Quantum Maxwell Erasure Decoder for qLDPC codes
Quantum Physics
2026-01-16 v1 Information Theory
math.IT
Abstract
We introduce a quantum Maxwell erasure decoder for CSS quantum low-density parity-check (qLDPC) codes that extends peeling with bounded guessing. Guesses are tracked symbolically and can be eliminated by restrictive checks, giving a tunable tradeoff between complexity and performance via a guessing budget: an unconstrained budget recovers Maximum-Likelihood (ML) performance, while a constant budget yields linear-time decoding and approximates ML. We provide theoretical guarantees on asymptotic performance and demonstrate strong performance on bivariate bicycle and quantum Tanner codes.
Keywords
Cite
@article{arxiv.2601.10713,
title = {Quantum Maxwell Erasure Decoder for qLDPC codes},
author = {Bruno Costa Alves Freire and François-Marie Le Régent and Anthony Leverrier},
journal= {arXiv preprint arXiv:2601.10713},
year = {2026}
}
Comments
8 pages, 3 figures, submitted to the IEEE ISIT 2026