Quantum topology optimization of ground structures using noisy intermediate-scale quantum devices

Abstract: To arrive at some viable product design, product development processes frequently use numerical simulations and mathematical programming techniques. Topology optimization, in particular, is one of the most promising techniques for generating insightful design choices. Topology optimization problems reduce to an NP-hard combinatorial optimization problem, where the combination of the existence or absence of the material at some positions is optimized. In this study, we examine the usage of quantum computers as a potential solution to topology optimization problems. The proposed method consists of two variational quantum algorithms (VQAs): the first solves the state equilibrium equation for all conceivable material configurations, while the second amplifies the likelihood of an optimal configuration in quantum superposition using the first VQA's quantum state. Several experiments, including a real device experiment, show that the proposed method successfully obtained the optimal configurations. These findings suggest that quantum computers could be a potential tool for solving topology optimization problems and they open the window to the near-future product designs.