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Topological order and memory time in marginally-self-correcting quantum memory

Siva, Karthik and Yoshida, Beni (2017) Topological order and memory time in marginally-self-correcting quantum memory. Physical Review A, 95 (3). Art. No. 032324. ISSN 2469-9926. http://resolver.caltech.edu/CaltechAUTHORS:20160622-115346833

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Abstract

We examine two proposals for marginally-self-correcting quantum memory: the cubic code by Haah and the welded code by Michnicki. In particular, we prove explicitly that they are absent of topological order above zero temperature, as their Gibbs ensembles can be prepared via a short-depth quantum circuit from classical ensembles. Our proof technique naturally gives rise to the notion of free energy associated with excitations. Further, we develop a framework for an ergodic decomposition of Davies generators in CSS codes which enables formal reduction to simpler classical memory problems. We then show that memory time in the welded code is doubly exponential in inverse temperature via the Peierls argument. These results introduce further connections between thermal topological order and self-correction from the viewpoint of free energy and quantum circuit depth.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevA.95.032324DOIArticle
http://journals.aps.org/pra/abstract/10.1103/PhysRevA.95.032324PublisherArticle
https://arxiv.org/abs/1603.07805arXivDiscussion Paper
ORCID:
AuthorORCID
Siva, Karthik0000-0002-8981-761X
Alternate Title:Topological Order and Memory Time in Marginally Self-Correcting Quantum Memory
Additional Information:© 2017 American Physical Society. (Received 22 April 2016; published 22 March 2017) We would like to thank J. Preskill and K. Temme for discussions and O. Motrunich for providing computational resources for numerics. This work was supported through Summer Undergraduate Research Fellowship (SURF) and NSF Grant No. PHY-1125565 at the California Institute of Technology. Research at Perimeter Institute was supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation.
Group:Institute for Quantum Information and Matter, IQIM
Funders:
Funding AgencyGrant Number
Summer Undergraduate Research Fellowship (SURF)UNSPECIFIED
NSFPHY-1125565
Industry CanadaUNSPECIFIED
Ontario Ministry of Research and InnovationUNSPECIFIED
Record Number:CaltechAUTHORS:20160622-115346833
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20160622-115346833
Official Citation:Topological order and memory time in marginally-self-correcting quantum memory Karthik Siva and Beni Yoshida Phys. Rev. A 95, 032324
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:68589
Collection:CaltechAUTHORS
Deposited By: Jacquelyn O'Sullivan
Deposited On:27 Jun 2016 17:54
Last Modified:22 Mar 2017 17:06

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