Quantum processes of inherent dynamical nature, such as quantum walks, defy a description in terms of an equilibrium statistical physics ensemble. Until now, identifying the general principles behind the underlying unitary quantum dynamics has remained a key challenge. Here, we show and experimentally observe that split-step quantum walks admit a characterization in terms of a dynamical topological order parameter (DTOP). This integer-quantized DTOP measures, at a given time, the winding of the geometric phase accumulated by the wavefunction during a quantum walk. We observe distinct dynamical regimes in our experimentally realized quantum walks, and each regime can be attributed to a qualitatively different temporal behavior of the DTOP. Upon identifying an equivalent many-body problem, we reveal an intriguing connection between the nonanalytic changes of the DTOP in quantum walks and the occurrence of dynamical quantum phase transitions.

固有动力学性质的量子过程，例如量子行走，无法用平衡统计物理系综来描述。到目前为止，确定基本单一量子动力学背后的一般原理仍然是一项关键挑战。在这里，我们展示并通过实验观察到，分步量子行走允许根据动态拓扑序参数 (DTOP) 进行表征。这个整数量化的 DTOP 在给定时间测量由波函数在量子游走期间累积的几何相位的缠绕。我们在实验实现的量子行走中观察到不同的动态机制，并且每个机制都可以归因于 DTOP 质量上不同的时间行为。在识别出等效的多体问题后，