Gibbs sampling via cluster expansions

Abstract

We acknowledge the use of IBM Quantum services for this work. 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 present results for measuring both the dynamical structure factor and the specific heat of different Gibbs states of spin systems. *All authors and the research as a whole were supported by the Quantum Science Center (QSC), a National Quantum Science Initiative of the Department Of Energy (DOE), managed by Oak Ridge National Laboratory (ORNL). We acknowledge the use of IBM Quantum services for this work through the QSC.