Herold, M., Kastoryano, M., Campbell, E. et al. (1 more author) (2017) Cellular automaton decoders of topological quantum memories in the fault tolerant setting. New Journal of Physics, 19. 063012. ISSN 1367-2630
Abstract
Active error decoding and correction of topological quantum codes—in particular the toric code—remains one of the most viable routes to large scale quantum information processing. In contrast, passive error correction relies on the natural physical dynamics of a system to protect encoded quantum information. However, the search is ongoing for a completely satisfactory passive scheme applicable to locally interacting two-dimensional systems. Here, we investigate dynamical decoders that provide passive error correction by embedding the decoding process into local dynamics. We propose a specific discrete time cellular-automaton decoder in the fault tolerant setting and provide numerical evidence showing that the logical qubit has a survival time extended by several orders of magnitude over that of a bare unencoded qubit. We stress that (asynchronous) dynamical decoding gives rise to a Markovian dissipative process. We hence equate cellular-automaton decoding to a fully dissipative topological quantum memory, which removes errors continuously. In this sense, uncontrolled and unwanted local noise can be corrected for by a controlled local dissipative process. We analyze the required resources, commenting on additional polylogarithmic factors beyond those incurred by an ideal constant resource dynamical decoder.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2017 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, 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 SCIENCE RESEARCH COUNCIL (EPSRC) EP/M024261/1 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 15 Jun 2017 10:31 |
Last Modified: | 15 Jun 2017 10:31 |
Published Version: | https://doi.org/10.1088/1367-2630/aa7099 |
Status: | Published |
Publisher: | IOP Publishing |
Refereed: | Yes |
Identification Number: | 10.1088/1367-2630/aa7099 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:117725 |