  We propose a Monte Carlo algorithm designed to simulate quantum as well as
classical systems at equilibrium, bridging the algorithmic gap between quantum
and classical thermal simulation algorithms. The method is based on a novel
decomposition of the quantum partition function that can be viewed as a series
expansion about its classical part. We argue that the algorithm is optimally
suited to tackle quantum many-body systems that exhibit a range of behaviors
from `fully-quantum' to `fully-classical', in contrast to many existing
methods. We demonstrate the advantages of the technique by comparing it against
existing schemes. We also illustrate how our method allows for the unification
of quantum and classical thermal parallel tempering techniques into a single
algorithm and discuss its practical significance.
