Restart Belief: A General Quantum LDPC Decoder

TL;DR

The paper introduces the restart belief (RB) decoder, a novel quantum LDPC decoding algorithm inspired by branch-and-bound principles, which improves reliability and speed over existing belief propagation methods.

Contribution

It presents a new RB decoder that enhances quantum LDPC decoding by addressing quantum degeneracy issues, achieving faster and more accurate error correction.

Findings

RB decoder is faster than existing algorithms.

RB decoder achieves higher accuracy in quantum error correction.

Approaches error correction up to the code distance.

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.