Coarse-grained lattice protein folding on a quantum annealer Tomas Babej,∗ Mark Fingerhuth,† and Christopher Ing‡ ProteinQure Inc., Toronto, Canada (Dated: March 6, 2018) 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 size of conformational space, new algorithms are required for folding longer proteins sequences. Preliminary work was performed by Babbush et al.  to fold a small peptide on a planar lattice using a quantum annealing device. We extend this work to provide improved Ising-type Hamiltonian encodings for the problem of finding the lowest energy conformation of a lattice protein, in some cases obtaining a significant quadratic to quasilinear decrease in circuit complexity. Additionally we generalize to three spatial dimensions, which is necessary in order to obtain results with higher correlation to the actual atomistic shape of the protein. We 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 whitepaper 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) the first ever protein folded on a cubic lattice with a quantum annealing device. Keywords: Quantum computing, quantum annealing, protein folding, lattice folding, graph theory
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