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When tackling binary optimization problems using quantum algorithms, the
conventional Ising representation and Quantum Approximate Optimization
Algorithm (QAOA) encounter difficulties in efficiently handling errors for
large-scale problems involving multiple constraints. To address these
challenges, this paper presents a hybrid framework that combines the use of
standard Ising Hamiltonians to solve a subset of the constraints, while
employing non-Ising formulations to represent and address the remaining
constraints. The resolution of these non-Ising constraints is achieved through
either penalty dephasing or the quantum Zeno effect. This innovative approach
leads to a collection of quantum circuits with adaptable structures, depending
on the chosen representation for each constraint. Furthermore, this paper
introduces a novel technique that utilizes the quantum Zeno effect by
frequently measuring the constraint flag, enabling the resolution of any
optimization constraint. Theoretical properties of these algorithms are
discussed, and their performance in addressing practical aircraft loading
problems is highly promising, showcasing significant potential for a wide range
of industrial applications.
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