Solving SAT and MaxSAT with a quantum annealer: Foundations and a preliminary report

Abstract

Quantum annealers (QA) are specialized quantum computers that minimize objective functions over discrete variables by physically exploiting quantum effects. Current QA platforms allow for the optimization of quadratic objectives defined over binary variables, that is, they solve quadratic unconstrained binary optimization (QUBO) problems. In the last decade, QA systems as implemented by D-Wave have scaled with Moore-like growth. Current architectures provide 2048 sparsely-connected qubits, and continued exponential growth is anticipated. We explore the feasibility of such architectures for solving SAT and MaxSAT problems as QA systems scale. We develop techniques for effectively encoding SAT and MaxSAT into QUBO problems compatible with sparse QA architectures. We provide the theoretical foundations for this mapping, and present encoding techniques that combine offline Satisfiability and Optimization Modulo Theories with on-the-fly placement and routing. Preliminary empirical tests on a current generation 2048-qubit D-Wave system support the feasibility of the approach. We provide details on our SMT model of the SAT-encoding problem in the hopes that further research may improve upon the scalability of this application of SMT technology. Further, these models generate hard SMT problems which may be useful as benchmarks for solvers.