  Lattice models have been used extensively over the past thirty years to
examine the principles of protein folding and design. These models can be used
to determine the conformation of the lowest energy fold out of a large number
of possible conformations. However, due to the size of the conformational
space, new algorithms are required for folding longer proteins sequences.
Preliminary work was performed by Babbush et al. (2012) to fold a small peptide
on a planar lattice using a quantum annealing device. We extend this work by
providing improved Ising-type Hamiltonian encodings for the problem of finding
the lowest energy conformation of a lattice protein. We demonstrate a decrease
in quantum circuit complexity from quadratic to quasilinear in certain cases.
Additionally, we generalize to three spatial dimensions in order to obtain
results with higher correlation to the actual atomistic 3D structure of the
protein and outline our heuristic approach for splitting large problem
instances into smaller subproblems that can be directly solved with the current
D-Wave 2000Q architecture. To the best of our knowledge, this work sets a new
record for lattice protein folding on a quantum annealer by folding Chignolin
(10 residues) on a planar lattice and Trp-Cage (8 residues) on a cubic lattice.
