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Universal transversal gates with color codes: A simplified approach

Kubica, Aleksander and Beverland, Michael E. (2015) Universal transversal gates with color codes: A simplified approach. Physical Review A, 91 (3). Art. No. 032330. ISSN 1050-2947. doi:10.1103/PhysRevA.91.032330.

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We provide a simplified yet rigorous presentation of the ideas from Bombín's paper (arXiv:1311.0879v3). Our presentation is self-contained, and assumes only basic concepts from quantum error correction. We provide an explicit construction of a family of color codes in arbitrary dimensions and describe some of their crucial properties. Within this framework, we explicitly show how to transversally implement the generalized phase gate R_n =diag(1,e^(2πi/2^n)), which deviates from the method in the aforementioned paper, allowing an arguably simpler proof. We describe how to implement the Hadamard gate H fault tolerantly using code switching. In three dimensions, this yields, together with the transversal controlled-NOT (CNOT), a fault-tolerant universal gate set {H,cnot,R_3} without state distillation.

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Additional Information:© 2015 American Physical Society. Received 16 October 2014; published 31 March 2015. We would like to thank H. Bombín for introducing us to color codes and taking the time to explain his results. We would like to thank J. Haah, B. Yoshida, O. Landon-Cardinal, G. Alagic, and J. Preskill for helpful comments on the manuscript. We thank F. Pastawski for pointing out bipartition as a possible construction of the set T . We acknowledge funding provided by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (NFS Grant PHY-1125565) with support of the Gordon and Betty Moore Foundation (GBMF-12500028).
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSF Physics Frontiers CenterUNSPECIFIED
Gordon and Betty Moore FoundationGBMF-12500028
Issue or Number:3
Classification Code:PACS: 03.67.Lx, 03.67.Pp
Record Number:CaltechAUTHORS:20150501-072926649
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:57129
Deposited By: Tony Diaz
Deposited On:01 May 2015 15:49
Last Modified:10 Nov 2021 21:08

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