Encoding the At-Most-One Constraint for QUBO and Quantum Annealing: Experiments with the N-Queens problem
Philippe Codognet · 2023
We present experiments in solving constrained optimization and constraint satisfaction problems by means of Quantum Annealing in terms of QUBO (Quadratic Unconstrained Binary Optimization). We investigate different QUBO formulations for the encoding of integers into Booleans and for the encoding of the At-Most-One constraint, which is used in combinatorial problems requiring capacity constraints. We compare four different QUBO models and report experiments done on the D-Wave annealing computer and the "quantum-inspired" Fixstars Amplify Annealing Engine. For this, we consider a simple example taken from the domain of Constraint Satisfaction Problems (CSP), the N-queens problem, as its formulation involves multiple instances of the At-Most-One constraints.