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Cost of Universality: A Comparative Study of the Overhead of State Distillation and Code Switching with Color Codes

Beverland, Michael E. and Kubica, Aleksander and Svore, Krysta M. (2021) Cost of Universality: A Comparative Study of the Overhead of State Distillation and Code Switching with Color Codes. PRX Quantum, 2 (2). Art. No. 020341. ISSN 2691-3399.

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Estimating and reducing the overhead of fault-tolerance (FT) schemes is a crucial step toward realizing scalable quantum computers. Of particular interest are schemes based on two-dimensional (2D) topological codes such as the surface and color codes that have high thresholds but lack a natural implementation of a non-Clifford gate. In this work, we directly compare two leading FT implementations of the T gate in 2D color codes under circuit noise across a wide range of parameters in regimes of practical interest. We report that implementing the T gate via code switching to a three-dimensional (3D) color code does not offer substantial savings over state distillation in terms of either space or space-time overhead. We find a circuit-noise threshold of 0.07(1)% for the T gate via code switching, almost an order of magnitude below that achievable by state distillation in the same setting. To arrive at these results, we provide and simulate an optimized code-switching procedure, and bound the effect of various conceivable improvements. Many intermediate results in our analysis may be of independent interest. For example, we optimize the 2D color code for circuit noise yielding its largest threshold to date 0.37(1)%, and adapt and optimize the restriction decoder finding a threshold of 0.80(5)% for the 3D color code with perfect measurements under Z noise. Our work provides a much-needed direct comparison of the overhead of state distillation and code switching, and sheds light on the choice of future FT schemes and hardware designs.

Item Type:Article
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URLURL TypeDescription Paper
Beverland, Michael E.0000-0003-0954-4509
Svore, Krysta M.0000-0001-9500-9443
Additional Information:© 2021 The Author(s). Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. (Received 2 January 2021; accepted 21 April 2021; published 15 June 2021) M.E.B. acknowledges relevant scientific discussions with many researchers from the QEC community, including Thomas Bohdanowicz, Héctor Bombín Ben Brown, Earl Campbell, Nicolas Delfosse, Austin Fowler, Jeongwan Haah, Tomas Jochym O’Connor, Cody Jones, Andrew Landahl, Ying Li, Michael Newman, Adam Paetznick, John Preskill, and Marcus P da Silva. He is especially grateful for the encouragement for this project from David Poulin. M.E.B. also wishes to think Achiamar Lee Rivera for her unwavering support throughout this research. A.K. is deeply indebted to Héctor Bombín for many colorful discussions. A.K. acknowledges funding provided by the Simons Foundation through the “It from Qubit” Collaboration. Research at Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Colleges and Universities. This work was completed prior to A.K. joining AWS Center for Quantum Computing.
Group:AWS Center for Quantum Computing
Funding AgencyGrant Number
Simons FoundationUNSPECIFIED
Department of Innovation, Science and Economic Development (Canada)UNSPECIFIED
Ontario Ministry of Colleges and UniversitiesUNSPECIFIED
Issue or Number:2
Record Number:CaltechAUTHORS:20210626-183436417
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:109594
Deposited By: George Porter
Deposited On:28 Jun 2021 15:45
Last Modified:28 Jun 2021 15:45

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