Variational Quantum Algorithm for Constrained Topology Optimization

TL;DR

This paper introduces a new variational quantum algorithm designed to efficiently solve constrained topology optimization problems by encoding configurations and constraints separately, demonstrated on structural design cases.

Contribution

The paper presents a novel quantum algorithm that performs parallel search for optimal configurations while satisfying physical constraints, with a new constraint encoding scheme.

Findings

Algorithm successfully applied to compliance minimization problems

Gate complexity analyzed and discussed

Demonstrated on truss and beam structures

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.