Spatial Regionalization: A Hybrid Quantum Computing Approach

Quantum computing has shown significant potential to address complex optimization problems; however, its application remains confined to specific problems at limited scales. Spatial regionalization remains largely unexplored in quantum computing due to its complexity and large number of variables. In this paper, we introduce the first hybrid quantum-classical method to spatial regionalization by decomposing the problem into manageable subproblems, leveraging the strengths of both classical and quantum computation. This study establishes a foundational framework for effectively integrating quantum computing methods into realistic and complex spatial optimization tasks. Our initial results show a promising quantum performance advantage for a broad range of spatial regionalization problems and their variants.