Gibbs states (i.e., thermal states) can be used for several applications such
as quantum simulation, quantum machine learning, quantum optimization, and the
study of open quantum systems. Moreover, semi-definite programming,
combinatorial optimization problems, and training quantum Boltzmann machines
can all be addressed by sampling from well-prepared Gibbs states. With that,
however, comes the fact that preparing and sampling from Gibbs states on a
quantum computer are notoriously difficult tasks. Such tasks can require large
overhead in resources and/or calibration even in the simplest of cases, as well
as the fact that the implementation might be limited to only a specific set of
systems. We propose a method based on sampling from a quasi-distribution
consisting of tensor products of mixed states on local clusters, i.e.,
expanding the full Gibbs state into a sum of products of local "Gibbs-cumulant"
type states easier to implement and sample from on quantum hardware. We begin
with presenting results for 4-spin linear chains with XY spin interactions, for
which we obtain the ZZ dynamical spin-spin correlation functions. We also
present the results of measuring the specific heat of the 8-spin chain Gibbs
state ρ8.Comment: 8 pages, 8 figures, and supplementary materia