  The spread of intelligent transportation systems in urban cities has caused
heavy computational loads, requiring a novel architecture for managing
large-scale traffic. In this study, we develop a method for globally
controlling traffic signals arranged on a square lattice by means of a quantum
annealing machine, namely the D-Wave quantum annealer. We first formulate a
signal optimization problem that minimizes the imbalance of traffic flows in
two orthogonal directions. Then we reformulate this problem as an Ising
Hamiltonian, which is fully compatible with quantum annealers. The new control
method is compared with a conventional local control method for a large
50-by-50 city, and the results exhibit the superiority of our global control
method in suppressing traffic imbalance over wide parameter ranges.
Furthermore, the solutions to the global control method obtained with the
quantum annealing machine are better than those obtained with conventional
simulated annealing. In addition, we prove analytically that the local and the
global control methods converge at the limit where cars have equal
probabilities for turning and going straight. These results are verified with
numerical experiments.
