Fast implementation of controlled-π phase gates and preparation of cluster states with Rydberg superatoms

In this paper, we propose a scheme for rapidly implementing a controlled- π phase gate by combining the Lewis–Riesenfeld invariant and quantum Zeno dynamics. We demonstrate the adiabatic shortcut by using Rydberg superatoms in distant-atom–cavity systems. Furthermore, we utilize the controlled- π phase gate to achieve the preparation of N -particle cluster states. Additionally, the impact of decoherence and operational imperfections is discussed. Numerical simulation demonstrates that the proposed scheme has high fidelities and robustness against both cavity leakage and atomic spontaneous emission.