Classical and Quantum Optimization with Neural Networks

Professor Joe Gomes; University of Iowa, Department of Chemical and Biochemical Engineering

Bio: Joe Gomes is an assistant professor in the Chemical and Biochemical Engineering Department at the University of Iowa. He received a B.S. in Chemical Engineering from the University of Illinois-Chicago and a Ph.D. in Chemical Engineering from the University of California-Berkeley. He was a postdoctoral researcher in the Chemistry and Bioengineering Departments at Stanford University. Dr. Gomes conducts research in the areas of theoretical chemistry, machine learning, energy materials, and catalysis.

Abstract: Many important challenges in science and technology can be cast as optimization problems. The development of improved heuristic algorithms for determining approximate solutions to these optimization problems has high potential for impact across many disciplines. We propose an efficient heuristic algorithm for solving hard optimization problems which we refer to as “Classical Quantum Optimization” (CQO). Our approach consists of: (1) converting the optimization problem of interest into a (classical or quantum) spin glass Hamiltonian where the ground state configuration of this system encodes the optimal solution to the problem at hand, and (2) the variational optimization of a neural network representation of the ground state of the many-body system given by the problem-specific Hamiltonian. We demonstrate the utility of CQO on optimization problems found in graph theory. We compare CQO against other widely used heuristic solver algorithms and exact results when possible. The results show that CQO achieves state-of-the-art approximation ratio solutions for the MaxCut problem. We highlight potential applications of CQO towards solving the quantum chemical electronic structure problem.