  One of the most promising applications for quantum computers is the dynamic
simulation of quantum materials. Current hardware, however, sets stringent
limitations on how long such simulations can run before decoherence begins to
corrupt results. The Jarzynski equality, a fluctuation theorem that allows for
the computation of equilibrium free energy differences from an ensemble of
short, non-equilibrium dynamics simulations, can make use of such short-time
simulations on quantum computers. Here, we present a quantum algorithm based on
the Jarzynski equality for computing free energies of quantum materials. We
demonstrate our algorithm using the transverse field Ising model on both a
quantum simulator and real quantum hardware. As the free energy is a central
thermodynamic property that allows one to compute virtually any equilibrium
property of a physical system, the ability to perform this algorithm for larger
quantum systems in the future has implications for a wide range of applications
including the construction of phase diagrams, prediction of transport
properties and reaction constants, and computer-aided drug design.
