Floquet chiral quantum walk in a quantum computer

Abstract

Chiral edge states in a quantum Hall effect are the paradigmatic example of a quasiparticle with chirality. In even space-time dimensions, the Nielsen-Ninomiya theorem strictly forbids chiral states in physical isolation. The exceptions to this theorem only occur in the presence of nonlocality, non-Hermiticity, or by embedding the system at the boundary of the higher-dimensional bulk. In this Letter, using the IBM quantum computer platform, we realize a Floquet chiral quantum walk enabled by nonlocality. The unitary time-evolution operator is described by an effective Floquet Hamiltonian with long-ranged coupling. We find that the chiral wave packets lack the common features of conventional wave phenomena such as localization. The absence of localization is witnessed by the robustness against external perturbations. However, the intrinsic quantum errors of the current quantum device give rise to a 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 a conventional nonchiral model.