  Quantum computing (QC) has gained popularity due to its unique capabilities
that are quite different from that of classical computers in terms of speed and
methods of operations. This paper proposes hybrid models and methods that
effectively leverage the complementary strengths of deterministic algorithms
and QC techniques to overcome combinatorial complexity for solving large-scale
mixed-integer programming problems. Four applications, namely the molecular
conformation problem, job-shop scheduling problem, manufacturing cell formation
problem, and the vehicle routing problem, are specifically addressed.
Large-scale instances of these application problems across multiple scales
ranging from molecular design to logistics optimization are computationally
challenging for deterministic optimization algorithms on classical computers.
To address the computational challenges, hybrid QC-based algorithms are
proposed and extensive computational experimental results are presented to
demonstrate their applicability and efficiency. The proposed QC-based solution
strategies enjoy high computational efficiency in terms of solution quality and
computation time, by utilizing the unique features of both classical and
quantum computers.
