Optimal Control of Traffic Signals using Quantum Annealing

Abstract: Quadratic unconstrained binary optimization (QUBO) is the mathematical formalism for phrasing and solving a class of optimization problems that are combinatorial in nature. Due to their natural equivalence with the two dimensional Ising model for ferromagnetism in statistical mechanics, problems from the QUBO class can be solved on quantum annealing hardware. In this paper, we report a QUBO formatting of the problem of optimal control of time-dependent traffic signals on an artificial grid-structured road network so as to ease the flow of traffic, and the use of D-Wave Systems' quantum annealer to solve it. Since current-generation D-Wave annealers have a limited number of qubits and limited inter-qubit connectivity, we adopt a hybrid (classical/quantum) approach to this problem. As traffic flow is a continuous and evolving phenomenon, we address this time-dependent problem by adopting a workflow to generate and solve multiple problem instances periodically.