QUBO formulation using inequalities for problems with complex constraints
Tomoko Komiyama, Tomohiro Suzuki · 2024
Quantum annealing is an optimization technique that uses quantum fluctuation effects to search for solutions and is being applied as a metaheuristic method. Quantum annealing solves a problem expressed as quadratic unconstrained binary optimization (QUBO). Many practical problems have complex constraints, and formulating them can lead to third-order or higher expressions. In such cases, higher-order expressions have been converted to QUBO by order reduction. Various order reduction methods have been used, but they have issues, such as the need to add more auxiliary variables and difficulty in obtaining optimal solutions. This paper discusses a method for formulating problems with complex constraints using inequalities. In this approach, each constraint is defined as a linear function and added together to form an inequality. The inequality is then transformed to QUBO by introducing a slack variable. The application to the quantum minimum fill-in algorithm, a fill-in reduction ordering algorithm for sparse matrices, and the maximum satisfiability problem are also presented. The results of solving these problems with a quantum-inspired annealing machine show that higher-quality solutions are obtained with fewer variables than when using higher-order expressions with order reduction.