Complexity-controlled QUBO formulation for topology optimization via anisotropic mesh adaptation

69/2026

Complexity-controlled QUBO formulation for topology optimization via anisotropic mesh adaptation

Friday 4th September 2026

Zecchi, A. A.; Ferro, N.; Perotto, S.

QUBO formulation provides a natural route to address topology optimization of continuum structures with classical heuristic, quantum-inspired, and quantum annealing solvers. Their practical applicability, however, is still limited by the number of binary variables that can be handled, especially on near-term quantum hardware. In this work, we tackle this bottleneck by proposing QUBOSIMPATY algorithm which combines a QUBO formulation of the SIMP minimum compliance problem with anisotropic recovery-based mesh adaptation, enriched with metric-based complexity control. Specifically, we exploit anisotropic mesh adaptation to reduce the number of density degrees of freedom, while retaining directional resolution along the sharp material-void interfaces that characterize optimized layouts. A metric rescaling procedure is applied to prescribe the number of mesh vertices, and hence the number of binary variables, so as to comply with the severe size constraints imposed by quantum annealing hardware. Numerical tests in two and three dimensions are carried out with classical QUBO heuristics, including simulated annealing and tabu search. Moreover, a proof-of-concept experiment is performed on quantum annealing hardware. The results show that the proposed strategy improves the suppression of intermediate densities while keeping the optimization problem within the admissible size range.