Nonequilibrium fluctuation theorems provide a correspondence between properties of quantum systems in thermal equilibrium and work distributions arising in nonequilibrium processes. Building upon these theorems, we present a quantum algorithm to prepare a purification of the thermal state of a quantum system of interest. Unlike previous algorithms based on a thermalization process that brings an infinite-temperature state to one at finite temperature, our algorithm assumes access to the purification of the thermal state of H0 to prepare a purification of the thermal state of H1=H0+V at the same temperature. When the perturbation V is small, even with a trivial nonequilibrium process our algorithm provides a significant improvement over prior quantum algorithms in terms of complexity by exploiting the similarity between the two thermal states. Further improvements arise from a judicious choice of the nonequilibrium process.
I will start the talk with a review of fluctuation theorems relevant to this work before describing the thermal state preparation algorithm in detail. The essential ingredients of our algorithm are the definition of a "work operator", introduction of a work cutoff and an approximation of the exponentiated work operator on a subspace of work values above the cutoff. Special cases of when H0 and H1 commute and when they are both local spin Hamiltonians will be discussed. For the transverse field Ising model I will numerically demonstrate the effect of using different nonequilibrium processes on the complexity of the algorithm.