Quantum Modeling of Spatial Contiguity Constraints

TL;DR

This paper introduces quantum formulations for spatial regionalization problems with contiguity constraints, using a flow model and hybrid approaches to enable quantum optimization on small and large datasets.

Contribution

It presents novel quantum models incorporating spatial contiguity, including a scale-aware DQM and hybrid methods for larger problems, advancing quantum spatial optimization.

Findings

Quantum flow model enforces spatial contiguity constraints.

Hybrid quantum-classical approach manages larger datasets.

Framework paves the way for practical quantum spatial optimization.

Abstract

Quantum computing has demonstrated potential for solving complex optimization problems; however, its application to spatial regionalization remains underexplored. Spatial contiguity, a fundamental constraint requiring spatial entities to form connected components, significantly increases the complexity of regionalization problems, which are typically challenging for quantum modeling. This paper proposes novel quantum formulations based on a flow model that enforces spatial contiguity constraints. Our scale-aware approach employs a Discrete Quadratic Model (DQM), solvable directly on quantum annealing hardware for small-scale datasets. In addition, it designs a hybrid quantum-classical approach to manage larger-scale problems within existing hardware limitations. This work establishes a foundational framework for integrating quantum methods into practical spatial optimization tasks.