Graph representations are a powerful concept for solving complex problems across natural science, as patterns of connectivity can give rise to a multitude of emergent phenomena. Graph-based approaches have proven particularly fruitful in quantum communication and quantum search algorithms in highly branched quantum networks. Here, we introduce a previously unidentified paradigm for the direct experimental realization of excitation dynamics associated with three-dimensional networks by exploiting the hybrid action of spatial and polarization degrees of freedom of photon pairs in complex waveguide circuits with tailored birefringence. This testbed for the experimental exploration of multiparticle quantum walks on complex, highly connected graphs paves the way toward exploiting the applicative potential of fermionic dynamics in integrated quantum photonics.

图形表示法是解决自然科学中复杂问题的有力概念，因为连通性模式会引起多种新兴现象。在高度分支的量子网络中，基于图的方法已被证明在量子通信和量子搜索算法中特别有用。在这里，我们通过利用复杂的具有双折射的波导电路中的光子对的空间和偏振自由度的混合作用，为与三维网络相关的激发动力学的直接实验实现引入了一个以前未知的范例。该试验台是对复杂的多粒子量子步态进行实验性探索的平台，