Decoding quantum low density parity check codes with diffusion

• URL: http://arxiv.org/abs/2509.22347v1
• Date: Fri, 26 Sep 2025 13:46:52 GMT
• Title: Decoding quantum low density parity check codes with diffusion
• Authors: Zejun Liu, Anqi Gong, Bryan K. Clark,
• Abstract summary: We introduce a diffusion model framework to infer logical errors from syndrome measurements in quantum low-density parity-check codes.<n>We show that masked diffusion decoders are more accurate, often faster on average, and always faster in the worst case than other state-of-the-art decoders.
• Score: 0.5855198111605814
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: An efficient decoder is essential for quantum error correction, and data-driven neural decoders have emerged as promising, flexible solutions. Here, we introduce a diffusion model framework to infer logical errors from syndrome measurements in quantum low-density parity-check codes. Using the bivariate bicycle code with realistic circuit-level noise, we show that masked diffusion decoders are more accurate, often faster on average, and always faster in the worst case than other state-of-the-art decoders, including belief propagation with ordered statistics decoding (BP-OSD) and autoregressive neural decoders. We show that by using fewer diffusion steps during inference one can gain significant speed at minimal cost in accuracy. By examining the factored attention from our trained neural network we find that, despite being trained solely on paired samples of syndrome-logical errors, this diffusion decoder learns the structure of the quantum codes. We also compare both masked and continuous diffusion decoders on code-capacity noise models, finding that masked diffusion decoders scale better than continuous diffusion decoders.

Related papers

• Consistency Flow Model Achieves One-step Denoising Error Correction Codes [28.89866643527586]
  We introduce the Error Correction Consistency Flow Model (ECCFM) for high-fidelity one-step decoding.<n>ECCFM attains lower bit-error rates (BER) than autoregressive and diffusion-based baselines.<n>It delivers inference speeds up from 30x to 100x faster than denoising diffusion decoders.
  arXiv  Detail & Related papers  (2025-12-01T08:07:51Z)
• Neural Decoders for Universal Quantum Algorithms [0.43553942673960666]
  We introduce a modular attention-based neural decoder that learns gate-induced correlations.<n>Our decoders achieve fast inference and logical error rates comparable to most-likely-error decoders.<n>These results establish neural decoders as practical, versatile, and high-performance tools for quantum computing.
  arXiv  Detail & Related papers  (2025-09-14T17:51:46Z)
• 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)
• Breadth-first graph traversal union-find decoder [0.0]
  We develop variants of the union-find decoder that simplify its implementation and provide potential decoding speed advantages. We show how these methods can be adapted to decode non-topological quantum low-density-parity-check codes.
  arXiv  Detail & Related papers  (2024-07-22T18:54:45Z)
• Faster Diffusion: Rethinking the Role of the Encoder for Diffusion Model Inference [95.42299246592756]
  We study the UNet encoder and empirically analyze the encoder features. We find that encoder features change minimally, whereas the decoder features exhibit substantial variations across different time-steps. We validate our approach on other tasks: text-to-video, personalized generation and reference-guided generation.
  arXiv  Detail & Related papers  (2023-12-15T08:46:43Z)
• Neural network decoder for near-term surface-code experiments [0.7100520098029438]
  Neural-network decoders can achieve a lower logical error rate compared to conventional decoders. These decoders require no prior information about the physical error rates, making them highly adaptable.
  arXiv  Detail & Related papers  (2023-07-06T20:31:25Z)
• 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)
• Modular decoding: parallelizable real-time decoding for quantum computers [55.41644538483948]
  Real-time quantum computation will require decoding algorithms capable of extracting logical outcomes from a stream of data generated by noisy quantum hardware. We propose modular decoding, an approach capable of addressing this challenge with minimal additional communication and without sacrificing decoding accuracy. We introduce the edge-vertex decomposition, a concrete instance of modular decoding for lattice-surgery style fault-tolerant blocks.
  arXiv  Detail & Related papers  (2023-03-08T19:26:10Z)
• 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)
• Denoising Diffusion Error Correction Codes [92.10654749898927]
  Recently, neural decoders have demonstrated their advantage over classical decoding techniques. Recent state-of-the-art neural decoders suffer from high complexity and lack the important iterative scheme characteristic of many legacy decoders. We propose to employ denoising diffusion models for the soft decoding of linear codes at arbitrary block lengths.
  arXiv  Detail & Related papers  (2022-09-16T11:00:50Z)
• 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)
• Adversarial Neural Networks for Error Correcting Codes [76.70040964453638]
  We introduce a general framework to boost the performance and applicability of machine learning (ML) models. We propose to combine ML decoders with a competing discriminator network that tries to distinguish between codewords and noisy words. Our framework is game-theoretic, motivated by generative adversarial networks (GANs)
  arXiv  Detail & Related papers  (2021-12-21T19:14:44Z)

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.