Nonadiabatic noncyclic geometric quantum computation in Rydberg atoms

Abstract

Nonadiabatic geometric quantum computation (NGQC) has been developed to realize fast and robust geometric gate. However, the previous NGQC is that all of the gates are performed with exactly the same amount of time, whether the geometric rotation angle is large or small, due to the limitation of cyclic condition. Here, we propose an unconventional scheme, called nonadiabatic noncyclic geometric quantum computation (NNGQC), that arbitrary single-and two-qubit geometric gate can be constructed via noncyclic non-Abelian geometric phase. Consequently, this scheme makes it possible to accelerate the implemented geometric gates against the effects from the environmental decoherence. Moreover, our scheme only needs to adjust the amplitude and phase of field in a microvave-coupled or Raman-process-induced resonant two-level system without complex control. Specifically, we consider Rydberg atoms based on the proposed unconventional Rydberg blockade regime for two-qubit gate. After a numerical analysis under same experimental conditions, we found that NNGQC can greatly suppress the decoherence error than NGQC. Therefore, our scheme opens the possibility for fast and robust geometric quantum computation on neutral-atom-based quantum system.