  The quest for real-time dynamic optimization solutions in the process
industry represents a formidable computational challenge, particularly within
the realm of applications like model-predictive control, where rapid and
reliable computations are critical. Conventional methods can struggle to
surmount the complexities of such tasks. Quantum computing and quantum
annealing emerge as \textit{avant-garde} contenders to transcend conventional
computational constraints. We convert a dynamic optimization problem,
{characterized by an optimization problem with a system of
differential-algebraic equations embedded}, into a Quadratic Unconstrained
Binary Optimization problem, enabling quantum computational approaches. The
empirical findings synthesized from classical methods, simulated annealing,
quantum annealing via D-Wave's quantum annealer, and hybrid solver
methodologies, illuminate the intricate landscape of computational prowess
essential for tackling complex and high-dimensional dynamic optimization
problems. Our findings suggest that while quantum annealing is a maturing
technology that currently does not outperform state-of-the-art classical
solvers, continuous improvements could eventually aid in increasing efficiency
within the chemical process industry.
