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Generating topological order: No speedup by dissipation

König, Robert and Pastawski, Fernando (2014) Generating topological order: No speedup by dissipation. Physical Review B, 90 (4). Art. No. 045101. ISSN 1098-0121. doi:10.1103/PhysRevB.90.045101.

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We consider the problem of converting a product state to a ground state of a topologically ordered system through a locally generated open-system dynamic. Employing quantum-information tools, we show that such a conversion takes an amount of time proportional to the diameter of the system. Our result applies to typical two-dimensional topologically ordered systems as well as, for example, the three-dimensional and four-dimensional toric codes. It is tight for the toric code, giving a scaling with the linear system size. Our results have immediate operational implications for the preparation of topologically ordered states, a crucial ingredient for topological quantum computation: Dissipation cannot provide any significant speedup compared to unitary evolution.

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Additional Information:© 2014 American Physical Society. Received 30 October 2013; revised manuscript received 3 June 2014; published 1 July 2014. R.K. gratefully acknowledges support by NSERC and thanks the Isaac Newton Institute for their hospitality. F.P. would like to acknowledge 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 No. PHY-1125565).
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSF Physics Frontiers CenterUNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
Issue or Number:4
Classification Code:PACS: 03.67.Lx, 03.65.Vf
Record Number:CaltechAUTHORS:20150320-150651942
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:55949
Deposited By: Tony Diaz
Deposited On:20 Mar 2015 22:56
Last Modified:10 Nov 2021 20:52

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