Core Concepts
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.
Abstract
The paper presents a method to transform Boolean and integer FlatZinc builtins into equivalent Quadratic Integer Programs (QIP(FD)). FlatZinc is a subset of the MiniZinc modeling language, which is commonly used to define constraint satisfaction or optimization problems (CSP/COP).
The key highlights are:
FlatZinc programs can be automatically transformed into QIP(FD) problems, which can then be further converted into Quadratic Unconstrained Binary Optimization (QUBO) problems. This allows solving a wide range of satisfaction and optimization problems using Quantum Computing, particularly Quantum Annealers.
The authors provide a detailed mapping of various FlatZinc builtins (e.g. array_int_element, int_div, bool_and, etc.) to their equivalent QIP(FD) representations using linear equations, linear inequalities, and binary variable products.
The QIP(FD) formulation ensures that the finite domains of the integer variables are respected, with the domains represented as bounds-consistent integer intervals.
The transformation preserves the structure and semantics of the original FlatZinc program, allowing the resulting QIP(FD) to be solved using Quantum Computing techniques.
The authors plan to implement a MiniZinc-to-QUBO workflow based on this work, further enabling the use of Quantum Computers for solving a broad range of constraint satisfaction and optimization problems.
Stats
The paper does not contain any specific numerical data or metrics. It focuses on the theoretical transformation of FlatZinc builtins to QIP(FD) representations.
Quotes
"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."
"This gives us the opportunity to transform a large class of MiniZinc programs into QUBO problems and solve them also by Quantum Computing, e.g. with Quantum Annealers."