Geometry-Induced Domain-Wall Pinning and Z2 Asymmetry in Nominally One-Dimensional Rydberg Arrays

This study investigates how the physical geometry of neutral-atom Rydberg arrays—specifically when arranged in 2D planes to mimic 1D models—affects quantum state configurations. The authors explore whether these systems, which are intended to simulate simple 1D Ising models, exhibit unexpected behaviors due to their spatial layout, such as corners and engineered vacancies.

The researchers utilized the QuEra Aquila quantum processor to perform quasi-adiabatic evolution on two specific 1D-like geometries: a 33-atom closed triangular array and a 47-atom square array with a single atom vacancy. By fine-tuning the laser detuning and Rabi frequency, they balanced the measurement statistics to achieve near-zero net magnetization. They then analyzed the spatial distribution of Rydberg states (excited) versus ground states and the resulting domain-wall statistics to identify deviations from standard 1D Ising model behavior.

The experiments revealed that the 1D models do not behave uniformly when embedded in a 2D plane. In the triangular array, next-nearest-neighbor interactions at the corners pin domain walls, lifting translational degeneracy. In the square array, the corners and the vacancy create a strong site-resolved texture; specifically, atoms adjacent to the vacancy and at the vertices show a marked preference for the Rydberg state. This breaks the expected Z2 symmetry of the Ising model, as the system exhibits a clear bias in its antiferromagnetic ordering that is not predicted by simple 1D theory.

These findings demonstrate that the physical arrangement of qubits in analog quantum computers can introduce unintended geometric constraints that significantly alter the system's Hamiltonian. For researchers using Rydberg arrays for quantum simulation or optimization, this highlights that "1D" models are not truly one-dimensional when implemented on a 2D grid, and that geometric features must be carefully accounted for to predict or control quantum state outcomes.