Reframing Population Genetic Structure as a Quantum Optimization Problem

Population genetic structure is commonly inferred using statistical and ordination-based methods that emphasize variance partitioning or likelihood-based clustering. While powerful, these approaches may undersample the full space of possible population partitions, particularly in systems characterized by weak genetic differentiation and high connectivity. Here, I present a proof-of-concept framework that reframes population genetic distance data as a combinatorial optimization problem, enabling structure to be interrogated through a distinct computational lens. Pairwise genetic distances derived from mitochondrial COI sequences of the shell-boring polychaete Polydora websteri are represented as a weighted graph and optimized using a quantum-inspired implementation of the Max-Cut problem via the Quantum Approximate Optimization Algorithm (QAOA). Using small, tractable datasets, I demonstrate that this approach recovers partitions consistent with classical analyses without claiming improved inference or computational advantage. Rather, the contribution of this work lies in establishing a transparent and reproducible mapping between population genetic distance structure and quantum-ready optimization frameworks, providing methodological groundwork for future studies using high-dimensional genomic SNP data.