Zeno Freezing and Anti-Zeno Acceleration of the Dynamic Evolution of Topological Boundary States

Measurements fundamentally alter the evolution of a quantum system by disturbing its state, which can either freeze its dynamics (quantum Zeno effect, ZE) or accelerate transitions (anti-Zeno effect, AZE). While these effects are well established for ordinary quantum states, their impact on topological states - renowned for their robustness against disorder - has remained unexplored. Here we explore this interplay in a classical wave analog of quantum dynamics, demonstrating both theoretically and experimentally that topological boundary states can be controlled by quantumlike measurements implemented in spatially modulated acoustic waveguides. By introducing controlled perturbations, we emulate repeated measurements and reveal how they freeze or accelerate boundary-state tunneling. Using a geometric framework based on the quantum metric, we identify the general conditions for ZE and AZE, and further uncover a new tunneling mechanism enabled by varying measurement strength. These results establish quantumlike measurement as a versatile tool for manipulating topological states and wave propagation, with broad relevance to photonic, elastic, and quantum systems.