  We propose an experimental design for universal continuous-variable quantum
computation that incorporates recent innovations in linear-optics-based
continuous-variable cluster state generation and cubic-phase gate
teleportation. The first ingredient is a protocol for generating the
bilayer-square-lattice cluster state (a universal resource state) with temporal
modes of light. With this state, measurement-based implementation of Gaussian
unitary gates requires only homodyne detection. Second, we describe a
measurement device that implements an adaptive cubic-phase gate, up to a random
phase-space displacement. It requires a two-step sequence of homodyne
measurements and consumes a (non-Gaussian) cubic-phase state.

Quantum Physics