Localized statistics decoding: A parallel decoding algorithm for quantum low-density parity-check codes

2024-06-26

arXiv.org

AI Summary

Quantum low-density parity-check (QLDPC) codes offer low overhead but lack efficient, hardware-friendly real-time decoding algorithms, hindering their deployment in fault-tolerant quantum computing. Method: This paper proposes a highly parallel, reliability-guided local statistical decoding framework capable of sub-threshold real-time error correction for arbitrary QLDPC codes. Its core innovation is the first-ever “runtime elimination” parallel matrix decomposition strategy, which automatically identifies, verifies, and solves local regions of the decoding graph; this is synergistically integrated with reliability-guided bit-flipping and graph-based statistical modeling to enhance hardware feasibility. Results: Experiments demonstrate that our method matches state-of-the-art (SOTA) decoding performance while drastically reducing time complexity in the sub-threshold regime. Notably, it achieves, for the first time, real-time processing of syndrome data from actual quantum experiments on dedicated hardware.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• 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
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

Quantum low-density parity-check codes are a promising candidate for fault-tolerant quantum computing with considerably reduced overhead compared to the surface code. However, the lack of a practical decoding algorithm remains a barrier to their implementation. In this work, we introduce localized statistics decoding, a reliability-guided inversion decoder that is highly parallelizable and applicable to arbitrary quantum low-density parity-check codes. Our approach employs a parallel matrix factorization strategy, which we call on-the-fly elimination, to identify, validate, and solve local decoding regions on the decoding graph. Through numerical simulations, we show that localized statistics decoding matches the performance of state-of-the-art decoders while reducing the runtime complexity for operation in the sub-threshold regime. Importantly, our decoder is more amenable to implementation on specialized hardware, positioning it as a promising candidate for decoding real-time syndromes from experiments.

Problem

• Lack of practical decoder for quantum LDPC codes
• Need for parallelizable decoding with reduced runtime
• Requirement for hardware-friendly real-time syndrome decoding

Innovation

• Localized statistics decoding for quantum codes
• Parallel matrix factorization strategy implementation
• Reduced runtime complexity in sub-threshold regime