  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.
