Fractals are fascinating, not only for their aesthetic appeal but also for allowing the investigation of physical properties in non-integer dimensions. In these unconventional systems, many intrinsic features might come into play, including the fractal dimension and the fractal geometry. Despite abundant theoretical studies, experiments in fractal networks remain elusive. Here we experimentally investigate quantum transport in fractal networks by performing continuous-time quantum walks in fractal photonic lattices. We unveil the transport properties through the photon evolution patterns, the mean square displacement and the Pólya number. Contrarily to classical fractals, we observe anomalous transport governed solely by the fractal dimension. In addition, the critical point at which there is a transition from normal to anomalous transport depends on the fractal geometry. Our experiment allows the verification of physical laws in a quantitative manner and reveals the transport dynamics in great detail, thus opening a path to the understanding of more complex quantum phenomena governed by fractality.

分形令人着迷，不仅因为它们的美学吸引力，而且还因为它允许研究非整数维度的物理特性。在这些非常规系统中，许多内在特征可能会发挥作用，包括分形维数和分形几何。尽管进行了大量的理论研究，但分形网络的实验仍然难以捉摸。在这里，我们通过在分形光子晶格中执行连续时间量子游走来实验研究分形网络中的量子传输。我们通过光子演化模式、均方位移和 Pólya 数揭示了传输特性。与经典分形相反，我们观察到仅由分形维数控制的异常传输。此外，从正常传输到异常传输的临界点取决于分形几何。我们的实验允许以定量的方式验证物理定律，并详细揭示传输动力学，从而为理解由分形支配的更复杂的量子现象开辟了道路。