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arXiv:1811.05241 · Laser Physics Letters

Criteria of minimum squeezing for quantum cluster state generation

S. B. Korolev, A. D. Manukhova, K. S. Tikhonov, T. Yu. Golubeva, Yu. M. Golubev

Published May 30, 2018• 9 citations
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Abstract

Abstract In this paper, we assess the possibilities of generating cluster states with different topologies possessed by the finite squeezing resource of the initial oscillators used to generate the 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.

DOI
10.1088/1612-202x/aac03e

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Abstract In this paper, we assess the possibilities of generating cluster states with different topologies possessed by the finite squeezing resource of the initial oscillators used to generate the 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.
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Cluster states for measurement-based quantum computing can be created with entangling operations of arbitrary low success probability. This will place a lower bound on the minimum lifetime of the qubits used in the implementation. Here, we present a simple scaling argument for the T2{T}_{2}T2​ time of the qubits for various cluster-state geometries, and we estimate the size of the qubit reservoir that is needed for the creation of miniclusters.
The topology of classical networks is determined by physical links between nodes, and after a network request the links are used to establish the desired connections. Quantum networks offer the possibility to generate different kinds of entanglement prior to network requests, which can substitute links and allow one to fulfill multiple network requests with the same resource state. We utilize this to design entanglement-based quantum networks tailored to their desired functionality, independent of the underlying physical structure. The kind of entanglement to be stored is chosen to fulfill all desired network requests (i.e. parallel bipartite or multipartite communications between specific nodes chosen from some finite set), but in such a way that the storage requirement is minimized. This can be accomplished by using multipartite entangled states shared between network nodes that can be transformed by local operations to different target states. We introduce a clustering algorithm to identify connected clusters in the network for a given desired functionality, i.e. the required network topology of the entanglement-based network, and a merging algorithm that constructs multipartite entangled resource states with reduced memory requirement to fulfill all desired network requests. This leads to a significant reduction in required time and resources, and provides a powerful tool to design quantum networks that is unique to entanglement-based networks.
Cluster states are versatile quantum resources and an essential building block for measurement-based quantum computing. The possibility to generate cluster states in specific systems may thus serve as an indicator regarding if and to what extent these systems can be harnessed for quantum technologies and quantum information processing in particular. Here, we apply this analysis to networks of degenerate optical parametric oscillators (DOPOs), also called coherent Ising machines (CIMs). CIMs are distinguished by their highly flexible coupling capabilities, which makes it possible to use them, e.g., to emulate large spin systems. As CIMs typically operate with coherent states (and superpositions thereof), it is natural to consider cluster states formed by superpositions of coherent states, i.e., coherent cluster states. As we show, such coherent cluster states can, under ideal conditions, be generated in DOPO networks with the help of beam splitters and classical pumps. Our subsequent numerical analysis provides the minimum requirements for the generation of coherent cluster states under realistic conditions. Moreover, we discuss how nonequilibrium pumps can improve the generation of coherent cluster states. In order to assess the quality of the cluster-state generation, we map the generated states to an effective spin space using modular variables, which allows us to apply entanglement criteria tailored for spin-based cluster states.