Speaker
Description
We investigate the quantum-circuit realization of protected edge states in one-dimensional discrete-time quantum walks. Quantum walks provide a versatile framework for studying topological phenomena in periodically driven quantum systems, where the interplay between coin operations, conditional translations, and spatially varying parameters can give rise to localized states at interfaces between distinct topological phases. In this work, we develop a quantum-circuit representation of a one-dimensional quantum walk supporting protected edge states and analyze the corresponding quasienergy spectrum and spatial probability distributions. By engineering the coin and shift operations through elementary quantum gates, we establish a direct connection between the effective dynamics of the quantum walk and its circuit implementation. Particular attention is given to the robustness of the edge states against perturbations and to their signatures in measurable probability distributions. Numerical simulations are used to characterize the localization and topological protection of the interface states, while quantum-circuit simulations provide a framework for studying their implementation on quantum hardware. This approach demonstrates how programmable quantum circuits can be employed to investigate topological phases and protected boundary phenomena in discrete-time quantum systems, providing a bridge between theoretical models of quantum walks and experimentally accessible quantum simulations.
