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

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 conflictresolution 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.

Reverse quantum annealing approach to portfolio optimization problems

“…These machines are manufactured by D-Wave Systems and appeared on the market in 2011, and while being limited in programmability with respect to other experimental devices under testing by other companies, are still the only available quantum devices that feature a sufficient amount of quantum memory (qubits) to be applied to non-trivial problems at the time of writing. For this reason they are subject to extensive empirical investigation by several groups around the world, not only for scientific and research purposes [1,2], but also for performance evaluation on structured real world optimization challenges [3,4,5]. It is expected that as quantum computing devices mature, they'd become available to enterprises for use through dedicated cloud services [6].…”

Quantum adiabatic machine learning by zooming into a region of the energy surface

“…One promising near-term avenue for quantum machine learning is quantum annealing [17] (for recent reviews see [18][19][20]) which can, e.g., perform binary classification [21,22], learn Bayesian network structure [23], implement quantum Boltzmann machines [24], train deep generative models [25], and implement support vector machines [26]. Quantum annealing is the only current quantum computing paradigm that has resulted in architectures with a large enough number of-albeit relatively noisy-qubits [27][28][29] to address both real-world and fundamental science prob-lems, e.g., in air traffic control [30], computational biology [31][32][33], and high-energy physics [34][35][36]. Under the adiabatic theorem of quantum mechanics, quantum annealing evolves from an initial transverse field Hamiltonian to the target problem Hamiltonian, ensuring that the system remains in the ground state if the system is perturbed slowly enough, as given by the energy gap between the ground state and the first excited state [37][38][39].…”

Domain wall encoding of discrete variables for quantum annealing and QAOA

“…Moreover, conflicts can occur if certain pairs of events, occuring at t k and t l overlap, which means that either 0 ≤ t l − t k < T k or 0 ≤ t k − t l < T l . In both the domain wall and one hot encoding, single variable penalties correspond to single body Ising terms in the encoding, therefore, the problem structure is not changed by adding such penalties, which could correspond for example to penalties for delaying a flight in [17].…”