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Quantum Gibbs Samplers: the commuting case | Michael J. Kastoryano
; Fernando G. S. L. Brandao
; | Date: |
11 Sep 2014 | Abstract: | We analyze the problem of preparing quantum Gibbs states of lattice spin
Hamiltonians with local and commuting terms on a quantum computer and in
nature. Our central result is an equivalence between the behavior of
correlations in the Gibbs state and the mixing time of the semigroup which
drives the system to thermal equilibrium (the Gibbs sampler). 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. We consider two distinct classes of Gibbs samplers,
one of which being the well-studied Davies generators modelling the dynamics on
the system due to 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 clustering of correlations holds in the Gibbs state. As concrete
applications of our formalism, we show that for every one-dimensional lattice
system, or for systems in lattices of any dimension at high enough
temperatures, the Gibbs samplers of commuting Hamiltonians are always gapped,
giving an efficient way of preparing these states on a quantum computer. | Source: | arXiv, 1409.3435 | Services: | Forum | Review | PDF | Favorites |
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