Quantum Maxwell Erasure Decoder for qLDPC codes

2026-01-15

AI Summary

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.

Technology Category

• Machine Learning: Quantum Machine Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• quantum error correction
• qLDPC codes
• erasure decoding
• maximum-likelihood decoding
• decoding complexity

Innovation

• quantum Maxwell decoder
• qLDPC codes
• bounded guessing
• symbolic tracking
• linear-time decoding