Neural Belief-Matching Decoding for Topological Quantum Error Correction Codes

• URL: http://arxiv.org/abs/2603.21730v1
• Date: Mon, 23 Mar 2026 09:15:48 GMT
• Title: Neural Belief-Matching Decoding for Topological Quantum Error Correction Codes
• Abstract summary: Topological codes, such as the toric code, offer hardware-efficient architectures.<n>We propose two key improvements for the decoding of toric code.<n>The first is replacing the BP decoder by a neural BP decoder, giving rise to the neural belief-matching decoder.
• Score: 2.9506547907696006
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum error correction (QEC) is critical for scalable fault-tolerant quantum computing. Topological codes, such as the toric code, offer hardware-efficient architectures but their Tanner graphs contain many girth-4 cycles that degrade the performance of belief-propagation (BP) decoding. For this reason, BP decoding is typically followed by a more complex second stage decoder such as minimum-weight perfect matching. These combined decoders achieve a remarkable performance, albeit at the cost of increased complexity. In this paper we propose two key improvements for the decoding of toric code. The first one is replacing the BP decoder by a neural BP decoder, giving rise to the neural belief-matching decoder which substantially decreases the average decoding complexity. The main drawback of this approach is the high cost associated with the training of the neural BP decoder. To address this issue, we impose a convolutional architecture on the neural BP decoder, enabling weight sharing across the spatially homogeneous structure of the code's factor graph. This design allows a model trained on a modest-size topological code to be directly transferred to much larger instances, preserving decoding quality while dramatically lowering the training burden. Our numerical experiments on toric-code lattices of various sizes demonstrate that this technique does not result in a noticeable loss in performance.

Related papers

• Efficient foundation decoders for fault-tolerant quantum computing [11.676261938547562]
  We propose a unified framework for efficient foundation decoders.<n>A central feature of NTU is its ability to align decoding tasks across code distances.<n>We instantiate NTU-Transformer as a transformer-based neural decoder.
  arXiv  Detail & Related papers  (2026-06-25T14:58:33Z)
• Lottery BP: Unlocking Quantum Error Decoding at Scale [5.762904293390605]
  Existing decoding algorithms (decoders) suffer from one or more of inaccuracy, costliness, and incompatibility.<n>This paper contributes in three aspects, including decoder, decoder architecture, and decoding simulator.
  arXiv  Detail & Related papers  (2026-04-28T15:41:05Z)
• A scalable and real-time neural decoder for topological quantum codes [8.06084037728433]
  Fault-tolerant quantum computing will require error rates far below those achievable with physical qubits.<n>Quantum error correction (QEC) bridges this gap, but depends on decoders being simultaneously fast, accurate, and scalable.<n>Here we introduce AlphaQubit 2, a neural-network decoder that achieves near-optimal logical error rates for both surface and colour codes.
  arXiv  Detail & Related papers  (2025-12-08T17:24:59Z)
• Efficient and Universal Neural-Network Decoder for Stabilizer-Based Quantum Error Correction [44.698141103370546]
  GraphQEC is a code-agnostic decoder leveraging machine-learning on the graph structure of stabilizer codes with linear time complexity.<n>Our approach represents the first universal solution for real-time quantum error correction across arbitrary stabilizer codes.
  arXiv  Detail & Related papers  (2025-02-27T10:56:53Z)
• Learning Linear Block Error Correction Codes [62.25533750469467]
  We propose for the first time a unified encoder-decoder training of binary linear block codes. We also propose a novel Transformer model in which the self-attention masking is performed in a differentiable fashion for the efficient backpropagation of the code gradient.
  arXiv  Detail & Related papers  (2024-05-07T06:47:12Z)
• Progressive-Proximity Bit-Flipping for Decoding Surface Codes [8.971989179518214]
  Topological quantum codes, such as toric and surface codes, are excellent candidates for hardware implementation. Existing decoders often fall short of meeting requirements such as having low computational complexity. We propose a novel bit-flipping (BF) decoder tailored for toric and surface codes.
  arXiv  Detail & Related papers  (2024-02-24T22:38:05Z)
• Graph Neural Networks for Enhanced Decoding of Quantum LDPC Codes [6.175503577352742]
  We propose a differentiable iterative decoder for quantum low-density parity-check (LDPC) codes. The proposed algorithm is composed of classical belief propagation (BP) decoding stages and intermediate graph neural network (GNN) layers.
  arXiv  Detail & Related papers  (2023-10-26T19:56:25Z)
• The END: An Equivariant Neural Decoder for Quantum Error Correction [73.4384623973809]
  We introduce a data efficient neural decoder that exploits the symmetries of the problem. We propose a novel equivariant architecture that achieves state of the art accuracy compared to previous neural decoders.
  arXiv  Detail & Related papers  (2023-04-14T19:46:39Z)
• Deep Quantum Error Correction [73.54643419792453]
  Quantum error correction codes (QECC) are a key component for realizing the potential of quantum computing. In this work, we efficiently train novel emphend-to-end deep quantum error decoders. The proposed method demonstrates the power of neural decoders for QECC by achieving state-of-the-art accuracy.
  arXiv  Detail & Related papers  (2023-01-27T08:16:26Z)
• Neural Belief Propagation Decoding of Quantum LDPC Codes Using Overcomplete Check Matrices [60.02503434201552]
  We propose to decode QLDPC codes based on a check matrix with redundant rows, generated from linear combinations of the rows in the original check matrix. This approach yields a significant improvement in decoding performance with the additional advantage of very low decoding latency.
  arXiv  Detail & Related papers  (2022-12-20T13:41:27Z)
• Graph Neural Networks for Channel Decoding [71.15576353630667]
  We showcase competitive decoding performance for various coding schemes, such as low-density parity-check (LDPC) and BCH codes. The idea is to let a neural network (NN) learn a generalized message passing algorithm over a given graph. We benchmark our proposed decoder against state-of-the-art in conventional channel decoding as well as against recent deep learning-based results.
  arXiv  Detail & Related papers  (2022-07-29T15:29:18Z)
• Improved decoding of circuit noise and fragile boundaries of tailored surface codes [61.411482146110984]
  We introduce decoders that are both fast and accurate, and can be used with a wide class of quantum error correction codes. Our decoders, named belief-matching and belief-find, exploit all noise information and thereby unlock higher accuracy demonstrations of QEC. We find that the decoders led to a much higher threshold and lower qubit overhead in the tailored surface code with respect to the standard, square surface code.
  arXiv  Detail & Related papers  (2022-03-09T18:48:54Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.