Conversion of Boolean and Integer FlatZinc Builtins to Quadratic or Linear Integer Problems

TL;DR

This paper presents a method to convert high-level FlatZinc models with Boolean and integer variables into quadratic or linear integer problems suitable for quantum computing, enabling quantum solvers to handle complex constraint models.

Contribution

It introduces a systematic approach to reformulate FlatZinc builtins into quadratic or linear integer problems for quantum optimization.

Findings

Reformulation of FlatZinc models into quadratic integer programs.

Transformation of quadratic integer programs into QUBO models.

Facilitation of quantum computing solutions for constraint satisfaction problems.

Abstract

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.