AUTHOR=Wang Jun , He Wan-Ting , Wang Hai-Bo , Ai Qing TITLE=Universal quantum gates by nonadiabatic holonomic evolution for the surface electron JOURNAL=Frontiers in Physics VOLUME=12 YEAR=2024 URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2024.1348804 DOI=10.3389/fphy.2024.1348804 ISSN=2296-424X ABSTRACT=

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 holonomic gate. Only the electron with spin up experiences the holonomic 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.