This paper introduces Quantum-Enhanced Constraint Satisfaction (QECS), a novel algorithm designed to accelerate the solution of complex optimization problems using quantum annealing. Traditional constraint satisfaction algorithms often struggle with large, high-dimensional search spaces, limiting their effectiveness. QECS leverages quantum annealing to efficiently explore the solution space, potentially offering exponential speedups compared to classical methods. The core mechanism centers on using quantum annealing to identify and exploit local optima, significantly reducing the computational cost of finding optimal solutions. We present a detailed analysis of the algorithm's performance, demonstrating its potential for substantial improvements in optimization tasks across diverse problem domains.
Constraint satisfaction or optimisation models -- even if they are formulated in high-level modelling languages -- need to be reduced into an equivalent format before they can be solved by the use of Quantum Computing. In this paper we show how Boolean and integer FlatZinc builtins over finite-domain integer variables can be equivalently reformulated as linear equations, linear inequalities or binary products of those variables, i.e. as finite-domain quadratic integer programs. Those quadratic integer programs can be further transformed into equivalent Quadratic Unconstrained Binary Optimisation problem models, i.e. a general format for optimisation problems to be solved on Quantum Computers especially on Quantum Annealers.