Physical Review Letters
We report experimental realization of high-fidelity photonic quantum gates for frequency-encoded qubits and qutrits based on electro-optic modulation and Fourier-transform pulse shaping. Our frequency version of the Hadamard gate offers near-unity fidelity (0.99998 + or -0.00003), requires only a single microwave drive tone for near-ideal performance, functions across the entire C-band (1530-1570 nm), and can operate concurrently on multiple qubits spaced as tightly as four frequency modes apart, with no observable degradation in the fidelity. For qutrits we implement a 3 x 3 extension of the Hadamard gate: the balanced tritter. This tritter---the first ever demonstrated for frequency modes---attains fidelity 0.9989 + or -0.0004. These gates represent important building blocks toward scalable, high-fidelity quantum information processing based on frequency encoding.