One of the most promising nascent technologies, quantum computation faces a major challenge: The need for stable computational building blocks. We present the quantum-optical realization of non-adiabatic holonomies that can be used as single-qubit quantum gates. The hallmark topological protection of non-Abelian geometric phases reduces the need for quantum error correction on a fundamental physical level, while the inherent non-adiabaticity of the structures paves the way for unprecedented miniaturization. To demonstrate their versatility, we realize the Hadamard and Pauli-X gates, experimentally show their non-Abelian nature, and combine them into a single-qubit quantum algorithm, the PQ penny flipover. The planar geometry of such designs enables them to be substituted for the conventional directional coupler meshes currently in wide-spread use in photonic quantum architectures across all platforms.
@article{arxiv.2401.04014,
title = {Non-adiabatic holonomies as photonic quantum gates},
author = {Vera Neef and Julien Pinske and Tom A. W. Wolterink and Karo Becker and Matthias Heinrich and Stefan Scheel and Alexander Szameit},
journal= {arXiv preprint arXiv:2401.04014},
year = {2024}
}