Quantum annealing with inequality constraints: the set cover problem

This paper presents two novel approaches for solving the set cover problem (SCP) with multiple inequality constraints on quantum annealers. The first method uses the augmented Lagrangian approach to represent the constraints, while the second method employs a higher-order binary optimization (HUBO) formulation. Our experimental analysis demonstrate that both approaches outperform the standard approach with slack variables for solving problems with inequality constraints on D-Wave quantum annealers. The results show that the augmented Lagrangian method can be successfully used to implement a large number of inequality constraints, making it applicable to a wide range of constrained problems beyond the SCP. The HUBO formulation performs slightly better than the augmented Lagrangian method in solving the SCP, but it is less scalable in terms of embeddability in the quantum chip. These findings could impact the use of quantum annealers for solving constrained optimization problems.