Floquet Chiral Quantum Walk in Quantum Computer

Abstract

Chiral edge states in quantum Hall effect are the paradigmatic example of the quasi-particle with chirality. In even space-time dimensions, the Nielsen-Ninomiya theorem strictly forbids the chiral states in physical isolation. The exceptions to this theorem only occur in the presence of non-locality, non-Hermiticity, or by embedding the system at the boundary of the higher-dimensional bulk. In this work, using the IBM quantum computer platform, we realize the floquet chiral quantum walk enabled by non-locality. The unitary time evolution operator is described by the effective floquet Hamiltonian with infinitely long-ranged coupling. We find that the chiral wave packets lack the common features of the conventional wave phenomena such as Anderson localization. The absence of localization is witnessed by the robustness against the external perturbations. However, the intrinsic quantum errors of the current quantum device give rise to the finite lifetime where the chiral wave packet eventually disperses in the long-time limit. Nevertheless, we observe the stability of the chiral wave by comparing it with the conventional non-chiral model.