Quantum walks are powerful kernels in quantum computing protocols, and possess strong capabilities in speeding up various simulation and optimization tasks. One striking example is provided by quantum walkers evolving on glued trees¹, which demonstrate faster hitting performances than classical random walks. However, their experimental implementation is challenging, as this involves highly complex arrangements of an exponentially increasing number of nodes. Here, we propose an alternative structure with a polynomially increasing number of nodes. We successfully map such graphs on quantum photonic chips using femtosecond-laser direct writing techniques in a geometrically scalable fashion. We experimentally demonstrate quantum fast hitting by implementing two-dimensional quantum walks on graphs with up to 160 nodes and a depth of eight layers, achieving a linear relationship between the optimal hitting time and the network depth. Our results open up a scalable path towards quantum speed-up in classically intractable complex problems.

量子游走是量子计算协议中的强大内核，并且具有加快各种仿真和优化任务的强大功能。量子步行者在胶合树上进化提供了一个引人注目的例子¹，与传统的随机走步相比，其击球性能更快。但是，它们的实验实现具有挑战性，因为这涉及到节点数量呈指数增长的高度复杂的安排。在这里，我们提出了一种节点数量呈多项式增长的替代结构。我们使用飞秒激光直接写入技术以几何可缩放的方式成功地在量子光子芯片上绘制了这样的图。我们通过在具有多达160个节点和八层深度的图形上实现二维量子游走，以实现最佳命中时间与网络深度之间的线性关系，通过实验证明了量子快速命中。我们的结果为经典棘手的复杂问题开辟了一条通往量子加速的可扩展途径。