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How fast do stabilizer Hamiltonians thermalize?

Temme, Kristan and Kastoryano, Michael (2015) How fast do stabilizer Hamiltonians thermalize? . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20161004-093445721

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Abstract

We present rigorous bounds on the thermalization time of the family of quantum mechanical spin systems known as stabilizer Hamiltonians. The thermalizing dynamics are modeled by a Davies master equation that arises from a weak local coupling of the system to a large thermal bath. Two temperature regimes are considered. First we clarify how in the low temperature regime, the thermalization time is governed by a generalization of the energy barrier between orthogonal ground states. When no energy barrier is present the Hamiltonian thermalizes in a time that is at most quadratic in the system size. Secondly, we show that above a universal critical temperature, every stabilizer Hamiltonian relaxes to its unique thermal state in a time which scales at most linearly in the size of the system. We provide an explicit lower bound on the critical temperature. Finally, we discuss the implications of these result for the problem of self-correcting quantum memories with stabilizer Hamiltonians.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
https://arxiv.org/abs/1505.07811arXivDiscussion Paper
Additional Information:Dated: May 29, 2015. We thank F. Pastawski and F. Brandao for helpful discussions. This work was supported by the Carlsbergfond, the Villum foundation, the Humboldt foundation, 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).
Group:Institute for Quantum Information and Matter, IQIM
Funders:
Funding AgencyGrant Number
CarlsbergfondUNSPECIFIED
Villum FoundationUNSPECIFIED
Alexander von Humboldt FoundationUNSPECIFIED
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSF Physics Frontiers CenterUNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
NSFPHY-0803371
NSFPHY-1125565
Record Number:CaltechAUTHORS:20161004-093445721
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20161004-093445721
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:70804
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:04 Oct 2016 18:13
Last Modified:04 Oct 2016 18:13

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