Skip to content
DraconiticResearch
Search Sources API
203,203 studies31 sourcesUpdated 18 min ago
PreprintarXiv licencearXiv

Certified Non-Degenerate Maximum-Likelihood Benchmarking of Quantum LDPC Decoders

  • Michele Banfi
  • Marco Ferrari
  • Antonino Favano
  • Alberto Tarable
  • Luca Barletta
Open at sourcePDFDOICite

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.

Related

  1. Restricted Maximum Likelihood Estimation in Generalized Linear Mixed Models
    Luca Maestrini, Francis K. C. Hui, A. H. Welsh
    Statistical SciencePeer-reviewedLicence not statedFull text21 citedStatisticsOpenAlex
  2. Maximum Likelihood Estimation and Likelihood Ratio Tests for the Power Spherical Distribution
    Sharindi Amasha Samaraweera, Leif Ellingson
    arXivPreprintarXiv licenceFull textStatisticsarXiv
  3. Maximum likelihood estimation in the ergodic Volterra Ornstein-Uhlenbeck process
    Mohamed Ben Alaya, Martin Friesen, Jonas Kremer
    Stochastic Processes and their ApplicationsPeer-reviewedCC BYStatisticsHAL
  4. Asymptotic Theory for Restricted Maximum Likelihood Estimators in Generalized Linear Mixed Models
    Zhanzhongyu Gao, Huadong Mo, Ziyang Lyu
    arXivPreprintCC BY 4.0Full textStatisticsarXiv
  5. Maximum Likelihood Degrees via One-Edge Chordal Completion
    Nilava Metya
    arXivPreprintCC BY-SA 4.0Full textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{banfi2026certified,
  title = {{Certified Non-Degenerate Maximum-Likelihood Benchmarking of Quantum LDPC Decoders}},
  author = {Michele Banfi and Marco Ferrari and Antonino Favano and Alberto Tarable and Luca Barletta},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.28008},
  eprint = {2610.28008},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.28008},
}
RIS
TY  - UNPB
TI  - Certified Non-Degenerate Maximum-Likelihood Benchmarking of Quantum LDPC Decoders
AU  - Michele Banfi
AU  - Marco Ferrari
AU  - Antonino Favano
AU  - Alberto Tarable
AU  - Luca Barletta
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.28008
UR  - https://arxiv.org/abs/2610.28008
AB  - 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.
ER  -