Multiple-qubit nonadiabatic noncyclic geometric quantum computation in Rydberg atoms

Abstract Single- and two-qubit nonadiabatic noncyclic geometric quantum computation (NNGQC) have been put forward in theory (Liu B.-J. et al. , Phys. Rev. Res. 2 (2020) 043130). The features of single-qubit NNGQC have been experimentally verified and the experimental technical route of the two-qubit case has been discussed in detail (Zhang J. W. et al. , Phys. Rev. Lett. 127 (2021) 030502). The multiple-qubit quantum logic gate is critical for quantum computation. Although combining a series of single- and two-qubit NNGQC gates can form universal operations and create arbitrary multiple-qubit gates, the created multiple-qubit gate often consumes more quantum resource and requires longer evolution time, which makes it more fragile to systematic error and decoherence. In this article, we propose a scheme to directly construct the multiple-qubit NNGQC gates in Rydberg atoms. The numerical results show that the proposed quantum gates have high fidelity and are robust to systemic error and decoherence. Our scheme may be applied in the future quantum computation and many-body quantum science studies.