One-Step Implementation of Time-Optimal Three-Qubit Nonadiabatic Holonomic Gates via Dipole–Dipole Interaction in Rydberg Atoms

In this study, a one-step scheme is proposed to implement time-optimal three-qubit nonadiabatic holonomic gates using unconventional Rydberg pumping mechanism. The system dynamics of three Rydberg atoms are investigated in the regime of dipole–dipole interaction, which may provide relatively strong interaction strengths. By analyzing the system dynamics of three atoms, an effective three-level interaction Hamiltonian is derived. Based on this, a three-qubit nonadiabatic holonomic gate can be implemented in one step by modulating Rabi frequencies of control pulses on the target atom. The scheme is further optimized using time-optimal control technology based on quantum-brachistochrone formalism, which minimizes the evolution time of the system and mitigates the influence from the environmental decoherence. Numerical simulations results show that the scheme is robust against the Doppler dephasing error, system parameter variations, and atomic spontaneous emissions. Therefore, it is hoped that the scheme may facilitate the realization of fault-tolerant quantum computation in Rydberg atoms.