Quintavalle, A.O., Vasmer, M., Roffe, J. et al. (1 more author) (2021) Single-shot error correction of three-dimensional homological product codes. PRX Quantum, 2 (2). 020340.
Abstract
Single-shot error correction corrects data noise using only a single round of noisy measurements on the data qubits, removing the need for intensive measurement repetition. We introduce a general concept of confinement for quantum codes, which roughly stipulates qubit errors cannot grow without triggering more measurement syndromes. We prove confinement is sufficient for single-shot decoding of adversarial errors and linear confinement is sufficient for single-shot decoding of local stochastic errors. Further to this, we prove that all three-dimensional homological product codes exhibit confinement in their X components and are therefore single shot for adversarial phase-flip noise. For local stochastic phase-flip noise, we numerically explore these codes and again find evidence of single-shot protection. Our Monte Carlo simulations indicate sustainable thresholds of 3.08(4)% and 2.90(2)% for three-dimensional (3D) surface and toric codes, respectively, the highest observed single-shot thresholds to date. To demonstrate single-shot error correction beyond the class of topological codes, we also run simulations on a randomly constructed family of 3D homological product codes.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2021. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license (https://creativecommons.org/licenses/by/4.0/). Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > Department of Physics and Astronomy (Sheffield) |
Funding Information: | Funder Grant number Engineering and Physical Sciences Research Council EP/M024261/1; EP/R043825/1 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 09 Jun 2022 10:15 |
Last Modified: | 09 Jun 2022 10:15 |
Status: | Published |
Publisher: | American Physical Society (APS) |
Refereed: | Yes |
Identification Number: | 10.1103/prxquantum.2.020340 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:187815 |