Deterministic implementation of weak quantum cubic nonlinearity

We propose a deterministic implementation of weak cubic nonlinearity, which is a basic building block of a full-scale continuous-variable quantum computation. Our proposal relies on preparation of a specific ancillary state and transferring its nonlinear properties onto the desired target bymeans of deterministic Gaussian operations and feed forward. We show that, despite the imperfections arising from the deterministic nature of the operation, the weak quantum nonlinearity can be implemented and verified with the current level of technology.