Universal linear Bogoliubov transformations through one-way quantum computation

We show explicitly how to realize an arbitrary linear unitary Bogoliubov transformation (LUBO) on a multi-mode quantum state through homodyne-based one-way quantum computation. Any LUBO can be approximated by means of a fixed, finite-sized, sufficiently squeezed Gaussian cluster state that allows for the implementation of beam splitters (in form of three-mode connection gates) and general one-mode LUBOs. In particular, we demonstrate that a linear four-mode cluster state is a sufficient resource for an arbitrary one-mode LUBO. Arbitrary input quantum states including non-Gaussian states could be efficiently attached to the cluster through quantum teleportation.