Topological phases with generalized global symmetries
- Creators
- Yoshida, Beni
Abstract
We present simple lattice realizations of symmetry-protected topological phases with q-form global symmetries where charged excitations have q spatial dimensions. Specifically, we construct d space-dimensional models supported on a (d+1)-colorable graph by using a family of unitary phase gates, known as multiqubit control-Z gates in quantum information community. In our construction, charged excitations of different dimensionality may coexist and form a short-range entangled state which is protected by symmetry operators of different dimensionality. Nontriviality of proposed models, in a sense of quantum circuit complexity, is confirmed by studying protected boundary modes, gauged models, and corresponding gapped domain walls. We also comment on applications of our construction to quantum error-correcting codes, and discuss corresponding fault-tolerant logical gates.
Additional Information
© 2016 American Physical Society. Received 2 September 2015; revised manuscript received 5 February 2016; published 15 April 2016. I would like to thank Z. Gu, A. Kubica, J. Preskill, B. Şahinoğlu, R. Thorngren, M. Walter, and D. Williamson for helpful discussions, conversations, and/or comments. Part of the work was completed during the visit 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 No. PHY-1125565). I was supported by a David and Ellen Lee Postdoctoral Fellowship. This research was supported in part by the National Science Foundation under Grant No. NSF PHY11-25915.Attached Files
Published - PhysRevB.93.155131.pdf
Submitted - 1508.03468v1.pdf
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Additional details
- Eprint ID
- 60754
- Resolver ID
- CaltechAUTHORS:20151005-094731380
- Institute for Quantum Information and Matter (IQIM)
- NSF Physics Frontiers Center
- Gordon and Betty Moore Foundation
- NSF
- PHY-0803371
- NSF
- PHY-1125565
- David and Ellen Lee Postdoctoral Fellowship
- NSF
- PHY11-25915
- Created
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2015-10-05Created from EPrint's datestamp field
- Updated
-
2021-11-10Created from EPrint's last_modified field
- Caltech groups
- Walter Burke Institute for Theoretical Physics, Institute for Quantum Information and Matter