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  • Open Access

Hypergraph-based approximate maximum likelihood decoding for quantum codes under circuit-level noise

Ke Chen1, Mingzheng Zhu1, Haishan Song1, Wei Xie1,*, and Xiang-Yang Li1,2

  • *Contact author: xxieww@ustc.edu.cn
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Phys. Rev. Research 8, 023191 – Published 20 May, 2026

DOI: https://doi.org/10.1103/ydb8-vd3x

Abstract

Maximum likelihood decoding (MLD) achieves optimal accuracy but is computationally infeasible for large-distance codes. Tensor-network-based MLD (TN-MLD) improves efficiency but has so far only been shown to work for small-distance surface codes. We introduce a hypergraph-based approximate MLD (HAMLD) that enables more efficient decoding of more general codes under circuit-level noise. Unlike TN-MLD, our HAMLD employs syndrome-guided hyperedge selection and probability-based truncation to reduce redundant computation. We benchmarked our approach on surface codes, color codes, and bivariate-bicycle (BB) codes under a circuit-level noise model. Numerical results demonstrate that HAMLD can decode BB codes with hundreds of qubits, which MLD and TN-MLD cannot handle. For a surface code with distance and repetition rounds both equal to 3, HAMLD achieves optimal decoding accuracy while being about 323× faster than MLD and about 551× faster than TN-MLD. HAMLD also achieves higher accuracy than common decoders—minimum-weight perfect matching, Chromobius, and BP+OSD—in the two smallest parameter settings we considered, reducing logical error rates by an average of 27.8% for surface codes, 58.5% for color codes, and 74.4% for BB codes through degeneracy-aware and precise hypergraph selection.

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Phys. Rev. Research 8, 023191– Published 20 May, 2026
  • Received 6 August 2025
  • Accepted 12 April 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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