Universal linear Bogoliubov transformations through one-way quantum computation

Abstract

We show explicitly how to realize an arbitrary linear unitary Bogoliubov (LUBO) transformation on a multimode quantum state through homodyne-based one-way quantum computation. Any LUBO transformation 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 LUBO transformations. In particular, we demonstrate that a linear four-mode cluster state is a sufficient resource for an arbitrary one-mode LUBO transformation. Arbitrary-input quantum states including non-Gaussian states could be efficiently attached to the cluster through quantum teleportation

Optimization of networks for measurement-based quantum computation

“…Then, the second and, in general, third modes of the cluster state are measured on suitable quadratures, which depend on the computation that we want to perform and are determined with the recipe of Ref. [15]. These quadrature measurements on each mode can be equivalently described as a suitable rotation matrix D meas , followed by a measurement in the same quadrature on all the modes, say,p.…”

“…This state has been shown to be a universal resource for gaussian single-mode quantum computation [15]. The input modes used to build the cluster state are assumed to possess realistic squeezing levels, such as those seen in the four-mode multimode state of Ref.…”

Gates for one-way quantum computation based on Einstein-Podolsky-Rosen entanglement

“…Therefore, the probabilistic problems existing in most qubit information systems of single photons [4][5][6] can be overcome. It has been theoretically and experimentally demonstrated that one-mode linear unitary Bogoliubov (LUBO) transformations corresponding to Hamiltonians that are quadratic in quadrature amplitude and phase operators of quantized optical modes (qumodes) can be implemented using a four-mode linear cluster state [13,14]. At the same time, the Deutsch-Jozsa algorithm for CVQC has been proposed [15].…”

Demonstration of a fully tunable entangling gate for continuous-variable one-way quantum computation

“…A half teleportation with a beam-splitter coupling corresponds to a squeezing gate [21,22]. Note that it can be eliminated by adding an additional coupling node at the edge of cluster states, by which full quantum teleportation with full Bell measurements is performed into the cluster state instead of half teleporation with half Bell measurement [17].…”

“…For example the fixed-strength entangling gate demonstrated in Ref. [10] cannot have its entanglement strength tuned, and therefore it cannot completely make use of the underlying structure of the cluster state [17].…”