# Towards Finding an Optimal Flight Gate Assignment on a Digital Quantum Computer

## TL;DR

This paper explores using a quantum algorithm called VQE to solve the airport gate assignment problem, showing promising results and better performance with entanglement, indicating potential for quantum optimization in complex logistical tasks.

## Contribution

The paper introduces a qubit-efficient binary encoding and applies CVaR-VQE to the gate assignment problem, demonstrating improved solution quality and favorable scaling on classical simulations.

## Key findings

- CVaR-VQE outperforms naive VQE in solution quality
- Entangling gates improve the performance of the ansatz
- Scaling of cost function calls is not exponential in tested regimes

## Abstract

We investigate the performance of the variational quantum eigensolver (VQE) for the optimal flight gate assignment problem. This problem is a combinatorial optimization problem that aims at finding an optimal assignment of flights to the gates of an airport, in order to minimize the passenger travel time. To study the problem, we adopt a qubit-efficient binary encoding with a cyclic mapping, which is suitable for a digital quantum computer. Using this encoding in conjunction with the Conditional Value at Risk (CVaR) as an aggregation function, we systematically explore the performance of the approach by classically simulating the CVaR-VQE. Our results indicate that the method allows for finding a good solution with high probability, and the method significantly outperforms the naive VQE approach. We examine the role of entanglement for the performance, and find that ans\"atze with entangling gates allow for better results than pure product states. Studying the problem for various sizes, our numerical data show that the scaling of the number of cost function calls for obtaining a good solution is not exponential for the regimes we investigate in this work.