  Signaled by non-analyticities in the time evolution of physical observables,
dynamic quantum phase transitions (DQPTs) emerge in quench dynamics of
topological systems and possess an interesting geometric origin captured by
dynamic topological order parameters (DTOPs). In this work, we report the
experimental study of DQPTs using discrete-time quantum walks of single
photons. We simulate quench dynamics between distinct Floquet topological
phases using quantum-walk dynamics, and experimentally characterize DQPTs and
the underlying DTOPs through interference-based measurements. The versatile
photonic quantum-walk platform further allows us to experimentally investigate
DQPTs for mixed states and in parity-time-symmetric non-unitary dynamics for
the first time. Our experiment directly confirms the relation between DQPTs and
DTOPs in quench dynamics of a topological system, and opens up the avenue of
simulating emergent topological phenomena using discrete-time quantum-walk
dynamics.
