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

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