Error tolerance of topological codes with independent bit-flip and measurement errors
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2016
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American Physical Society
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Abstract
Topological quantum error correction codes are currently among the most promising candidates for efficiently dealing with the decoherence effects inherently present in quantum devices. Numerically, their theoretical error threshold can be calculated by mapping the underlying quantum problem to a related classical statistical-mechanical spin system with quenched disorder. Here, we present results for the general fault-tolerant regime, where we consider both qubit and measurement errors. However, unlike in previous studies, here we vary the strength of the different error sources independently. Our results highlight peculiar differences between toric and color codes. This study complements previous results published in New J. Phys. 13, 083006 (2011).
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©2016 American Physical Society.
The authors thank ETH Zurich for CPU time on the Brutus cluster, the Santa Fe Institute for CPU time on the Scoville cluster, and the Centro de Supercomputacion y Visualizacion de Madrid (CeSViMa) for access to the Magerit cluster. M.A.M.-D. and H.B. acknowledge financial support from the Spanish MINECO Grant No. FIS2012-33152, the Spanish MINECO Grant No. FIS2015-67411, and the CAM research consortium QUITEMAD+, Grant No. S2013/ICE-2801. The research of M.A.M.-D. has been supported in part by the U.S. Army Research Office through Grant No. W911NF-14-1-0103. H.G.K. acknowledges support from the National Science Foundation (Grant No. DMR-1151387) and the Swiss National Science Foundation (Grant No. PP002-114713). Part of the research of H.G.K. is based upon work supported in part by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), via MIT Lincoln Laboratory Air Force Contract No. FA8721-05-C-0002. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of ODNI, IARPA, or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for governmental purpose notwithstanding any copyright annotation thereon.