We consider a railway dispatching problem: delay and conflict management on a single-track railway line. We examine the issue of train dispatching consequences caused by the arrival of an already delayed train to the segment being considered. This is a computationally hard problem and its solution is needed in a very short time in practice. We introduce a quadratic unconstrained binary optimization (QUBO) model of the problem that is suitable for solving on quantum annealer devices: an emerging alternative computational hardware technology. These offer a scalability of computationally hard problems better than that of classical computers. We provide a proof-of-principle demonstration of applicability through solving selected real-life problems from the Polish railway network. We carry out the actual calculation on the D-Wave 2000Q machine. We also include solutions of our model using classical algorithms for solving QUBO, including those based on tensor networks. These are of potential practical relevance in case of smaller instances and serve as a comparison for understanding the behavior of the actual quantum device.

中文翻译：

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单线铁路铁路调度与冲突管理优化的量子计算方法

我们考虑一个铁路调度问题：单轨铁路线上的延误和冲突管理。我们研究了由于已经延误的列车到达正在考虑的路段而导致的列车调度后果问题。这是一个计算困难的问题，在实践中需要在很短的时间内解决。我们介绍了适用于解决量子退火设备的问题的二次无约束二进制优化 (QUBO) 模型：一种新兴的替代计算硬件技术。这些提供了比经典计算机更好的计算难题的可扩展性。我们通过解决波兰铁路网络中选定的现实问题，提供适用性的原理验证演示。我们在 D-Wave 2000Q 机器上进行实际计算。我们还包括使用经典算法解决 QUBO 的模型的解决方案，包括基于张量网络的解决方案。这些在较小实例的情况下具有潜在的实际相关性，并可作为理解实际量子设备行为的比较。