Holonomic multi-controlled gates for single-photon states

TL;DR

This paper introduces a novel photonic waveguide network scheme utilizing non-Abelian holonomies to implement multi-controlled quantum gates, including Toffoli and OR gates, advancing photonic quantum computing capabilities.

Contribution

It proposes a new method using modulated photonic waveguides and non-Abelian holonomies to realize complex multi-controlled quantum gates in a scalable manner.

Findings

Design of adiabatic loops for single-qubit, CNOT, and SWAP gates.

Extension to larger M-pod structures enables multiply controlled operations.

Implementation of Deutsch quantum algorithm with connected tripods.

Abstract

Controlled and multi-controlled quantum gates, whose action on a target qubit depends on the state of multiple control qubits, represent a fundamental logical building block for complex quantum algorithms. We propose a scheme for realizing this class of gates based on non-Abelian holonomies in modulated photonic waveguide networks. Our approach relies on linear photonic cicuits formed by two star networks coupled via a two-path circuit. A star network with M peripheral waveguides coupled to a single central site, or M-pod, naturally generalizes the tripod structure used in non-Abelian Thouless pumping and stimulated Raman adiabatic passage (STIRAP). In the present work, we first analyze the minimal case of two connected tripods and design adiabatic driving loops that implement single-qubit, CNOT, and SWAP gates. We then show how extending the approach to larger M-pod structures enables the realization of multiply controlled operations, which we exemplify by designing Toffoli and the OR gate on two coupled pentapods. Finally, we demonstrate that networks of connected tripods can implement the Deutsch quantum query algorithm.