are limited by computing power and data scale, which restrict the decoding efficiency of color codes. There are many decoding methods that have been suggested to solve this problem. Machine learning is considered one of the most suitable solutions for decoding task of color code. We project the color code onto the surface code, use the deep Q network to iteratively train the decoding process of the color code and obtain the relationship between the inversion error rate and the logical error rate of the trained model and the performance of error correction. Our results show that through unsupervised learning, when iterative training is at least 300 times, a self-trained model can improve the error correction accuracy to 96.5%, and the error correction speed is about 13.8% higher than that of the traditional algorithm. We numerically show that our decoding method can achieve a fast prediction speed after training and a better error correction threshold.