Quantum algorithms for thermal equilibrium using fluctuation theorems

IQC-QuICS MATH CS Seminar - Rolando Somma, Los Alamos National Laboratory

Fluctuation theorems provide powerful computational tools to study thermal equilibrium. Building upon these theorems, I will present a quantum algorithm to prepare the thermal state of a quantum system H1, at inverse temperature β≥0, from the thermal state of a quantum system H0. The complexity of the algorithm, given by the number of times certain unitaries are used, is at most exponential in β|V|, where |V| is the spectral norm of V:=H1-H0. This is a significant improvement of prior quantum algorithms that have complexity exponential in β|H0| or β|H1|, since usually |V|<< |H0|,|H1|. I will also discuss uses of the algorithm to estimate properties like free energy differences, and ways to improve the complexity using non-equilibrium processes.

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