Campbell, E. (2019) A theory of single-shot error correction for adversarial noise. Quantum Science and Technology, 4 (2). 025006. ISSN 2058-9565
Abstract
Single-shot error correction is a technique for correcting physical errors using only a single round of noisy check measurements, such that any residual noise affects a small number of qubits. We propose a general theory of single-shot error correction and establish a sufficient condition called good soundness of the code's measurement checks. Good code soundness in topological (or low-density parity check, LDPC) codes is shown to entail a macroscopic energy barrier for the associated Hamiltonian. Consequently, 2D topological codes with local checks can not have good soundness. In tension with this, we also show that for any code a specific choice of measurement checks does exist that provides good soundness. In other words, every code can perform single-shot error correction but the required checks may be nonlocal and act on many qubits. If we desire codes with both good soundness and simple measurement checks (the LDPC property) then careful constructions are needed. Finally, we use a double application of the homological product to construct quantum LDPC codes with single-shot error correcting capabilities. Our double homological product codes exploit redundancy in measurements checks through a process we call metachecking.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2019 IOP Publishing Ltd. This is an author produced version of a paper subsequently published in Quantum Science and Technology. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Quantum computing; quantum error correction; single-shot error correction; homological product |
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 SCIENCE RESEARCH COUNCIL (EPSRC) EP/M024261/1 ENGINEERING AND PHYSICAL SCIENCE RESEARCH COUNCIL (EPSRC) EP/R043825/1 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 19 Feb 2019 12:27 |
Last Modified: | 08 Jan 2020 01:39 |
Published Version: | https://doi.org/10.1088/2058-9565/aafc8f |
Status: | Published |
Publisher: | IOP Publishing |
Refereed: | Yes |
Identification Number: | 10.1088/2058-9565/aafc8f |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:142719 |