  We propose general methodology of deterministic single-mode quantum
interaction nonlinearly modifying single quadrature variable of a continuous
variable system. The methodology is based on linear coupling of the system to
ancillary systems subsequently measured by quadrature detectors. The nonlinear
interaction is obtained by using the data from the quadrature detection for
dynamical manipulation of the coupling parameters. This measurement-induced
methodology enables direct realization of arbitrary nonlinear quadrature
interactions without the need to construct them from the lowest-order gates.
Such nonlinear interactions are crucial for more practical and efficient
manipulation of continuous quadrature variables as well as qubits encoded in
continuous variable systems.
