Engineering a Kerr-Based Deterministic Cubic Phase Gate via Gaussian Operations

We propose a deterministic, measurement-free implementation of a cubic phase gate for continuous-variable photonic quantum information processing. In our scheme, the applications of displacement and squeezing operations allow us to engineer the effective evolution of the quantum state propagating through an optical Kerr nonlinearity. Under appropriate conditions, we show that the input state evolves according to a cubic phase Hamiltonian and that the cubic phase gate error decreases inverse quartically with the amount of quadrature squeezing, even in the presence of linear loss. Finally, we study the experimental feasibility of the scheme and find that 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.