Quantum-Inspired Approximations to Constraint Satisfaction Problems

TL;DR

This paper introduces quantum-inspired algorithms for constraint satisfaction problems that leverage Boolean Fourier analysis to efficiently approximate solutions, showing competitive results against local solvers for SAT.

Contribution

It presents a novel approximation framework based on Fourier analysis inspired by quantum algorithms, enabling efficient retrieval of solutions in CSPs.

Findings

Competitive performance against local SAT solvers

Effective use of Fourier sparsity for solution retrieval

Potential for evolutionary solver design

Abstract

Two contrasting algorithmic paradigms for constraint satisfaction problems are successive local explorations of neighboring configurations versus producing new configurations using global information about the problem (e.g. approximating the marginals of the probability distribution which is uniform over satisfying configurations). This paper presents new algorithms for the latter framework, ultimately producing estimates for satisfying configurations using methods from Boolean Fourier analysis. The approach is broadly inspired by the quantum amplitude amplification algorithm in that it maximally increases the amplitude of the approximation function over satisfying configurations given sequential refinements. We demonstrate that satisfying solutions may be retrieved in a process analogous to quantum measurement made efficient by sparsity in the Fourier domain, and present a complete solver construction using this novel approximation. Freedom in the refinement strategy invites further opportunities to design solvers in an evolutionary computing framework. Results demonstrate competitive performance against local solvers for the Boolean satisfiability (SAT) problem, encouraging future work in understanding the connections between Boolean Fourier analysis and constraint satisfaction.