Quantum Algorithms for Drone Mission Planning

TL;DR

This work investigates near term quantum algorithms that have the potential to offer speed-ups against current classical methods and demonstrates how a large family of these problems can be formulated as a Mixed Integer Linear Program and then converted to a Quadratic Unconstrained Binary Optimisation (QUBO).

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.

Figures (7)

• Figure 1: (Left) Toy instance of drone mission with a single drone. Each edge has two associated parameters, the time taken to traverse the edge and the battery expended in the process. The drone in the problem has an initial battery of 4 units. (Right) One of the optimal routes the drone can take. At each node we show the current time and remaining battery level of the drone.
• Figure 2: (Left) Multi-agent TSP instance. Four drones must start and end at the base (circle). Edges shown must be traversed in either direction. (Right) Solution found using Gurobi with a running time of 180 seconds.
• Figure 3: Q-SWAP circuit. A classical optimiser is used to tune the optimal $\theta, \sigma,\tau$. Once this is done, they are added to the circuit and a new layer $e^{i \delta H},\, e^{i \theta V_{\sigma, \tau}}$ is added to optimise over.
• Figure 4: Circuit ansatzes for a various number nodes that can achieve all possible groundstates for the time indexed hamiltonian formulation of the travelling salesman problem. Parameters start randomised and then trained to reduce the expected cost of the route.
• Figure 5: TSP instances of sizes 6 and 7 nodes. Journeys start and end at the base, B.