Geometric quantum gates via dark paths in Rydberg atoms

Abstract

Nonadiabatic holonomic quantum gates are high-speed and robust. Nevertheless, they were found to be more fragile than the adiabatic gates when systematic errors become dominant. Inspired by the dark-path scheme that was used to partially relieve the systematic error in the absence of external noise, we construct a universal set of nonadiabatic holonomic $N$-qubit gates using the Rydberg-Rydberg interaction between atoms under off-resonant driving. Based on an effective four-level configuration in the Rydberg-atom system, the modified nonadiabatic holonomic geometric gates present a clear resilience to both systematic error in the whole parametric range and external noise. In our scheme, the conventional ultrastrong interaction between control atoms and the target atom for the nonadiabatic holonomic quantum computation is compensated by the detuning of the driving fields on the target atom. That idea yields a deeper understanding about the holonomic transformation. Moreover, our scheme is compact and scale-free with respect to $N$. It is interesting to find that the three-qubit gate is less susceptible to errors than the double-qubit one.

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Cited by in corpus (6)

• High-fidelity and robust controlled-Z gates implemented with Rydberg atoms via echoing rapid adiabatic passage
• Entangling distant systems via universal nonadiabatic passage
• Universal quantum control with dynamical correction
• Mitigation of systematic amplitude error in nonadiabatic holonomic operations
• Universal quantum gates by nonadiabatic holonomic evolution for the surface electron
• Implementing a Universal Set of Geometric Quantum Gates through Dressed-State assisted STA