The nonadiabatic holonomic quantum computation based on the geometric phase is robust against the built-in noise and decoherence. In this work, we theoretically propose a scheme to realize nonadiabatic holonomic quantum gates in a surface electron system, which is a promising two-dimensional platform for quantum computation. The holonomic gate is realized by a three-level structure that combines the Rydberg states and spin states via an inhomogeneous magnetic field. After a cyclic evolution, the computation bases pick up different geometric phases and thus perform a geometric gate. Only the electron with spin up experiences the geometric gate, while the electron with spin down is decoupled from the state-selective driving fields. The arbitrary controlled-U gate encoded on the Rydberg states and spin states can then be realized. The fidelity of the output state exceeds 0.99 with experimentally achievable parameters.
@article{arxiv.2307.09900,
title = {Universal quantum gates by nonadiabatic holonomic evolution for the surface electron},
author = {Jun Wang and Wan-Ting He and Hai-Bo Wang and Qing Ai},
journal= {arXiv preprint arXiv:2307.09900},
year = {2024}
}