aiqbench analysis
This research establishes a rigorous benchmarking framework for quantum low-density parity-check (QLDP) decoders, enabling direct comparison of decoding algorithms under realistic circuit-level noise. By certifying non-degenerate maximum-likelihood outcomes and quantifying undecided fractions via branch-and-bound search, the study provides critical metrics for evaluating decoder performance on specific QLDPC codes like bivariate bicycle codes.
Certified Non-Degenerate Maximum-Likelihood Benchmarking of Quantum LDPC Decoders
arXiv:2610.28008v1 Announce Type: cross Abstract: The measured logical error rate of a quantum low-density parity-check (QLDPC) code depends on the decoding algorithm. We develop a framework that certifies non-degenerate maximum-likelihood (ML) decoding outcomes on individual sampled shots under circuit-level noise, providing a common reference for comparing decoders and codes. Upper and lower bounds on the minimum correction cost in the true and competing logical classes establish success, failure, or an undecided outcome. Branch-and-bound search refines these intervals while retaining valid bounds under resource limits. Counting the outcomes bounds the empirical ML logical error rate, with interval width equal to the undecided fraction. Results for two bivariate bicycle codes show that best-first ordered statistics decoding (BF-OSD) tracks the non-degenerate ML benchmark closely while leaving some ML-correctable shots.
Abstract:The measured logical error rate of a quantum low-density parity-check (QLDPC) code depends on the decoding algorithm. We develop a framework that certifies non-degenerate maximum-likelihood (ML) decoding outcomes on individual sampled shots under circuit-level noise, providing a common reference for comparing decoders and codes. Upper and lower bounds on the minimum correction cost in the true and competing logical classes establish success, failure, or an undecided outcome. Branch-and-bound search refines these intervals while retaining valid bounds under resource limits. Counting the outcomes bounds the empirical ML logical error rate, with interval width equal to the undecided fraction. Results for two bivariate bicycle codes show that best-first ordered statistics decoding (BF-OSD) tracks the non-degenerate ML benchmark closely while leaving some ML-correctable shots.
Information Theory (cs.IT); Quantum Physics (quant-ph)
arXiv:2610.28008 [cs.IT]
(or arXiv:2610.28008v1 [cs.IT] for this version)
https://doi.org/10.48550/arXiv.2610.28008 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 218 words