  Molecular docking, which aims to find the most stable interacting
configuration of a set of molecules, is of critical importance to drug
discovery. Although a considerable number of classical algorithms have been
developed to carry out molecular docking, most focus on the limiting case of
docking two molecules. Since the number of possible configurations of N
molecules is exponential in N, those exceptions which permit docking of more
than two molecules scale poorly, requiring exponential resources to find
high-quality solutions. Here, we introduce a one-hot encoded quadratic
unconstrained binary optimization formulation (QUBO) of the multibody molecular
docking problem, which is suitable for solution by quantum annealer. Our
approach involves a classical pre-computation of pairwise interactions, which
scales only quadratically in the number of bodies while permitting well-vetted
scoring functions like the Rosetta REF2015 energy function to be used. In a
second step, we use the quantum annealer to sample low-energy docked
configurations efficiently, considering all possible docked configurations
simultaneously through quantum superposition. We show that we are able to
minimize the time needed to find diverse low-energy docked configurations by
tuning the strength of the penalty used to enforce the one-hot encoding,
demonstrating a 3-4 fold improvement in solution quality and diversity over
performance achieved with conventional penalty strengths. By mapping the
configurational search to a form compatible with current- and future-generation
quantum annealers, this work provides an alternative means of solving multibody
docking problems that may prove to have performance advantages for large
problems, potentially circumventing the exponential scaling of classical
approaches and permitting a much more efficient solution to a problem central
to drug discovery and validation pipelines.
