Gapped boundaries, group cohomology and fault-tolerant logical gates

Creators: Yoshida, Beni

Abstract

This paper attempts to establish the connection among classifications of gapped boundaries in topological phases of matter, bosonic symmetry-protected topological (SPT) phases and fault-tolerantly implementable logical gates in quantum error-correcting codes. We begin by presenting constructions of gapped boundaries for the d-dimensional quantum double model by using d-cocycles functions (d≥2). We point out that the system supports mm-dimensional excitations (m

Additional Information

© 2016 Elsevier Inc. Received 17 October 2016, Accepted 6 December 2016, Available online 14 December 2016. I would like to thank Isaac Kim, Fernando Pastawski, John Preskill and Chenjie Wang for helpful discussions and/or comments. Part of the work was completed during the visits to the Kavli Institute for Theoretical Physics. We acknowledge funding provided by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation (Grants No. PHY-0803371 and PHY-1125565). I was supported by the David and Ellen Lee Postdoctoral fellowship. This research was supported in part by the National Science Foundation under Grant No. NSF PHY11-25915. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation.

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