  This paper presents a new structural design framework, developed based on
iterative optimization via quantum annealing (QA). The novelty lies in its
successful design update using an unknown design multiplier obtained by
iteratively solving the optimization problems with QA. In addition, to align
with density-based approaches in structural optimization, multipliers are
multiplicative to represent design material and serve as design variables. In
particular, structural analysis is performed on a classical computer using the
finite element method, and QA is utilized for topology updating. The primary
objective of the framework is to minimize compliance under an inequality volume
constraint, while an encoding process for the design variable is adopted,
enabling smooth iterative updates to the optimized design. The proposed
framework incorporates both penalty methods and slack variables to transform
the inequality constraint into an equality constraint and is implemented in a
quadratic unconstrained binary optimization (QUBO) model through QA. To
demonstrate its performance, design optimization is performed for both truss
and continuum structures. Promising results from these applications indicate
that the proposed framework is capable of creating an optimal shape and
topology similar to those benchmarked by the optimality criteria (OC) method on
a classical computer.
