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CATEGORIES:CQIF Seminar
SUMMARY:Efficient quantum Gibbs samplers - Michael Kastory
ano (Freie Universitaet Berlin)
DTSTART;TZID=Europe/London:20141030T141500
DTEND;TZID=Europe/London:20141030T151500
UID:TALK54910AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/54910
DESCRIPTION:We analyze the problem of preparing quantum Gibbs
states of lattice spin Hamiltonians with local and
com- muting terms on a quantum computer and in na
ture. We introduce a framework for analyzing the
correlation and mixing characteristics of quantum
Gibbs states and quantum Gibbs samplers\, which is
rooted in the theory of non-commutative Lp spaces
. Our central result is an equivalence between the
behavior of correlations in the Gibbs state and t
he mixing time of the semigroup which drives the s
ystem to thermal equilibrium (the Gibbs sampler).
We construct two distinct classes of Gibbs sampler
s\, one of which being the well-studied Davies gen
erators modelling the dynamics on the system due t
o weak-coupling with a large Markovian environment
. We show that their gap is independent of system
size if\, and only if\, a certain strong form of c
lustering of correlations holds in the Gibbs state
. As concrete applications of our formalism\, we s
how that for every one-dimensional lattice system\
, or for systems in lattices of any dimension at h
igh enough temperatures\, the Gibbs samplers of co
mmuting Hamiltonians are always gapped\, giving an
efﬁcient way of preparing these states on a quant
um computer. We finally discuss the possible exten
sions to non-commuting Hamiltonian Gibbs samplers.
LOCATION:MR5\, Centre for Mathematical Sciences\, Wilberfo
rce Road\, Cambridge
CONTACT:William Matthews
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