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An optimal dissipative encoder for the toric code

Dengis, John and König, Robert and Pastawski, Fernando (2014) An optimal dissipative encoder for the toric code. New Journal of Physics, 16 . Art. No. 013023. ISSN 1367-2630. doi:10.1088/1367-2630/16/1/013023.

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We consider the problem of preparing specific encoded resource states for the toric code by local, time-independent interactions with a memoryless environment. We propose the construction of such a dissipative encoder which converts product states to topologically ordered ones while preserving logical information. The corresponding Liouvillian is made up of four local Lindblad operators. For a qubit lattice of size L × L, we show that this process prepares encoded states in time O(L), which is optimal. This scaling compares favorably with known local unitary encoders for the toric code which take time of order Ω(L^2) and require active time-dependent control.

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Additional Information:© 2014 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. 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 31 October 2013, revised 3 November 2013; Accepted for publication 9 December 2013; Published 16 January 2014. JD and RK gratefully acknowledge funding provided by NSERC. RK would like to thank John Preskill for discussions, and the Institute for Quantum Information and Matter for their hospitality. FP would like to thank Iman Marvian, Ignacio Cirac and John Preskill for helpful discussions and comments. 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 numbers PHY-0803371 and PHY-1125565).
Group:Institute for Quantum Information and Matter
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Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSF Physics Frontiers CenterUNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
Classification Code:PACS: 03.67.-a, 03.65.Fd, 03.65.Vf
Record Number:CaltechAUTHORS:20140228-100623385
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Official Citation:An optimal dissipative encoder for the toric code John Dengis et al 2014 New J. Phys. 16 013023
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:44056
Deposited On:28 Feb 2014 19:45
Last Modified:12 Jul 2022 19:44

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