Quantifying the effects of local many-qubit errors and nonlocal two-qubit errors on the surface code

Austin G. Fowler and John M. Martinis
Phys. Rev. A 89, 032316 – Published 12 March 2014

Abstract

Topological quantum error correction codes are known to be able to tolerate arbitrary local errors given sufficient qubits. This includes correlated errors involving many local qubits. In this work, we quantify this level of tolerance, numerically studying the effects of many-qubit errors on the performance of the surface code. We find that if increasingly large-area errors are at least moderately exponentially suppressed, arbitrarily reliable quantum computation can still be achieved with practical overhead. We furthermore quantify the effect of nonlocal two-qubit correlated errors, which would be expected in arrays of qubits coupled by a polynomially decaying interaction, and when using many-qubit coupling devices. We surprisingly find that the surface code is very robust to this class of errors, despite a provable lack of a threshold error rate when such errors are present.

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  • Received 27 January 2014

DOI:https://doi.org/10.1103/PhysRevA.89.032316

©2014 American Physical Society

Authors & Affiliations

Austin G. Fowler1,2 and John M. Martinis1

  • 1Department of Physics, University of California, Santa Barbara, California 93106, USA
  • 2Centre for Quantum Computation and Communication Technology, School of Physics, The University of Melbourne, Victoria 3010, Australia

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Issue

Vol. 89, Iss. 3 — March 2014

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