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Photons generally weakly interact with each other. While this feature is often useful, for instance, in communication, controllably inducing strong photon-photon interactions is necessary for deterministic, all-optical quantum information processing. Consequently, the weak nonlinearity in optics has historically motivated the use of measurement-based feedback schemes for photonic quantum information processing. Here, we theoretically investigate if coherent photonic quantum information processing could be realized by enhancing weak nonlinearities via Gaussian operations. We find that a Kerr medium with weak material nonlinearity can be engineered to implement a coherent cubic phase gate. Recent progress in developing photonic platforms supporting strong spatial and temporal confinement of pulsed light in low loss and low dispersion nonlinear waveguides could enable an experimental demonstration in the near future.
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