Universal linear Bogoliubov transformations through one-way quantum computation

TL;DR

This paper presents a method to implement any linear unitary Bogoliubov transformation on multi-mode quantum states using a fixed Gaussian cluster state in one-way quantum computation, enabling efficient processing of Gaussian and non-Gaussian states.

Contribution

It introduces a practical scheme for realizing arbitrary linear Bogoliubov transformations via homodyne-based one-way quantum computation with minimal resource states.

Findings

Any LUBO can be approximated with a finite squeezed Gaussian cluster state.

A four-mode cluster state suffices for any one-mode LUBO.

Non-Gaussian states can be integrated via quantum teleportation.

Abstract

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.