Embedding Inequality Constraints for Quantum Annealing Optimization
Quantum annealing is a model for quantum computing that is aimed at solving hard optimization problems by representing them as quadratic unconstrained binary optimization (QUBO) problems. Although many NP-hard problems can easily be formulated as binary-variable problems with a quadratic objective function, such formulations typically also include constraints, which are not allowed in a QUBO. Hence, such constraints are usually incorporated in the objective function as additive penalty terms. While there is substantial previous work on implementing linear equality constraints, the case of inequality constraints has not much been studied. In this paper, we propose a new approach for formulating and embedding inequality constraints as penalties and describe early implementation results.
Research presented in this article was supported by the Laboratory Directed Research and Development program of Los Alamos National Laboratory under project numbers 20180267ER and 20190065DR. This work was also supported by the U.S. Department of Energy through Los Alamos National Laboratory. Los Alamos National Laboratory is operated by Triad National Security, LLC for the National Nuclear Security Administration of the U.S. Department of Energy (contract no. 89233218CNA000001).
- 6.D-Wave Systems Inc.: D-Wave’s Ocean Software. https://ocean.dwavesys.com/
- 7.D-Wave Systems Inc.: Measuring computation time on D-Wave systems. User Manual 09–1107A-G, 2 February 2018Google Scholar
- 9.Gurobi Optimization Inc.: Gurobi optimizer reference manual (2015)Google Scholar
- 14.Vyskocil, T., Djidjev, H.: Optimization approach to constraint embedding for quantum annealers. Technical report LA-UR-18-30971, Los Alamos National Laboratory (2018)Google Scholar
- 15.Vyskocil, T., Djidjev, H.: Simple constraint embedding for quantum annealers. In: International Conference on Rebooting Computing (2018, to appear)Google Scholar