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Quantum Self-Correction in the 3D Cubic Code Model

Bravyi, Sergey and Haah, Jeongwan (2013) Quantum Self-Correction in the 3D Cubic Code Model. Physical Review Letters, 111 (20). Art. No. 200501. ISSN 0031-9007. http://resolver.caltech.edu/CaltechAUTHORS:20120522-120847872

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Abstract

A big open question in the quantum information theory concerns the feasibility of a self-correcting quantum memory. A quantum state recorded in such memory can be stored reliably for a macroscopic time without need for active error correction, if the memory is in contact with a cold enough thermal bath. Here we report analytic and numerical evidence for self-correcting behavior in the quantum spin lattice model known as the 3D cubic code. We prove that its memory time is at least L^(cβ), where L is the lattice size, β is the inverse temperature of the bath, and c>0 is a constant coefficient. However, this bound applies only if the lattice size L does not exceed a critical value which grows exponentially with β. In that sense, the model can be called a partially self-correcting memory. We also report a Monte Carlo simulation indicating that our analytic bounds on the memory time are tight up to constant coefficients. To model the readout step we introduce a new decoding algorithm, which can be implemented efficiently for any topological stabilizer code. A longer version of this work can be found in Bravyi and Haah, arXiv:1112.3252.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1112.3252arXivDiscussion Paper
http://dx.doi.org/10.1103/PhysRevLett.111.200501DOIArticle
http://link.aps.org/doi/10.1103/PhysRevLett.111.200501PublisherArticle
Alternate Title:Analytic and numerical demonstration of quantum self-correction in the 3D Cubic Code
Additional Information:© 2013 American Physical Society. Received 13 June 2013; published 12 November 2013. We would like to thank David DiVincenzo, John Preskill, and Barbara Terhal for helpful discussions. S. B. is supported in part by the DARPA QuEST program under Contract No. HR0011-09-C-0047 and IARPA QCS program under Contract No. D11PC20167. J.H. is supported in part by the Korea Foundation for Advanced Studies and by the Institute for Quantum Information and Matter, a NSF Physics Frontiers Center with support from the Gordon and Betty Moore Foundation. Computational resources for this work were provided by IBM Blue Gene Watson supercomputer center.
Group:Institute for Quantum Information and Matter, IQIM
Funders:
Funding AgencyGrant Number
Defense Advanced Research Projects Agency (DARPA) QuESTHR00011-09-C-0047
IARPA QCS ProgramD11PC20167
Korean Foundation for Advanced Studies UNSPECIFIED
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSF Physics Frontiers CenterUNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
Subject Keywords:PACS: 03.67.Pp, 03.65.Vf, 03.67.Ac
Record Number:CaltechAUTHORS:20120522-120847872
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20120522-120847872
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:31597
Collection:CaltechAUTHORS
Deposited By: Joy Painter
Deposited On:22 May 2012 22:34
Last Modified:23 Dec 2013 19:25

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