Fast fusion of entangled states by transitionless quantum driving

Entangled states are of significant importance in the realms of quantum communication and quantum information processing. Fusion technology has been proven as a viable method to prepare large-size entangled states from two or more small-size entangled states in a quantum electrodynamics (QED) system. However, most fusion schemes in QED systems require precise control over the evolution time, thereby amplifying the difficulty in the experiment. Therefore, it is of great importance to find a scheme to fuse entangled states in a QED system without requiring precise control over the evolution time. In this study, we propose a fusion scheme to efficiently prepare large-scale entangled states by transitionless quantum driving (TQD) with Rydberg superatoms. We position an ultracold ensemble of n individual ladder-type Rydberg atoms within the blockade sphere, thereby forming a superatom. Subsequently, we encode quantum information onto the collective state of the Rydberg superatoms. Through the combined use of quantum Zeno dynamics and TQD, the scheme enables the fast fusion of an m -qubits W (GHZ) state and an n -qubits W (GHZ) state into a ( m + n −2)-qubits W (GHZ) state without the requirement for precise control over the evolution time. Moreover, the impact of decoherence factors, operational imperfection, and noise on fidelity is taken into account. Numerical simulations suggest that the proposed method demonstrates high fidelity.