Quantum Computing for Optimizing Aircraft Loading

The aircraft loading optimization problem is a computationally hard problem with the best known classical algorithm scaling exponentially with the number of objects. We propose a quantum approach based on a multi-angle variant of the QAOA algorithm (Multi-Angle Layered Variational Quantum Algorithm (MAL-VQA)) designed to utilize a smaller number of two qubit gates in the quantum circuit as compared to the standard QAOA algorithm so that the quantum optimization algorithm can be run on near-term ion-trap quantum processing units (QPU). We also describe a novel cost function implementation that can handle many different types of inequality constraints without the overhead of introducing slack variables in the quantum circuit so that larger problems with complex constraints may be represented on near-term QPUs which have low qubit counts. We demonstrate the performance of the algorithm on different instances of the aircraft loading problem by execution on IonQ QPUs Aria and Forte. Our experiments obtain the optimal solutions for all the problem instances studied ranging from 12 qubits to 28 qubits. This shows the potential scalability of the method to significantly larger problem sizes with the improvement of quantum hardware in the near future as well as the robustness of the quantum algorithm against varying initial guesses and varying constraints of different problem instances.