Universal quantum gates by nonadiabatic holonomic evolution for the surface electron

TL;DR

This paper proposes a theoretical scheme for implementing nonadiabatic holonomic quantum gates on surface electrons, leveraging geometric phases for robust quantum computation with high fidelity.

Contribution

It introduces a novel method to realize geometric quantum gates in a surface electron system using a three-level structure with Rydberg and spin states.

Findings

Fidelity exceeds 0.99 with realistic parameters

Controlled-U gate can be implemented on Rydberg and spin states

Scheme is robust against noise and decoherence

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 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.