CoChat
Sign Up
Cited by 105Quantum Computing Algorithms and ArchitectureQuantum Information and CryptographyError Correcting Code Techniques

The DOI matches its Crossref record; 26 of the 26 references it cites were found in a registry or an index.

Optimal and efficient decoding of concatenated quantum block codes

Open access
Poulin, David·2006·Physical Review A
DOI 10.1103/physreva.74.052333
Open this paper in CoChat — free accountOpen PDF

Abstract

We consider the problem of optimally decoding a quantum error correction code---that is, to find the optimal recovery procedure given the outcomes of partial ``check'' measurements on the system. In general, this problem is NP hard. However, we demonstrate that for concatenated block codes, the optimal decoding can be efficiently computed using a message-passing algorithm. We compare the performance of the message-passing algorithm to that of the widespread blockwise hard decoding technique. Our Monte Carlo results using the five-qubit and Steane's code on a depolarizing channel demonstrate significant advantages of the message-passing algorithms in two respects: (i) Optimal decoding increases by as much as 94$%$ the error threshold below which the error correction procedure can be used to reliably send information over a noisy channel; and (ii) for noise levels below these thresholds, the probability of error after optimal decoding is suppressed at a significantly higher rate, leading to a substantial reduction of the error correction overhead.

Overview

Integrity signals

Registry

Crossref · 10.1103/physreva.74.052333

Cites

26 of 26 references verified0 citation errors · 0 not checkable

Statistics

Recomputing p-values needs the paper’s full text.

Verification

Claims the paper makes

We couldn’t retrieve this paper’s full text, so its claims and self-check weren’t run. The registry and citation checks still apply.

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

Citations

Cites

Show all 26 references

Research works printed but not linked: 3

  1. P. W. Shor, 1996, Proceedings of the 37th Symposium on the Foundations of Computer Science
  2. A. Y. Kitaev, 1997, Proceedings of the Third International Conference on Quantum Communication and Measurement
  3. D. Aharonov, 1997, Proc. 29th Ann. ACM Symp. on Theory of Computing

Cited by

Sorted by citations

Items 101–104 of 104

Related

See all

Metadata

Authors
Poulin, D.
Affiliations
California Institute of Technology (US)
Corresponding author
Poulin, David
Venue
Physical Review A
Publisher
American Physical Society (APS)
Published
2006-11-22
Volume
74
Issue
5
ISSN
  • 0556-2791 (ISSN-L)
  • 1050-2947
  • 1094-1622
DOI
10.1103/physreva.74.052333
OpenAlex
W2109785828
Cited by
105
References
26
Citations by year
2026: 6 · 2025: 12 · 2024: 7 · 2023: 5 · 2022: 12 · 2021: 8 · 2020: 1 · 2019: 4 · 2018: 9 · 2017: 9 · 2016: 1 · 2015: 4 · 2014: 8 · 2013: 2
FWCI
3.81
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review A (publishedVersion)
  • arXiv (Cornell University) (publishedVersion)
  • CaltechAUTHORS (California Institute of Technology) (submittedVersion)
  • CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
  • arXiv (Cornell University)
Funders
  • National Science Foundation
  • Gordon and Betty Moore Foundation
  • California Institute of Technology
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
  • Physical Sciences › Computer Science › Computer Networks and Communications › Error Correcting Code Techniques
Keywords
quantum error correction, optimal decoding, message passing algorithm, five-qubit code, Steane code, depolarizing channel, error threshold, decoding overhead, NP-hardness

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review