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We propose a nonadiabatic non-Abelian geometric quantum operation scheme torealize universal quantum computation with mesoscopic Rydberg atoms. A singlecontrol atom entangles a mesoscopic ensemble of target atoms through long-rangeinteractions between Rydberg states. We demonstrate theoretically that both thesingle qubit and two-qubit quantum gates can achieve high fidelities around orabove 99.9% in ideal situations. Besides, to address the experimental issue ofRabi frequency fluctuation (Rabi error) in Rydberg atom and ensemble, we applythe dynamical-invariant-based zero systematic-error sensitivity (ZSS) optimalcontrol theory to the proposed scheme. Our numerical simulations show that theaverage fidelity could be 99.98% for single ensemble qubit gate and 99.94% fortwo-qubit gate even when the Rabi frequency of the gate laser acquires 10%fluctuations. We also find that the optimized scheme can also reduce errorscaused by higher-order perturbation terms in deriving the Hamiltonian of theensemble atoms. To address the experimental issue of decoherence error betweenthe ground state and Rydberg levels in Rydberg ensemble, we introduce adispersive coupling regime between Rydberg and ground levels, based on whichthe Rydberg state is adiabatically discarded. The numerical simulationdemonstrate that the quantum gate is enhanced. By combining strong Rydberg atominteractions, nonadiabatic geometric quantum computation, dynamical invariantand optimal control theory together, our scheme shows a new route to constructfast and robust quantum gates with mesoscopic atomic ensembles. Our studycontributes to the ongoing effort in developing quantum information processingwith Rydberg atoms trapped in optical lattices or tweezer arrays.

Optimized Geometric Quantum Computation with mesoscopic ensemble of Rydberg Atoms