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Coherence in logical quantum channels

Iverson, Joseph K. and Preskill, John (2020) Coherence in logical quantum channels. New Journal of Physics, 22 (7). Art. No. 073066. ISSN 1367-2630. doi:10.1088/1367-2630/ab8e5c.

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We study the effectiveness of quantum error correction against coherent noise. Coherent errors (for example, unitary noise) can interfere constructively, so that in some cases the average infidelity of a quantum circuit subjected to coherent errors may increase quadratically with the circuit size; in contrast, when errors are incoherent (for example, depolarizing noise), the average infidelity increases at worst linearly with circuit size. We consider the performance of quantum stabilizer codes against a noise model in which a unitary rotation is applied to each qubit, where the axes and angles of rotation are nearly the same for all qubits. In particular, we show that for the toric code subject to such independent coherent noise, and for minimal-weight decoding, the logical channel after error correction becomes increasingly incoherent as the length of the code increases, provided the noise strength decays inversely with the code distance. A similar conclusion holds for weakly correlated coherent noise. Our methods can also be used for analyzing the performance of other codes and fault-tolerant protocols against coherent noise. However, our result does not show that the coherence of the logical channel is suppressed in the more physically relevant case where the noise strength is held constant as the code block grows, and we recount the difficulties that prevented us from extending the result to that case. Nevertheless our work supports the idea that fault-tolerant quantum computing schemes will work effectively against coherent noise, providing encouraging news for quantum hardware builders who worry about the damaging effects of control errors and coherent interactions with the environment.

Item Type:Article
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URLURL TypeDescription Paper
Iverson, Joseph K.0000-0003-4665-8839
Preskill, John0000-0002-2421-4762
Additional Information:© 2020 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft. Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Received 22 February 2020; Accepted 29 April 2020; Accepted Manuscript online 29 April 2020; Published 31 July 2020. We would like to thank Michael Beverland, Robin Blume-Kohout, Benjamin Brown, Aaron Chew, Andrew Darmawan, Andrew Doherty, Steven Flammia, Daniel Gottesman, Tomas Jochym-O'Connor, Aleksander Kubica, Richard Kueng, David Poulin, and Leonid Pryadko for valuable discussions. We gratefully acknowledge support from ARO-LPS (W911NF-18-1-0103) and NSF (PHY-1733907). The Institute for Quantum Information and Matter is an NSF Physics Frontiers Center.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Army Research Office (ARO)W911NF-18-1-0103
Subject Keywords:quantum error correcting codes, coherent noise, toric code, surface code, quantum computing
Issue or Number:7
Record Number:CaltechAUTHORS:20200827-141821017
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Official Citation:Joseph K Iverson and John Preskill 2020 New J. Phys. 22 073066
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:105131
Deposited By: Tony Diaz
Deposited On:27 Aug 2020 21:58
Last Modified:12 Jul 2022 19:47

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