Variational Quantum Algorithm for Constrained Topology Optimization

Abstract: One of the challenging scientific computing problems is topology optimization, where searching through the combinatorially complex configurations and solving the constraints of partial differential equations need to be done simultaneously. In this paper, a novel variational quantum algorithm for constrained topology optimization is proposed, which allows for the single-loop parallel search for the optimal configuration that also satisfies the physical constraints. The optimal configurations and the solutions to physical constraints are encoded with two separate registers. A constraint encoding scheme is also proposed to incorporate volume and connectivity constraints in optimization. The gate complexity of the proposed quantum algorithm is analyzed. The algorithm is demonstrated with compliance minimization problems including truss structures and Messerschmitt-B\"{o}lkow-Blohm beams.