Quantum Annealing Applied to De-Conflicting Optimal Trajectories for Air Traffic Management

TL;DR

This paper demonstrates how to map air traffic conflict resolution problems to QUBO form and successfully solve challenging subproblems using current quantum annealers with high probability.

Contribution

It introduces a novel conflict graph representation for ATM problems and benchmarks quantum annealing performance on real-world instances.

Findings

Quantum annealers solve most challenging subproblems with 99% success rate

Mapping ATM conflict resolution to QUBO enables quantum optimization techniques

Real-world instances can be decomposed into smaller subproblems suitable for current quantum hardware

Abstract

We present the mapping of a class of simplified air traffic management (ATM) problems (strategic conflict resolution) to quadratic unconstrained boolean optimization (QUBO) problems. The mapping is performed through an original representation of the conflict-resolution problem in terms of a conflict graph, where nodes of the graph represent flights and edges represent a potential conflict between flights. The representation allows a natural decomposition of a real world instance related to wind-optimal trajectories over the Atlantic ocean into smaller subproblems, that can be discretized and are amenable to be programmed in quantum annealers. In the study, we tested the new programming techniques and we benchmark the hardness of the instances using both classical solvers and the D-Wave 2X and D-Wave 2000Q quantum chip. The preliminary results show that for reasonable modeling choices the most challenging subproblems which are programmable in the current devices are solved to optimality with 99% of probability within a second of annealing time.