Abstract
Complex networks structures have been extensively used for describing complex natural and technological systems, like the Internet or social networks. More recently, complex network theory has been applied to quantum systems, where complex network topologies may emerge in multiparty quantum states and quantum algorithms have been studied in complex graph structures. In this work, we study multimode Continuous Variables entangled states, named cluster states, where the entanglement structure is arranged in typical real-world complex networks shapes. Cluster states are a resource for measurement-based quantum information protocols, where the quality of a cluster is assessed in terms of the minimal amount of noise it introduces in the computation. We study optimal graph states that can be obtained with experimentally realistic quantum resources, when optimized via analytical procedure. We show that denser and regular graphs allow for better optimization. In the spirit of quantum routing, we also show the reshaping of entanglement connections in small networks via linear optics operations based on numerical optimization.
Highlights
In the last few decades, network theory has provided a natural framework for describing complex natural, social, and technological structures [1,2]
We study Continuous Variables (CV) entangled states, named CV graph states or CV cluster states, arranged with shapes that are typical of real-world complex networks, in order to investigate their properties for quantum computing or quantum networking protocols
Quantum routing protocols have been mainly studied in the Discrete Variables (DV) approach [27,28], while here we study the particular setting of CV quantum resources
Summary
In the last few decades, network theory has provided a natural framework for describing complex natural, social, and technological structures [1,2]. Recurrent types of complex networks, like the scale-free networks, have been recovered in phenomena at different scales, where the functionality of the systems seems to be closely related to their structure [3,4]. Complex networks have gained attention in the quantum realm, where several theoretical works [5,6,7,8,9,10] show that complex structures may play a role in quantum information technologies. Network structures are clearly at the base of quantum communication protocols [11], and appear in particular kinds of multiparty entangled states that allow for measurement-based quantum computing (MBQC) protocols [12]. New records have been established in superconductor [13,14,15] and Rydberg [16,17] based technologies, and extremely large entangled states have been generated in the optical domain [18,19,20,21]
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