Simulating thermal quantum quenches with a variational quantum algorithm

Noisy intermediate-scale quantum (NISQ) devices hold great promise in the modeling of quantum physical systems in and out of equilibrium. Thermal quantum quenches are a particularly important example that are both relevant for the discovery of fundamental physics phenomena and the simulation of complex materials. In a thermal quantum quench, a system initially at thermal equilibrium with a finite temperature is abruptly brought out of equilibrium by a sudden change in the parameters of its Hamiltonian. To enable simulations of the complex post-quench dynamics on NISQ devices, which are limited to shallow and narrow circuits, we develop a variational quantum algorithm that combines the recent adaptive variational quantum dynamics simulation (AVQDS) method with a density matrix quantum Monte-Carlo technique for thermal state preparation. We benchmark this new method using simulations of sudden thermal quenches in the mixed-field Ising chain, focusing on thermodynamic observables and the Loschmidt echo. We compare noiseless quantum simulation results with exact diagonalization and comment on the impact of finite temperature on the post-quench dynamics.