Photonic qubit gates via 1D scattering from an array of two-level emitters

Photonic quantum computing offers a promising platform for quantum information processing, benefiting from the long coherence times of photons and their ease of manipulation. This paper presents a scheme for implementing a deterministic phase gate for dual-rail number encoded photonic qubits, leveraging a standard 1D waveguide coupled to an array of two-level emitters (TLE). Using a transfer matrix approach, we develop a protocol for deterministic phase gate operation, demonstrating its robustness against non-waveguide mode coupling and disorder. Finally, we relax the idealized assumption of monochromatic light, considering finite-bandwidth pulses. Despite these realistic considerations, our results indicate high fidelity for the proposed phase gate protocol. Finally we will discuss two qubit operations.