Restart Belief: A General Quantum LDPC Decoder

2025-11-17

AI Summary

Quantum low-density parity-check (QLDPC) codes suffer from degeneracy-induced stagnation and slow convergence under standard belief propagation (BP) decoding, preventing attainment of the theoretical distance bound. To address this, we propose Restarted Belief Propagation (RB), a novel BP-based decoder that integrates branch-and-bound optimization principles into the BP framework: it dynamically reinitializes node beliefs during iterations to actively escape degeneracy-driven local minima. RB preserves BP’s hardware efficiency—requiring no auxiliary codes or structural modifications. Experiments across diverse QLDPC code families demonstrate that RB achieves both the fastest convergence and highest error-correction accuracy among existing BP variants, yielding significantly lower logical error rates. Notably, RB is the first BP-style decoder to stably approach the code distance limit under generic settings. This work establishes RB as the state-of-the-art general-purpose BP decoder for practical quantum error correction.

Technology Category

• Machine Learning: Quantum Machine Learning
• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Hardware-friendly quantum low-density parity-check (QLDPC) decoders are commonly built upon belief propagation (BP) processing. Yet, quantum degeneracy often prevents BP from achieving reliable convergence. To overcome this fundamental limitation, we propose the restart belief (RB) decoder, an iterative BP-based algorithm inspired by branch-and-bound optimization principles. From our analysis we find that the RB decoder represents both the fastest and most accurate decoding algorithm applicable to QLDPC codes to date, conceived with the explicit goal of approaching error correction up to the code distance.

Problem

• Overcoming quantum degeneracy in belief propagation decoders
• Developing hardware-friendly QLDPC decoding with reliable convergence
• Approaching quantum error correction up to the code distance

Innovation

• Restart Belief decoder overcomes quantum degeneracy in BP
• It applies branch-and-bound principles to iterative decoding
• This hardware-friendly approach achieves fastest QLDPC decoding accuracy