Quantum-Inspired Constraint Satisfaction with Non-Deterministic Search

Jincheng Zhang

Published Sep 5, 2026• 0 citations

Abstract

Constraint satisfaction problems (CSPs) represent a significant class of computationally challenging problems. Traditional deterministic search algorithms often struggle to find optimal or even feasible solutions within reasonable timeframes, particularly as the problem size and complexity increase. This paper proposes a novel approach to CSP solving inspired by the principles of quantum mechanics, specifically leveraging non-deterministic search strategies. The core idea is to mimic quantum phenomena like superposition and interference through probabilistic branching and quantum-inspired algorithms, such as quantum walks. This framework aims to enhance the exploration of the solution space, significantly improving the chances of identifying a valid solution. The proposed method is evaluated theoretically and through conceptual design, demonstrating its potential to address the limitations of classical CSP solvers. The key contribution lies in the integration of quantum-inspired techniques within a CSP framework, offering a promising avenue for tackling complex constraint satisfaction tasks. The algorithm utilizes a probability distribution to guide the search, represented as (Pi, Si), where Pi is the probability of selecting branch *i* and Si is the set of variables that can be assigned values in branch *i*. The objective function is then defined as minimizing the expected number of steps to find a solution, denoted as E[Steps], where Steps = Σi (Pi * |Si|) . We aim to reduce the expected number of steps to find a valid solution to a given CSP.

DOI: 10.5281/zenodo.22314563

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