Quantum Algorithms for Drone Mission Planning

TL;DR

This paper explores the application of near-term quantum algorithms to solve complex drone mission planning problems, formulating them as QUBO problems and testing solutions on quantum annealers and variational algorithms.

Contribution

It introduces a versatile QUBO formulation for drone routing problems and compares quantum annealing, QAOA, and VQE methods against classical solvers.

Findings

Quantum annealers can find solutions comparable to classical solvers.

QAOA and VQE show promise but require further optimization.

Formulation scales clearly with problem size and constraints.

Abstract

Mission planning often involves optimising the use of ISR (Intelligence, Surveillance and Reconnaissance) assets in order to achieve a set of mission objectives within allowed parameters subject to constraints. The missions of interest here, involve routing multiple UAVs visiting multiple targets, utilising sensors to capture data relating to each target. Finding such solutions is often an NP-Hard problem and cannot be solved efficiently on classical computers. Furthermore, during the mission new constraints and objectives may arise, requiring a new solution to be computed within a short time period. To achieve this we investigate near term quantum algorithms that have the potential to offer speed-ups against current classical methods. We demonstrate how a large family of these problems can be formulated as a Mixed Integer Linear Program (MILP) and then converted to a Quadratic Unconstrained Binary Optimisation (QUBO). The formulation provided is versatile and can be adapted for many different constraints with clear qubit scaling provided. We discuss the results of solving the QUBO formulation using commercial quantum annealers and compare the solutions to current edge classical solvers. We also analyse the results from solving the QUBO using Quantum Approximate Optimisation Algorithms (QAOA) and discuss their results. Finally, we also provide efficient methods to encode to the problem into the Variational Quantum Eigensolver (VQE) formalism, where we have tailored the ansatz to the problem making efficient use of the qubits available.