Quantum-assisted finite-element design optimization

TL;DR

This paper presents a novel quantum-assisted finite-element method that uses a D-Wave quantum processor to optimize object shapes based on sound pressure simulations, integrating quantum and classical techniques.

Contribution

It introduces a quantum-assisted approach for shape optimization in finite-element design, demonstrating how quantum annealing can be integrated into the process.

Findings

Successful implementation of quantum-assisted shape optimization

Demonstrated minimization of sound pressure around an object

Framework for integrating quantum annealing with classical finite-element methods

Abstract

Quantum annealing devices such as the ones produced by D-Wave systems are typically used for solving optimization and sampling tasks, and in both academia and industry the characterization of their usefulness is subject to active research. Any problem that can naturally be described as a weighted, undirected graph may be a particularly interesting candidate, since such a problem may be formulated a as quadratic unconstrained binary optimization (QUBO) instance, which is solvable on D-Wave's Chimera graph architecture. In this paper, we introduce a quantum-assisted finite-element method for design optimization. We show that we can minimize a shape-specific quantity, in our case a ray approximation of sound pressure at a specific position around an object, by manipulating the shape of this object. Our algorithm belongs to the class of quantum-assisted algorithms, as the optimization task runs iteratively on a D-Wave 2000Q quantum processing unit (QPU), whereby the evaluation and interpretation of the results happens classically. Our first and foremost aim is to explain how to represent and solve parts of these problems with the help of a QPU, and not to prove supremacy over existing classical finite-element algorithms for design optimization.