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Optimization problems associated with the interaction of linked particles areat the heart of polymer science, protein folding and other important problemsin the physical sciences. In this review we explain how to recast theseproblems as constraint satisfaction problems such as linear programming,maximum satisfiability, and pseudo-boolean optimization. By encoding problemsthis way, one can leverage substantial insight and powerful solvers from thecomputer science community which studies constraint programming for diverseapplications such as logistics, scheduling, artificial intelligence, andcircuit design. We demonstrate how to constrain and embed lattice heteropolymerproblems using several strategies. Each strikes a unique balance between numberof constraints, complexity of constraints, and number of variables. Finally, weshow how to reduce the locality of couplings in these energy functions so theycan be realized as Hamiltonians on existing quantum annealing machines. Weintend that this review be used as a case study for encoding relatedcombinatorial optimization problems in a form suitable for adiabatic quantumoptimization.

advances in chemical physics

Construction of Energy Functions for Lattice Heteropolymer Models: A  Case Study in Constraint Satisfaction Programming and Adiabatic Quantum  Optimization