New-type geometric gates in atomic arrays without Rydberg blockade

TL;DR

This paper introduces a novel geometric controlled-phase gate for atomic arrays that operates without Rydberg blockade, offering robustness, efficiency, and insensitivity to atomic motion, expanding the possibilities for quantum control.

Contribution

It proposes a new geometric gate scheme combining non-adiabatic holonomic and unconventional geometric control without Rydberg blockade, reducing resource requirements.

Findings

Effective with large atomic spacings

Insensitive to atomic thermal motions

Requires fewer resources than Rydberg blockade schemes

Abstract

The Rydberg blockade effect plays an important role in realizing two-qubit gates in atomic arrays. Meanwhile, such mechanics will increase the crosstalk between atoms and enhance the decoherence. In this paper, we propose a new scheme to realize the controlled-phase gate without Rydberg blockade. The scheme works effectively with large atomic spacings and is insensitive to the thermal motions of atoms. The proposal is robust against random noises due to the geometric characteristic and operates fast based on the non-adiabatic evolution. The proposed gate is actually a new-type geometric gate that consolidates the non-adiabatic holonomic control and the unconventional geometric control simultaneously. The interference between two different types of geometric phases can be investigated. Furthermore, we show that the scheme with weak Rydberg interaction requires much less physical resources than the present Rydberg blockade scheme. Therefore, our proposal provides a fast and robust way to realize geometric quantum control, and it may trigger the discoveries of new geometric gates in high-dimensional Hilbert space.