Development of Hamiltonian for Structural Applications by Quantum Annealing Assuming Finite Element Method

Abstract

ABSTRACT Quantum annealing is emerging as a practical tool for large‐scale combinatorial optimization. We map continuum displacements and element densities to binary variables, turning both deformation analysis and topology optimization into quadratic unconstrained binary optimization (QUBO) problems that run on today's annealers. Two formulations are compared: one derived from the stiffness equation and another from the minimum total potential energy. Benchmarks show the energy‐based QUBO matches finite‐element displacements and stresses more closely and avoids the rapid term‐count growth that slows the stiffness‐based form. The numerical demonstrations reported here include deformation analysis of a 100‐element plate model and topology optimization of cantilever beams discretized with up to 60 triangular elements or 32 rectangular elements. These examples are intended as proof‐of‐concept demonstrations under current hardware and encoding limitations rather than as large‐scale industrial benchmarks. Leveraging this model, a single QUBO embedding density variables–implemented with combinatorial random‐number sums and a quadratic volume penalty–yields two‐dimensional beam layouts that are quantitatively compared with those obtained using the classical Optimality Criteria (OC) method.