In this paper, a flexible and effective scheme is proposed to realize nonadiabatic geometric quantum gates with the invariant based reverse engineering and the nonadiabatic holonomic quantum computation ($\mathrm{NHQC}+$) presented in recent work [B.-J. Liu et al., Phys. Rev. Lett. 123, 100501 (2019)] for extensible geometric quantum computation. The scheme provides variabilities for most of control parameters, and can build up multiple evolution paths with different geometric phases acquired in a cycling evolution. As the computational basis can be covered by the evolution paths, the realization of the nonadiabatic geometric quantum computation is possible without auxiliary levels. Moreover, multiple types of nonadiabatic geometric quantum gates can also be easily constructed by only adjusting boundary conditions of control parameters with the method. To show the applications of the scheme, we discuss the implementations of nonadiabatic geometric quantum gates of spin qubits in a double-quantum-dot system with numerical simulations. The results indicate that the scheme possesses robustness against the errors and noise. Therefore, the scheme may offer some interesting perspectives for the realization of the nonadiabatic geometric quantum computation.

• Received 20 October 2019
• Accepted 21 February 2020

DOI:https://doi.org/10.1103/PhysRevA.101.032322