Accurate control of two-level systems is a longstanding problem in quantum mechanics. One such quantum system is the frequency-bin qubit: a single photon existing in superposition of two discrete frequency modes. In this Letter, we demonstrate fully arbitrary control of frequency-bin qubits in a quantum frequency processor for the first time. We numerically establish optimal settings for multiple configurations of electro-optic phase modulators and pulse shapers, experimentally confirming near-unity mode-transformation fidelity for all fundamental rotations. Performance at the single-photon level is validated through the rotation of a single frequency-bin qubit to 41 points spread over the entire Bloch sphere, as well as tracking of the state path followed by the output of a tunable frequency beam splitter, with Bayesian tomography confirming state fidelities ${\mathcal{F}}_{\rho }>0.98$ for all cases. Such high-fidelity transformations expand the practical potential of frequency encoding in quantum communications, offering exceptional precision and low noise in general qubit manipulation.

• Received 18 June 2020
• Accepted 14 August 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.120503