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Thermalization Time Bounds for Pauli Stabilizer Hamiltonians

Temme, Kristan (2017) Thermalization Time Bounds for Pauli Stabilizer Hamiltonians. Communications in Mathematical Physics, 350 (2). pp. 603-637. ISSN 0010-3616. doi:10.1007/s00220-016-2746-0.

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We prove a general lower bound to the spectral gap of the Davies generator for Hamiltonians that can be written as the sum of commuting Pauli operators. These Hamiltonians, defined on the Hilbert space of N-qubits, serve as one of the most frequently considered candidates for a self-correcting quantum memory. A spectral gap bound on the Davies generator establishes an upper limit on the life time of such a quantum memory and can be used to estimate the time until the system relaxes to thermal equilibrium when brought into contact with a thermal heat bath. The bound can be shown to behave as λ≥O(N^(−1) exp(−2βϵ)), where ϵ is a generalization of the well known energy barrier for logical operators. Particularly in the low temperature regime we expect this bound to provide the correct asymptotic scaling of the gap with the system size up to a factor of N^(−1). Furthermore, we discuss conditions and provide scenarios where this factor can be removed and a constant lower bound can be proven.

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Additional Information:© 2016 Springer-Verlag Berlin Heidelberg. Received: 18 January 2016; Accepted: 19 July 2016; First Online: 30 September 2016. I would like to thank Anna Kómár for helpful discussion and for pointing out a mistake in a previous draft, as well as Olivier Landon-Cardinal, Michael J. Kastoryano and Fernando Pastawski for helpful discussions. This work was supported 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 PHY-1125565).
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
Issue or Number:2
Record Number:CaltechAUTHORS:20161109-150355058
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Official Citation:Temme, K. Commun. Math. Phys. (2017) 350: 603. doi:10.1007/s00220-016-2746-0
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:71894
Deposited By: Tony Diaz
Deposited On:09 Nov 2016 23:16
Last Modified:11 Nov 2021 04:52

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