Quantum computing for classical problems: variational quantum eigensolver for activated processes

The theory of stochastic processes impacts both physical and social sciences. At the molecular scale, stochastic dynamics is ubiquitous because of thermal fluctuations. The Fokker-Plank-Smoluchowski equation models the time evolution of the probability density of selected degrees of freedom in the diffusive regime and it is, therefore, a workhorse of physical chemistry. In this paper we report on the development and implementation of a variational quantum eigensolver to solve the Fokker-Planck-Smoluchowski eigenvalue problem. We show that such an algorithm, typically adopted to address quantum chemistry problems, can be effectively applied to classical systems, paving the way to new applications of quantum computers. We compute the conformational transition rate in a linear chain of rotors with nearest-neighbour interactions. We provide a method to encode the probability distribution for a given conformation of the chain on a quantum computer and assess its scalability in terms of operations. A performance analysis on noisy quantum emulators and quantum devices (IBMQ Santiago) is provided for a small chain which shows results in good agreement with the classical benchmark without any further addition of error mitigation techniques.