Criteria of minimum squeezing for quantum cluster state generation

Abstract

In this paper, we assess possibilities of generating cluster states with different topologies being possessed of a finite squeezing resource of the initial oscillators used to generate a cluster state. We obtained the condition on minimum squeezing required for generating a cluster with a given topology as a simple estimation in terms of the coefficients of the adjacency matrix.

Physical Realization of Measurement Based Quantum Computation

“…The degree of scalability for an effective QIP is the main obstacle towards the physical realization of cluster states. The scalability, at material level, deals with the limitations on the topology and size of cluster states [67]. This limitation directly restricts the number of logical operations needed to process large volumes of data.…”

“…The nature of such limitations varies depending on the materials used to physically realize qubits in a cluster state. As mentioned in Section 1, the physical realization approaches for cluster states realization in MBQC context can be broadly divided into two classes: continuous variables [68,69,70,71,72] and discrete variables [67,73,74] cluster states.…”

“…Hence, the initial degree of quadrature squeezing directly effects the entanglement of quantum oscillator being exploited to make cluster state. Among others, a relatively recent work [67], highlights the minimum squeezing criteria for cluster state generation.…”

Quantum computations on the ensemble of two-node cluster states obtained by sub-Poissonian lasers

“…The next step after the squeezed state of the oscillators is obtained is to entangle them. In this regard, the unitary transformation of the general form [3,13] has to be performed:…”

“…Here there is an arbitrary orthogonal matrix Q. It should be emphasized that the particular form of the matrix Q does not affect the topology of the cluster state and the values of nullifiers [3], although this matrix defines a unitary transformation U , and hence the procedure for creating a cluster state. Accordingly, any orthogonal matrix can be chosen which simplifies calculations.…”