Passive controlled-variable phase gate on photonic qubits via cascade emitter

Photonic qubits are promising candidates for enabling a universal quantum computer capable of long-distance network integration because photons offer long coherence times compared to matter-based qubits and light-speed transmission. We propose a scheme to implement a passive, deterministic, and low-footprint C-PHASE gate with arbitrary phase on photonic qubits encoded in the frequency basis. Our gate employs a cascade system with the ground to first excited state interacting with the control photon of a given polarization, and the first to second excited state transition interacting with the target photon of the orthogonal polarization. By controlling the detuning between the target photon and the frequency of the transition between the first and second excited states of the cascade emitter, we enable any controlled-phase operation from 0 to π. We show that the gate can be optimized by tuning the photon lineshapes and the cascade emitter’s transition rates. This gate does not utilize any active control and needs only a single cascade emitter, enabling low-footprint and more efficient decomposition of quantum circuits, especially those rooted in the quantum Fourier transform.