  Predicting the 3D structure of proteins is one of the most important problems
in current biochemical research. In this article, we explain how to combine
recent deep learning advances with the well known technique of quantum walks
applied to a Metropolis algorithm. The result, QFold, is a fully scalable
hybrid quantum algorithm that, in contrast to previous quantum approaches, does
not require a lattice model simplification and instead relies on the much more
realistic assumption of parameterization in terms of torsion angles of the
amino acids. We compare it with its classical analog for different annealing
schedules and find a polynomial quantum advantage, and implement a minimal
realization of the quantum Metropolis in the IBMQ Casablanca quantum system.
