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

  1. Stuart A. Rice and
  2. Aaron R. Dinner
  1. Ryan Babbush1,
  2. Alejandro Perdomo-Ortiz1,2,
  3. Bryan O'Gorman1,
  4. William Macready3 and
  5. Alan Aspuru-Guzik1

Published Online: 4 APR 2014

DOI: 10.1002/9781118755815.ch05

Advances in Chemical Physics: Volume 155

Advances in Chemical Physics: Volume 155

How to Cite

Babbush, R., Perdomo-Ortiz, A., O'Gorman, B., Macready, W. and Aspuru-Guzik, A. (2014) Construction of Energy Functions for Lattice Heteropolymer Models: Efficient Encodings for Constraint Satisfaction Programming and Quantum Annealing, in Advances in Chemical Physics: Volume 155 (eds S. A. Rice and A. R. Dinner), John Wiley & Sons, Inc., Hoboken, New Jersey. doi: 10.1002/9781118755815.ch05

Editor Information

  1. Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois

Author Information

  1. 1

    Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge, MA 02138, USA

  2. 2

    NASA Ames Quantum Laboratory, Ames Research Center, Moffett Field, CA 94035, USA

  3. 3

    D-Wave Systems, Inc., 100-4401 Still Creek Drive, Burnaby, British Columbia V5C 6G9, Canada

Publication History

  1. Published Online: 4 APR 2014
  2. Published Print: 11 APR 2014

ISBN Information

Print ISBN: 9781118755778

Online ISBN: 9781118755815

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Keywords:

  • constraint satisfaction programming;
  • integer'linear programming;
  • lattice heteropolymer models;
  • locality reductions;
  • pseudo'Boolean function;
  • quadratic unconstrained binary optimization (QUBO)

Summary

This chapter presents a general construction of the free energy function for the two-dimensional lattice heteropolymer model widely used to study the dynamics of proteins. It demonstrates how to map the lattice heteropolymer problem into forms that can be solved by using different types of technology and algorithms. The embedding strategies presented here apply to many discrete optimization problems. Mapping these problems to a constraint programming problem is a three-step process. The chapter provides a brief description of the process and expands upon each step as it applies to lattice folding. It explains the “circuit” construction that provides optimal efficiency at the cost of introducing high-ordered many-body terms. Finally, the chapter demonstrates the final steps required to embed a small instance of a particular lattice protein problem into a quadratic unconstrained binary optimization (QUBO) Hamiltonian.