Geometry-Induced Domain-Wall Pinning and $\mathbb{Z}_2$ Asymmetry in Nominally One-Dimensional Rydberg Arrays

Abstract

We perform experiments on QuEra's neutral-Rydberg-atom Aquila quantum computer, using quasi-adiabatic evolution on 1-dimensional models. We use hardware fine-tuning to balance the measurement statistics close to zero net magnetization, in two different geometric outlines: one closed triangular model with 33 atoms, and one 47-atom square with an engineered atom vacancy. The nature of this processor restricts the geometry of the atoms that can be programmed to a 2D plane. We report effects not predicted by the pure 1D Ising model, such as pinning of domain walls and $\mathbb{Z}_2$ symmetry breaking due to the interplay between van der Waals interactions and the Rydberg blockade. In particular, atoms around the atom vacancy and at the vertices of the 1-dimensional square-outline model strongly prefer the Rydberg state, leading to the effective model having a ferromagnetic bond across the vacancy.