Passive Photonic CZ Gate with Two-Level Emitters in Chiral Multimode Waveguide QED

Engineering deterministic photonic gates with simple resources is one of the long-standing challenges in photonic quantum computing. Here, we design a passive conditional gate between copropagating photons using an array of only two-level emitters. The key resource is to harness the effective photon-photon interaction induced by the chiral coupling of the emitter array to two waveguide modes with different resonant momenta at the emitter’s transition frequency. By studying the system’s multiphoton scattering response, we demonstrate that, in certain limits, this configuration induces a nonlinear <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><a:mi>π</a:mi></a:math>-phase shift between the polariton eigenstates of the system without distorting spectrally the wave packets. Then, we show how to harness this nonlinear phase shift to engineer a conditional, deterministic photonic gate in different qubit encodings, with a fidelity arbitrarily close to 1 in the limit of large number of emitters and coupling efficiency. Our configuration can be implemented in topological photonic setups with multiple chiral-edge modes, opening their use for quantum information processing, or in other setups where such chiral light-matter couplings can be effectively obtained, such as optical fibers or photonic-crystal optical and microwave waveguides.