Quantum hybrid algorithm for solving SAT problem

Abstract

Combinatorial problems usually have a large search space, and almost all classical algorithms for solving this class of problems are inefficient for real-life input sizes. Quantum algorithms have been introduced with the aim of reducing computational time. In addition, to speed up the computation while solving combinatorial problems, another approach is to reduce the search space and focus on a restricted area. In this work, we study a parameter that helps reduce the search space for the solution to the satisfiability problem (SAT). We propose an approach based on Grover's algorithm that considers the defined parameter to reduce the search space for the solution of the SAT problem. Our algorithm has a complexity of the order O(N/S), or O(N/lS) if there are l good solutions among the initial solutions, with N the number of potential solutions and S the reduction or subdivision factor of the space.