Quantum walks on graphs play an important role in the field of quantum algorithms. Fast hitting is one of the properties that quantum walk algorithms can utilize to outperform classical random walk algorithms. Fast hitting refers to a particle starting from the entrance node on a graph and trying to hit the exit node quickly. Especially, continuous-time quantum walks on random glued binary trees have been investigated in theories extensively for their exponentially faster hitting speed over classical random walks. Here, using heralded single photons to represent quantum walkers and laser-written waveguide arrays to simulate the theoretical graph, we are able to demonstrate the hitting efficiency of quantum walks with tree depth as high as 16 layers for the first time. Furthermore, we expand the graph’s branching rate from 2 to 5, revealing that quantum walks can exhibit more superiority over classical random walks as the branching rate increases. Our results may shed light on the physical implementation of quantum walk algorithms as well as quantum computation and quantum simulation.

中文翻译：

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量子快速命中映射在光子芯片上的粘合树

图上的量子行走在量子算法领域中起着重要作用。快速命中是量子游走算法可以用来胜过经典随机游走算法的特性之一。快速命中是指从图形上的入口节点开始并尝试快速命中出口节点的粒子。特别是，在随机胶合二叉树上的连续时间量子游走已在理论上得到了广泛研究，因为它们的撞击速度比经典随机游走指数快。在这里，我们使用先驱的单个光子来表示量子步行器，并使用激光写入的波导阵列来模拟理论图，我们首次能够证明树深度高达16层的量子步行的命中效率。此外，我们将图的分支率从2扩展到5 揭示了随着分支速率的增加，量子步态比经典的随机步态更具优势。我们的结果可能会揭示量子行走算法的物理实现以及量子计算和量子模拟。