Neural Network Decoder for topological PlanarSurface Codes with Depolarizing noise model

Qi-Di GAN, Ao-Qing Li, Fan Li, Tao Cheng, Hongyang Ma

Published Jul 4, 2024• 0 citations

Abstract

Abstract Decoding is the most important part of the error correction process. During thedecoding process, the main idea of this paper is to transfer the error measuredinside ancilla qubit to the boundary, and decompose the error into the productof stabilizer, logical error and pure error, stabilizer error do not affect logicalerror. Therefore, the result of error syndrome is only affected by pure error,while the error of stabilizer can be ignored. Decoding by neural network can takeadvantage of its high threshold and adaptability to training different codes. Thefocus of this work is to propose a suitable algorithm for neural network decodingof planar codes, so as to reduce the size of the neural network as much as possiblewithout compromising the decoding performance. Comparative experiments wereconducted using the minimum weight perfect matching(MWPM) decoder andthe neural network decoder to compare the decoding performance of planar codeswith code distances of 5, 7, and 9, respectively, demonstrating high threshold ofneural network decoder and its adaptability to training different codes. Takingthe planar code with code distance of 5 as an example, the pseudo-thresholdsobtained using the MWPM decoder and the neural network decoder are 0.005and 0.0068 respectively,increased by 36%. It shows that for planar code, theneural network decoder significantly outperforms the MWPM decoder.

DOI: 10.21203/rs.3.rs-4579308/v1

Related papers

Developing a Practical Neural-Network Surface Code Decoder under Circuit-Level Noise

Aarush Pancholi

Abstract. Suppressing qubit errors is one of the main challenges in building fault-tolerant quantum computers, requiring quantum error correction to protect fragile quantum information during computation cycles. The surface code is a leading approach because of its high error tolerance and compatibility with realistic hardware, but it requires a decoder that can accurately and quickly use the syndrome measurements to discern whether a logical error has occurred. This study investigates whether a feedforward neural-network can serve as a practical decoder for the surface code under circuit-level noise. Using the Stim software package, this study generates surface code circuits at multiple code distances and physical error rates and compiles them into detector samplers, then trains a PyTorch neural-network to predict whether a logical observable flip occurred from the syndrome data. The neural-network decoder is compared against Minimum-Weight Perfect Matching (MWPM), focusing on metrics including logical error rate and inference speed. The results show that the neural-network decoder performs competitively with MWPM for code distances 3 and 5 and provides inference time advantages at higher physical error rates as its inference time remains relatively constant over increasing physical error rates. However, MWPM outperforms the neural-network at distance 7, suggesting that scalability remains a major limitation for neural-network decoders. These results show that neural-networks are a promising approach for tackling quantum error correction, although future work is still needed to improve these models for real systems at larger code distances.

Aug 2, 20260 citations

Decoding the surface code using graph neural networks

Moritz Lange

Quantum error correction is essential to achieve fault-tolerant quantum computation in the presence of noisy qubits. Among the most promising approaches to quantum error correction is the surface code, thanks to a scalable two-dimensional architecture, only nearest-neighbor interactions, and a high error threshold. Decoding the surface code, i.e. finding the most likely error chain given a syndrome measurement outcome is a computationally complex task. Traditional decoders rely on classical algorithms, which, especially for larger systems, can be slow and may not always converge to the optimal solution. This thesis presents a novel approach to decoding the surface code using graph neural networks. By mapping the syndrome measurements to a graph and performing graph classification, we find that the graph neural networks can predict the most likely error configuration with high accuracy. Our results show that the GNN-based decoder outperforms the classic minimum weight perfect matching (MWPM) decoder in terms of accuracy. With a phenomenological noise model with depolarizing noise and perfect syndrome measurements, our networks beat MWPM up to code-size 15 across all relevant error rates. Furthermore, the GNN is capable of surpassing MWPM under circuit-level noise up to code size 7. We also show that training the network on repetition code data from a recent experiment [Google Quantum AI, Nature 614, 676 (2023)] produces per-step error rates comparable to those achieved with a matching decoder specifically adapted to the error rates of the physical qubits. This indicates that graph neural network decoders are capable of learning the underlying error distribution on the qubits. Our findings advance the field of quantum error correction and provide a promising new direction for the development of efficient decoding algorithms.

Oct 17, 20230 citations

Neural network decoder for near-term surface-code experiments

Boris Varbanov, Marc Serra-Peralta, David Byfield +1 more

Neural network decoders can achieve a lower logical error rate compared to conventional decoders, like minimum-weight perfect matching, when decoding the surface code. Furthermore, these decoders require no prior information about the physical error rates, making them highly adaptable. In this study, we investigate the performance of such a decoder using both simulated and experimental data obtained from a transmon-qubit processor, focusing on small-distance surface codes. We first show that the neural network typically outperforms the matching decoder due to better handling of errors leading to multiple correlated syndrome defects, such as Y errors. When applied to the experimental data of Google Quantum AI [R. Acharya , ], the neural network decoder achieves logical error rates approximately 25 % lower than minimum-weight perfect matching, approaching the performance of a maximum-likelihood decoder. To demonstrate the flexibility of this decoder, we incorporate the soft information available in the analog readout of transmon qubits and evaluate the performance of this decoder in simulation using a symmetric Gaussian-noise model. Considering the soft information leads to an approximately 10 % lower logical error rate, depending on the probability of a measurement error. The good logical performance, flexibility, and computational efficiency make neural network decoders well-suited for near-term demonstrations of quantum memories.

arXiv:2307.03280Physical Review ResearchJan 8, 202520 citations

Neural Decoders Reduce Logical Error Rates in Surface Code Quantum Systems

Lukas Schneider, Haruki Tanaka

Fault-tolerant quantum computation critically depends on the ability to detect and correct physical qubit errors faster than they accumulate. The surface code (SC) has emerged as the most experimentally promising quantum error correction (QEC) framework due to its high threshold and local stabilizer structure, yet its practical performance is bottlenecked by decoder efficiency. Traditional decoding approaches such as minimum-weight perfect matching (MWPM) achieve near-optimal accuracy under independent noise but struggle with correlated errors, circuit-level noise, and real-time latency constraints. This paper investigates how neural network (NN)-based decoders reduce logical error rates in SC quantum systems by learning complex syndrome-to-correction mappings from data. We propose a hybrid convolutional-recurrent neural architecture that processes stabilizer measurement syndromes across both spatial and temporal dimensions, enabling the decoder to capture correlated error patterns inherent in realistic hardware. Systematic simulations under depolarizing, biased, and circuit-level noise models demonstrate that the proposed neural decoder achieves a logical error rate reduction of up to 41.3% compared to MWPM at a physical error rate of p = 0.008, while maintaining sub-millisecond decoding latency compatible with superconducting qubit cycle times. These results establish that data-driven neural decoders represent a scalable and hardware-compatible pathway toward achieving the logical error rates required for practical fault-tolerant quantum computing.

Frontiers in Applied Physics and MathematicsMar 25, 20260 citations

Recurrent neural network decoding of rotated surface codes based on distributed strategy

Fan 帆 Li 李, Ao-Qing Li, Qi-Di GAN +1 more

Quantum error correction is a crucial technology for realizing quantum computers. These computers achieve fault-tolerant quantum computing by detecting and correcting errors using decoding algorithms. Quantum error correction using neural network-based machine learning methods is a promising approach that is adapted to physical systems without the need to build noise models. In this paper, we use a distributed decoding strategy, which effectively alleviates the problem of exponential growth of the training set required for neural networks as the code distance of quantum error-correcting codes increases. Our decoding algorithm is based on renormalization group decoding and recurrent neural network decoder. The recurrent neural network is trained through the ResNet architecture to improve its decoding accuracy. Then we test the decoding performance of our distributed strategy decoder, recurrent neural network decoder, and the classic minimum weight perfect matching (MWPM) decoder for rotated surface codes with different code distances under the circuit noise model, the thresholds of these three decoders are about 0.0052, 0.0051, and 0.0049, respectively. Our results demonstrate that the distributed strategy decoder outperforms the other two decoders, achieving approximately a 5% improvement in decoding efficiency compared to the MWPM decoder and approximately a 2% improvement compared to the recurrent neural network decoder.

Chinese Physics BFeb 22, 202410 citations

Decoding surface code with a distributed neural network–based decoder

Savvas Varsamopoulos, Koen Bertels, Carmen G. Almudéver

Abstract There has been a rise in decoding quantum error correction codes with neural network–based decoders, due to the good decoding performance achieved and adaptability to any noise model. However, the main challenge is scalability to larger code distances due to an exponential increase of the error syndrome space. Note that successfully decoding the surface code under realistic noise assumptions will limit the size of the code to less than 100 qubits with current neural network–based decoders. Such a problem can be tackled by a distributed way of decoding, similar to the renormalization group (RG) decoders. In this paper, we introduce a decoding algorithm that combines the concept of RG decoding and neural network–based decoders. We tested the decoding performance under depolarizing noise with noiseless error syndrome measurements for the rotated surface code and compared against the blossom algorithm and a neural network–based decoder. We show that a similar level of decoding performance can be achieved between all tested decoders while providing a solution to the scalability issues of neural network–based decoders.

arXiv:1901.10847Quantum Machine IntelligenceMar 13, 202041 citations