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Optimal and efficient decoding of concatenated quantum block codes
Open accessAbstract
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.
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“These outer codes have distances two and four respectively which, by utilizing the soft information provided by the inner surface codes30, double and quadruple the inner code distance.”
From Yoked surface codes (2025) · cites this paper as [30]
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“Passing this information to the outer code helps it to identify likely culprit errors30.”
From Yoked surface codes (2025) · cites this paper as [30]
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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
- 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
- green
- arxiv.org
- 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
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