Quantum-Inspired Probabilistic Constraint Satisfaction
Jincheng Zhang
This paper introduces a novel approach to constraint satisfaction problems (CSPs) inspired by the principles of quantum mechanics, specifically superposition and measurement. Traditional CSP solvers often rely on exhaustive search or heuristics, which can be computationally expensive, especially for large-scale problems. Our method, termed Quantum-Inspired Probabilistic Constraint Satisfaction (QIPCS), utilizes probabilistic representations of candidate solutions as superposition states. Each state is associated with a probability distribution reflecting the likelihood of different assignment values satisfying the constraints. The core mechanism involves simulating "measurement" operations, analogous to quantum measurement, to collapse these superposition states. This collapse process iteratively focuses the search on more promising regions of the solution space, guided by probabilistic constraints. We formulate the process mathematically, introducing notation for state representation, probability distributions, measurement operators, and the collapse mechanism. The key innovation lies in explicitly modeling quantum-like superposition and measurement, which we hypothesize can lead to more efficient exploration of the solution space compared to purely classical probabilistic techniques. We outline the theoretical framework and provide a conceptual description of the QIPCS algorithm, highlighting its potential advantages and future research directions.
•Aug 31, 2026•0 citations