  Protein folding is a central challenge in computational biology, with
important applications in molecular biology, drug discovery and catalyst
design. As a hard combinatorial optimisation problem, it has been studied as a
potential target problem for quantum annealing. Although several experimental
implementations have been discussed in the literature, the computational
scaling of these approaches has not been elucidated. In this article, we
present a numerical study of quantum annealing applied to a large number of
small peptide folding problems, aiming to infer useful insights for near-term
applications. We present two conclusions: that even naive quantum annealing,
when applied to protein lattice folding, has the potential to outperform
classical approaches, and that careful engineering of the Hamiltonians and
schedules involved can deliver notable relative improvements for this problem.
Overall, our results suggest that quantum algorithms may well offer
improvements for problems in the protein folding and structure prediction
realm.
