Construction of Energy Functions for Lattice Heteropolymer Models: Efficient Encodings for Constraint Satisfaction Programming and Quantum Annealing

Abstract

Optimization problems associated with the interaction of linked particles are at the heart of polymer science, protein folding and other important problems in the physical sciences. In this review we explain how to recast these problems as constraint satisfaction problems such as linear programming, maximum satisfiability, and pseudo-boolean optimization. By encoding problems this way, one can leverage substantial insight and powerful solvers from the computer science community which studies constraint programming for diverse applications such as logistics, scheduling, artificial intelligence, and circuit design. We demonstrate how to constrain and embed lattice heteropolymer problems using several strategies. Each strikes a unique balance between number of constraints, complexity of constraints, and number of variables. Finally, we show how to reduce the locality of couplings in these energy functions so they can be realized as Hamiltonians on existing quantum annealing machines. We intend that this review be used as a case study for encoding related combinatorial optimization problems in a form suitable for adiabatic quantum optimization.

Degeneracy, degree, and heavy tails in quantum annealing

“…These circumstances arise when random low-precision Ising spin glass instances are imposed on the full DW2X qubit connectivity graph. However, they do not arise when the connectivity of that graph is varied as described herein, and they become less common when more realistic [16][17][18][19] or combinatorially interesting problem classes are subject to (S)QA [3,20].…”

Exploiting Locality in Quantum Computation for Quantum Chemistry

“…Specifically, instead of painstakingly encoding quantum information into a classical computer, one may be able to use a quantum system to naturally represent another quantum system and bypass the seemingly insurmountable storage requirements. This idea eventually developed into the field of quantum computation, which is now believed to hold promise for the solution of problems ranging from factoring numbers [3] to image recognition [4] and protein folding [5,6].…”

Quantum Chemistry on a Photonic Chip

“…Only a subset of natural phenomena exhibit sufficiently strong quantum correlations as to be classically intractable. Certain regimes of organic [4] and inorganic chemistry [5], superconducting materials [6,7] and quantum magnetism [8], and microbiology, for instance photosynthesis [9], all fall into this regime. Here we will focus our attention on problems in the field of quantum chemistry.…”