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Quantum Maxwell Erasure Decoder for qLDPC codes
Bruno Costa Alves Freire, François-Marie Le Régent, Anthony Leverrier·January 15, 2026
Quantum Physicscs.IT
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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.