Non-adiabatic holonomies for photonic quantum computing

Quantum computation faces a major challenge: the need for stable quantum gates. Holonomies offer a way to increase the stability of quantum gates on a fundamental level, as their functionality directly arises from the geometry of the underlying Hilbert space. We present the quantum optical realization of holonomies as single-qubit quantum gates. Specifically, we implement them in a non-adiabatic scheme, which 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 our designs enables them to substitute directional couplers currently in widespread use in photonic quantum architectures across all platforms.