Geometric quantum gates via dark paths in Rydberg atoms

TL;DR

This paper presents a robust, scalable method for implementing nonadiabatic holonomic quantum gates using Rydberg atoms, which are resilient to systematic errors and external noise, advancing quantum computation reliability.

Contribution

The authors develop a universal set of nonadiabatic holonomic N-qubit gates with enhanced error resilience using dark-path schemes in Rydberg-atom systems, offering a deeper understanding of holonomic transformations.

Findings

Gates show resilience to systematic errors across the entire parameter range.

Three-qubit gates are less susceptible to errors than two-qubit gates.

The scheme is compact and scale-free with respect to the number of qubits.

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.