Isolated zero mode in a quantum computer from a duality twist

TL;DR

This paper demonstrates the creation and detection of an isolated zero mode in a quantum computer by leveraging duality twists in a transverse-field Ising model, revealing robust topological features in digitized quantum systems.

Contribution

It introduces a method to generate and observe an isolated zero mode in a quantum computer using Floquet driving and duality defects, advancing the study of topological defects in quantum devices.

Findings

Zero mode detected via persistent autocorrelation measurements

Zero mode resides at domain walls related by duality

Zero mode remains robust against perturbations

Abstract

Investigating the interplay of dualities, generalized symmetries, and topological defects beyond theoretical models is an important challenge in condensed matter physics and quantum materials. A simple model exhibiting this physics is the transverse-field Ising model, which can host a topological defect that performs the Kramers-Wannier duality transformation. When acting on one point in space, this duality defect imposes the duality twisted boundary condition and binds a single zero mode. This zero mode is unusual as it lacks a localized partner in the same $\mathbb{Z}_2$ sector and has an infinite lifetime, even in finite systems. Using Floquet driving of a closed Ising chain with a duality defect, we generate this zero mode in a digital quantum computer. We detect the mode by measuring its associated persistent autocorrelation function using an efficient sampling protocol and a compound strategy for error mitigation. We also show that the zero mode resides at the domain wall between two regions related by a Kramers-Wannier duality transformation. Finally, we highlight the robustness of the isolated zero mode to integrability- and symmetry-breaking perturbations. Our findings provide a method for exploring exotic topological defects, associated with noninvertible generalized symmetries, in digitized quantum devices.