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.

中文翻译：

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使用 D-Wave Quantum Annealer 在方格上优化交通信号

智能交通系统在城市中的普及造成了沉重的计算负载，需要一种新颖的架构来管理大规模交通。在这项研究中，我们开发了一种通过量子退火机（即 D-Wave 量子退火机）全局控制排列在方形晶格上的交通信号的方法。我们首先制定了一个信号优化问题，以最小化两个正交方向上的交通流不平衡。然后我们将这个问题重新表述为 Ising Hamiltonian，它与量子退火器完全兼容。将新的控制方法与传统的 50×50 城市的局部控制方法进行比较，结果表明我们的全局控制方法在抑制宽参数范围内的交通不平衡方面具有优越性。此外，量子退火机得到的全局控制方法的解比传统模拟退火得到的解更好。此外，我们通过分析证明局部和全局控制方法收敛于汽车转弯和直行概率相等的极限。这些结果通过数值实验得到验证。