Simulation of Nonequilibrium Dynamics on a Quantum Computer

We present a hybrid quantum-classical algorithm for the time evolution of out-of-equilibrium thermal states. The method depends on classically computing a sparse approximation to the density matrix and, then, time-evolving each matrix element via the quantum computer. For this exploratory study, we investigate a time-dependent Ising model with five spins on the Rigetti Forest quantum virtual machine and a one spin system on the Rigetti 8Q-Agave quantum processor.