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.
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.
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 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.
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.
We introduce a neural message-passing framework for decoding general concatenated stabilizer codes. Soft beliefs propagate bidirectionally across concatenation levels, and lightweight neural networks learn only to aggregate incoming messages. For the concatenated [[15,7,3]] quantum Hamming code, the resulting decoder achieves substantially higher thresholds than the state-of-the-art bidirectional hard-decision decoder under both bit-flip and depolarizing noise. In particular, the depolarizing pseudo-threshold nearly doubles, from 6.5% to 12.3%. For many-hypercube codes, a decoder fine-tuned on circuit-level errors in Knill's teleportation-based error correction can achieve lower logical-CNOT failure rates than their dedicated decoder, using a fixed number of message-passing iterations instead of extensive combinatorial search. Our framework provides a generic decoding tool for exploring the design space of concatenated codes, including non-CSS constructions, toward low-overhead fault tolerance.
Topological quantum error-correcting codes are a promising candidate for building fault-tolerant quantum computers. Decoding topological codes optimally, however, is known to be a computationally hard problem. Various decoders have been proposed that achieve approximately optimal error thresholds. Due to practical constraints, it is not known if there exists an obvious choice for a decoder. In this paper, we introduce a framework which can combine arbitrary decoders for any given code to significantly reduce the logical error rates. We rely on the crucial observation that two different decoding techniques, while possibly having similar logical error rates, can perform differently on the same error syndrome. We classify each error syndrome to the decoder which is more likely to decode it correctly using machine learning techniques. We apply our framework to an ensemble of minimum-weight perfect matching (MWPM) and hard-decision re-normalization-group decoders for the surface code in the depolarizing noise model. Our simulations show an improvement of 38.4%, 14.6%, and 7.1% over the pseudothreshold of MWPM in the instance of distance 5, 7, and 9 codes, respectively. Lastly, we discuss the advantages and limitations of our framework and applicability to other error-correcting codes. Our framework can provide a significant boost to error correction by combining the strengths of various decoders. In particular, it may allow for combining very fast decoders with moderate error-correcting capability to create a very fast ensemble decoder with high error-correcting capability.