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Preparing topologically ordered states by Hamiltonian interpolation

Ni, Xiaotong and Pastawski, Fernando and Yoshida, Beni and Koenig, Robert (2016) Preparing topologically ordered states by Hamiltonian interpolation. New Journal of Physics, 18 (9). Art. No. 093027. ISSN 1367-2630. doi:10.1088/1367-2630/18/9/093027.

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We study the preparation of topologically ordered states by interpolating between an initial Hamiltonian with a unique product ground state and a Hamiltonian with a topologically degenerate ground state space. By simulating the dynamics for small systems, we numerically observe a certain stability of the prepared state as a function of the initial Hamiltonian. For small systems or long interpolation times, we argue that the resulting state can be identified by computing suitable effective Hamiltonians. For effective anyon models, this analysis singles out the relevant physical processes and extends the study of the splitting of the topological degeneracy by Bonderson (2009 Phys. Rev. Lett. 103 110403). We illustrate our findings using Kitaev's Majorana chain, effective anyon chains, the toric code and Levin–Wen string-net models.

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Additional Information:©2016 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Received 12 May 2016; Accepted 24 August 2016; Published 14 September 2016. FP acknowledges funding provided by the Institute for Quantum Information and Matter, a NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation (Grants No. PHY-0803371 and PHY-1125565). FP would alos like to acknowledge insightful discussions with John Preskill, Brian Swingle, Julien Vidal and Chris Laumann. BY is supported by the David and Ellen Lee Postdoctoral fellowship and the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation. RK is supported by the Technische Universität at München— Institute for Advanced Study, funded by the German Excellence Initiative and the European Union Seventh Framework Programme under grant agreement no. 291763.
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 FoundationUNSPECIFIED
David and Ellen Lee Postdoctoral FellowshipUNSPECIFIED
Industry CanadaUNSPECIFIED
Ontario Ministry of Research and InnovationUNSPECIFIED
Technische Universität MünchenUNSPECIFIED
German Excellence InitiativeUNSPECIFIED
European Union FP7291763
Issue or Number:9
Record Number:CaltechAUTHORS:20160622-145044064
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Official Citation:Xiaotong Ni et al 2016 New J. Phys. 18 093027
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:68604
Deposited By: Jacquelyn O'Sullivan
Deposited On:27 Jun 2016 17:58
Last Modified:12 Jul 2022 19:42

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