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Symmetry-protected topological order at nonzero temperature

Roberts, Sam and Yoshida, Beni and Kubica, Aleksander and Bartlett, Stephen D. (2017) Symmetry-protected topological order at nonzero temperature. Physical Review A, 96 (2). Art. No. 022306. ISSN 2469-9926. doi:10.1103/PhysRevA.96.022306.

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We address the question of whether symmetry-protected topological (SPT) order can persist at nonzero temperature, with a focus on understanding the thermal stability of several models studied in the theory of quantum computation. We present three results in this direction. First, we prove that nontrivial SPT order protected by a global onsite symmetry cannot persist at nonzero temperature, demonstrating that several quantum computational structures protected by such onsite symmetries are not thermally stable. Second, we prove that the three-dimensional (3D) cluster-state model used in the formulation of topological measurement-based quantum computation possesses a nontrivial SPT-ordered thermal phase when protected by a generalized (1-form) symmetry. The SPT order in this model is detected by long-range localizable entanglement in the thermal state, which compares with related results characterizing SPT order at zero temperature in spin chains using localizable entanglement as an order parameter. Our third result is to demonstrate that the high-error tolerance of this 3D cluster-state model for quantum computation, even without a protecting symmetry, can be understood as an application of quantum error correction to effectively enforce a 1-form symmetry.

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Additional Information:© 2017 American Physical Society. Received 5 January 2017. Revised 13 June 2017. We acknowledge discussions with A. Doherty. B.Y. and A.K. would like to thank the University of Sydney for their hospitality. S.R. and B.Y. thank R. Raussendorf for his hospitality during their visit to the University of British Columbia. S.D.B. acknowledges support from the U. S. Army Research Office under Contract No. W911NF-14-1-0133, and the ARC via the Centre of Excellence in Engineered Quantum Systems (EQuS), Projects No. CE110001013 and No. DP170103073. 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. A.K. acknowledges funding provided by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (NFS Grant NO. PHY-1125565) with support of the Gordon and Betty Moore Foundation (Grant No. GBMF-12500028).
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Army Research Office (ARO)W911NF-14-1-0133
Australian Research CouncilCE110001013
Australian Research CouncilDP170103073
Industry CanadaUNSPECIFIED
Ontario Ministry of Research and InnovationUNSPECIFIED
Institute of Quantum Information and Matter (IQIM)UNSPECIFIED
NSF Physics Frontiers CenterPHY-1125565
Gordon and Betty Moore FoundationGBMF-12500028
Issue or Number:2
Record Number:CaltechAUTHORS:20170807-140223705
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Official Citation:Symmetry-protected topological order at nonzero temperature Roberts, Sam and Yoshida, Beni and Kubica, Aleksander and Bartlett, Stephen D. Phys. Rev. A, volume 96, issue 2, pages 022306, 2017, Aug, 10.1103/PhysRevA.96.022306
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:79856
Deposited By: Ruth Sustaita
Deposited On:07 Aug 2017 21:43
Last Modified:15 Nov 2021 17:51

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