Programmable color qubit quantum gates

We present what we believe to be a novel proposal for the implementation of temporal-modes quantum gates based on the third-order nonlinear process of difference frequency generation in an integrated photonic circuit, which allows switching from one Pauli gate to another by tuning the phase difference between the two pump pulses (in case of the σ x and σ y Pauli gates) and between the two states comprising the basis of single temporal-modes qubits (in the case of the σ z Pauli gate). We demonstrate that our proposal enables the preparation of any single temporal-mode qubit and rotations on the Bloch sphere by changing externally controllable parameters. We also analyze the effects of fabrication errors on the predicted quantum gate fidelity, finding that, even if some waveguide parameter deviates from the design, slight tuning of pump wavelengths can lead to recovering high-fidelity values.