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Nonadiabatic geometric quantum computation (NGQC) has been developed torealize fast and robust geometric gate. However, the conventional NGQC is thatall of the gates are performed with exactly the sameamount of time, whether thegeometric rotation angle is large or small, due to the limitation of cycliccondition. Here, we propose an unconventional scheme, called nonadiabaticnoncyclic geometric quantum computation(NNGQC), that arbitrary single- andtwo-qubit geometric gate can be constructed via noncyclic non-Abeliangeometricphase. Consequently, this scheme makes it possible to accelerate theimplemented geometric gatesagainst the effects from the environmentaldecoherence. Furthermore, this extensible scheme can be applied invariousquantum platforms, such as superconducting qubit and Rydberg atoms.Specifically, for single-qubit gate,we make simulations with practicalparameters in neutral atom system to show the robustness of NNGQC and alsocompare with NGQC using the recent experimental parameters to show that theNNGQC can significantly suppress the decoherence error. In addition, we alsodemonstrate that nontrivial two-qubit geometric gate can berealized viaunconventional Rydberg blockade regime within current experimentaltechnologies. Therefore, ourscheme provides a promising way for fast and robustneutral-atom-based quantum computation.

Nonadiabatic noncyclic geometric quantum computation in Rydberg atoms