Quantum Maxwell Erasure Decoder for qLDPC codes
This work addresses the challenge of efficient and reliable decoding of CSS-type quantum low-density parity-check (qLDPC) codes over erasure channels by proposing a Quantum Maxwell Erasure Decoder. The method integrates a bounded-guess peeling algorithm, symbolic guess tracking, and constraint-aware check elimination to effectively eliminate erroneous guesses. By introducing an adjustable guess budget mechanism, it achieves a flexible trade-off between decoding complexity and performance: under an unbounded budget, it attains maximum-likelihood performance, while with a constant budget, it enables linear-time decoding that closely approaches optimal performance. Theoretical analysis establishes asymptotic performance guarantees, and experiments on bivariate bicycle codes and quantum Tanner codes demonstrate superior decoding efficacy.