Cellular automaton decoders of topological quantum memories in the fault tolerant setting

Herold M, Kastoryano MJ, Campbell ET, Eisert J (2017)

Publication Type: Journal article

Publication year: 2017

Journal

New Journal of Physics Institute of Physics: Open Access Journals / Institute of Physics (IoP) and Deutsche Physikalische Gesellschaft

Book Volume: 19

Article Number: 063012

Journal Issue: 6

DOI: 10.1088/1367-2630/aa7099

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.

Involved external institutions

Freie Universität Berlin DE Germany (DE) University of Copenhagen DK Denmark (DK) University of Sheffield GB United Kingdom (GB)

How to cite

APA:

Herold, M., Kastoryano, M.J., Campbell, E.T., & Eisert, J. (2017). Cellular automaton decoders of topological quantum memories in the fault tolerant setting. New Journal of Physics, 19(6). https://doi.org/10.1088/1367-2630/aa7099

MLA:

Herold, Michael, et al. "Cellular automaton decoders of topological quantum memories in the fault tolerant setting." New Journal of Physics 19.6 (2017).

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