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 nonadiabatic evolution. The proposed gate is actually a geometric gate that consolidates the nonadiabatic holonomic control and the unconventional geometric control simultaneously. The interference between two different types of geometric phases can be investigated in the proposal. Furthermore, we show that the actuating quantity (the product of interaction strength and the evolution time) of the proposed scheme is 90 times smaller 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.

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• Quantum gates
• Rydberg atoms & molecules