Quantum Annealing is an alternative type of computation in which problems are encoded in quantum Hamiltonians (energy functions) and quantum dynamics is used to find solutions (ground states of minimal energy). Quantum computers such as the D-Wave systems are indeed implementing those ideas in hardware, as well as “quantum-inspired” devices based on classical electronics such as Fujitsu’s Digital Annealing Unit. All those systems use the same modeling language: Quadratic Unconstrained Binary Optimization (QUBO). However, QUBO is a low-level language and for modeling combinatorial problems such as constraint satisfaction and constrained optimization problems, we need to introduce higher-level abstractions in order to define complex constraints.

We present in this paper an experience report on the use of a constraint-based methodology coming from the Constraint Programming paradigm for solving combinatorial problems by quantum computing, in particular for systems based on quantum annealing. We give a general overview of our recent works on Quantum Annealing and QUBO modeling and try to formulate the lessons learned from these experiments and possible research directions.