  Characterizing thermally activated transitions in high-dimensional rugged
energy surfaces is a very challenging task for classical computers. Here, we
develop a quantum annealing scheme to solve this problem. First, the task of
finding the most probable transition paths in configuration space is reduced to
a shortest-path problem defined on a suitable weighted graph. Next, this
optimization problem is mapped into finding the ground state of a generalized
Ising model. A finite-size scaling analysis suggests this task may be solvable
efficiently by a quantum annealing machine. Our approach leverages on the
quantized nature of qubits to describe transitions between different system's
configurations. Since it does not involve any lattice space discretization, it
paves the way towards future biophysical applications of quantum computing
based on realistic all-atom models.
