Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session Z35: Thermodynamics in Quantum Information II
11:30 AM–2:18 PM,
Friday, March 18, 2022
Room: McCormick Place W-193B
Sponsoring Units: DQI GSNP DCMP
Chair: Ian Mondragon, Northwestern University
Abstract: Z35.00002 : Fast Thermalization from the Eigenstate Thermalization Hypothesis*
12:06 PM–12:18 PM
We consider two models of thermalization. In the first, the system is weakly coupled to a bath of (quasi)-free Fermions. We provide a quantitative derivation, with finite error bounds, of the effective Lindbladian governing the joint evolution. We show it is given by a finitely-resolved version of Davies' generator, whose fixed points include the (approximate) Gibbs state. The second is Quantum Metropolis Sampling, a quantum algorithm for preparing Gibbs states on a quantum computer. In both cases, no guarantee for fast convergence was previously known for non-commuting Hamiltonians.
The key feature of ETH we explore is that below a certain sufficiently small energy scale, the Hamiltonian can be modeled by random matrix theory. We show this gives quantum expander at nearby eigenstates of the Hamiltonian. This then implies fast convergence to the global Gibbs state, by mapping the problem to a one-dimensional classical random walk on the spectrum of the Hamiltonian. Our results explain finite-time thermalization in chaotic quantum systems and suggest a less stringent formulation of ETH in terms of quantum expanders.
*Caltech RA fellowship
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