Solving quantum statistical mechanics with variational autoregressive networks and quantum circuits

Abstract We extend the ability of an unitary quantum circuit by interfacing it with a classical autoregressive neural network. The combined model parametrizes variational density matrix as mixture pure states, where network generates bitstring samples input states to circuit. devise efficient algorithm jointly optimize and solve statistical mechanics problems. One can obtain thermal observables such free energy, entropy, specific heat. As byproduct, also gives access low energy excitation states. demonstrate applications approach properties spectra Ising resources that are feasible on near-term computers.