Universal transversal gates with color codes: A simplified approach
- Creators
- Kubica, Aleksander
- Beverland, Michael E.
Abstract
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.
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).Attached Files
Published - PhysRevA.91.032330.pdf
Submitted - 1410.0069v1.pdf
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Additional details
- Eprint ID
- 57129
- Resolver ID
- CaltechAUTHORS:20150501-072926649
- Institute for Quantum Information and Matter (IQIM)
- NSF Physics Frontiers Center
- PHY-1125565
- NSF
- GBMF-12500028
- Gordon and Betty Moore Foundation
- Created
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2015-05-01Created from EPrint's datestamp field
- Updated
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2021-11-10Created from EPrint's last_modified field
- Caltech groups
- Institute for Quantum Information and Matter