Quantum Modeling of Spatial Contiguity Constraints

2025-05-19

AI Summary

This paper addresses the quantum modeling challenge posed by connectivity constraints in spatial regionalization. We propose the first method to embed spatial continuity into a quantum optimization framework, formulating connectivity constraints as an end-to-end quantum-representable discrete quadratic model (DQM) built upon flow-based modeling—enabling native execution on quantum annealing hardware for small-scale instances. To balance accuracy and scalability, we further design a scale-adaptive hybrid quantum-classical framework, empirically validated on hundred-node-scale spatial problems. Our key contributions are: (1) the first explicit encoding of spatial connectivity within quantum optimization; (2) a hardware-executable DQM modeling paradigm tailored for spatial constraints; and (3) a foundational quantum-classical co-solution framework specifically designed for geospatial optimization. The approach bridges a critical gap between spatially constrained combinatorial problems and near-term quantum computing platforms.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Machine Learning: Quantum Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• Quantum modeling for spatial contiguity constraints in regionalization
• Flow-based quantum formulations to enforce spatial connectivity
• Hybrid quantum-classical approach for scalable spatial optimization

Innovation

• Quantum flow model enforces spatial contiguity constraints
• Scale-aware DQM for small datasets on quantum annealers
• Hybrid quantum-classical approach for larger-scale problems