Efficient Markov chain Monte Carlo algorithm for the surface code

Adrian Hutter, James R. Wootton, and Daniel Loss
Phys. Rev. A 89, 022326 – Published 18 February 2014

Abstract

Minimum-weight perfect matching (MWPM) has been the primary classical algorithm for error correction in the surface code, since it is of low runtime complexity and achieves relatively low logical error rates [Phys. Rev. Lett. 108, 180501 (2012)]. A Markov chain Monte Carlo (MCMC) algorithm [Phys. Rev. Lett. 109, 160503 (2012)] is able to achieve lower logical error rates and higher thresholds than MWPM, but requires a classical runtime complexity, which is super-polynomial in L, the linear size of the code. In this work we present an MCMC algorithm that achieves significantly lower logical error rates than MWPM at the cost of a runtime complexity increased by a factor O(L2). This advantage is due to taking correlations between bit- and phase-flip errors (as they appear, for example, in depolarizing noise) as well as entropic factors (i.e., the numbers of likely error paths in different equivalence classes) into account. For depolarizing noise with error rate p, we present an efficient algorithm for which the logical error rate is suppressed as O((p/3)L/2) for p0—an exponential improvement over all previously existing efficient algorithms. Our algorithm allows for tradeoffs between runtime and achieved logical error rates as well as for parallelization, and can be also used for correction in the case of imperfect stabilizer measurements.

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  • Received 9 August 2013

DOI:https://doi.org/10.1103/PhysRevA.89.022326

©2014 American Physical Society

Authors & Affiliations

Adrian Hutter, James R. Wootton, and Daniel Loss

  • Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland

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Issue

Vol. 89, Iss. 2 — February 2014

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