  The quest for improved sampling methods to solve statistical mechanics
problems of physical and chemical interest proceeds with renewed efforts since
the invention of the Metropolis algorithm, in 1953. In particular, the
understanding of thermally activated rare-event processes between long-lived
metastable states, such as protein folding, is still elusive. In this case, one
needs both the finite-temperature canonical distribution function and the
reaction current between the reactant and product states, to completely
characterize the dynamic. Here we show how to tackle this problem using a
quantum computer. We use the connection between a classical stochastic dynamics
and the Schroedinger equation, also known as stochastic quantization, to
variationally prepare quantum states allowing us to unbiasedly sample from a
Boltzmann distribution. Similarly, reaction rate constants can be computed as
ground state energies of suitably transformed operators, following the
supersymmetric extension of the formalism. Finally, we propose a hybrid
quantum-classical sampling scheme to escape local minima, and explore the
configuration space in both real-space and spin hamiltonians. We indicate how
to realize the quantum algorithms constructively, without assuming the
existence of oracles, or quantum walk operators. The quantum advantage
concerning the above applications is discussed.
