  Solving finite-temperature properties of quantum many-body systems is
generally challenging to classical computers due to their high computational
complexities. In this article, we present experiments to demonstrate a hybrid
quantum-classical simulation of thermal quantum states. By combining a
classical probabilistic model and a 5-qubit programmable superconducting
quantum processor, we prepare Gibbs states and excited states of Heisenberg XY
and XXZ models with high fidelity and compute thermal properties including the
variational free energy, energy, and entropy with a small statistical error.
Our approach combines the advantage of classical probabilistic models for
sampling and quantum co-processors for unitary transformations. We show that
the approach is scalable in the number of qubits, and has a self-verifiable
feature, revealing its potentials in solving large-scale quantum statistical
mechanics problems on near-term intermediate-scale quantum computers.
