  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.
