Quantum walks provide a speed-up in computational power for various quantum algorithms and serve as inspiration for the construction of complex graph representations. Many pioneering works have been dedicated to expanding the experimental state space and the complexity of graphs. However, these experiments are mostly limited to small experimental scale, which do not reach a many-body level and fail to reflect the multi-particle quantum interference effects among non-adjacent modes. Here, we present a quantum walk with three photons on a two-dimensional triangular lattice, which is mapped to a 19 × 19 × 19 high-dimensional state space and constructs a complex graph with 6859 nodes and 45,486 edges. By utilizing the statistical signatures of the output combinations and incorporating machine learning techniques, we successfully validate the nonclassical properties of the experiment. Our implementation provides a paradigm for exponentially expanding the state space and graph complexity of quantum walks, paving the way for surmounting the classical regime in large-scale quantum simulations.

量子游走为各种量子算法提供了计算能力的加速，并为构建复杂的图形表示提供了灵感。许多开创性的工作都致力于扩展实验状态空间和图的复杂性。然而，这些实验大多局限于小实验尺度，没有达到多体水平，无法反映非相邻模式之间的多粒子量子干涉效应。在这里，我们提出了一个在二维三角晶格上具有三个光子的量子游走，该量子游走被映射到 19 × 19 × 19 的高维状态空间，并构建了一个具有 6859 个节点和 45,486 条边的复杂图。通过利用输出组合的统计特征并结合机器学习技术，我们成功地验证了实验的非经典性质。我们的实现提供了一种范式，可以成倍地扩展量子游走的状态空间和图复杂性，为在大规模量子模拟中超越经典机制铺平了道路。