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Three-dimensional color code thresholds via statistical-mechanical mapping

Kubica, Aleksander and Beverland, Michael E. and Brandão, Fernando G. S. L. and Preskill, John and Svore, Krysta M. (2018) Three-dimensional color code thresholds via statistical-mechanical mapping. Physical Review Letters, 120 (18). Art. No. 180501. ISSN 0031-9007. doi:10.1103/PhysRevLett.120.180501.

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Three-dimensional (3D) color codes have advantages for fault-tolerant quantum computing, such as protected quantum gates with relatively low overhead and robustness against imperfect measurement of error syndromes. Here we investigate the storage threshold error rates for bit-flip and phase-flip noise in the 3D color code (3DCC) on the body-centered cubic lattice, assuming perfect syndrome measurements. In particular, by exploiting a connection between error correction and statistical mechanics, we estimate the threshold for 1D stringlike and 2D sheetlike logical operators to be p^((1))_(3DCC) ≃ 1.9% and p^((2))_(3DCC) ≃ 27.6%. We obtain these results by using parallel tempering Monte Carlo simulations to study the disorder-temperature phase diagrams of two new 3D statistical-mechanical models: the four- and six-body random coupling Ising models.

Item Type:Article
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URLURL TypeDescription Paper
Brandão, Fernando G. S. L.0000-0003-3866-9378
Additional Information:© 2018 American Physical Society. Received 30 September 2017; published 4 May 2018. We thank R. Andrist, H. Bombín, N. Delfosse, L. Pryadko, B. Yoshida, and I. Zintchenko for helpful discussions. A. K. would like to thank the QuArC group for their hospitality during a summer internship. We acknowledge funding provided by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (NSF Grant No. PHY-1125565) with support of the Gordon and Betty Moore Foundation (GBMF-2644).
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Gordon and Betty Moore FoundationGBMF-12500028
Issue or Number:18
Record Number:CaltechAUTHORS:20171004-145219476
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:82080
Deposited By: Joy Painter
Deposited On:05 Oct 2017 16:53
Last Modified:15 Nov 2021 19:48

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