Continuous Variables Graph States Shaped as Complex Networks: Optimization and Manipulation

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.

Cyber Attacks Visualization and Prediction in Complex Multi-Stage Network

“…The next phase of the research deals with identifying attack points and hardening the network to avoid vulnerability. The attack graph hardening techniques prescribed in the study (Ibrahim et al, 2020), (Sansavini & Parigi, 2020) that makes use of topological analysis gives a new dimension for managing cyber threats at the time of vulnerabilities. Thus, topological analysis for vulnerabilities became the backbone of the study and proposal.…”

Emergent complex quantum networks in continuous-variables non-Gaussian states

“…Here we go beyond such regular structures, motivated by the fact that CV quantum networks in optical setups can be easily reconfigured to arbitrary shapes [23]. We want to indeed replicate in the quantum regime some of the models that mimic real-world complex networks [24,25] in order to test their structural properties under local operations. In the remainder of the Article we refer to the network that describes the pattern A of C Z gates that are applied to create the Gaussian cluster state as the imprinted network.…”

“…The optical CV networks can be easily reconfigured in arbitrary shape [23]. They thus provide an excellent playground to explore whether mimicking real-world complex network structures [24,25] provides an advantage for quantum information technologies, including quantum simulation and communication [23,26] in a future quantum internet. Moreover, and this is a central point of our work, network theory gives us powerful tools for benchmarking these networks when affected by non-Gaussian operations.…”

“…and quantum physics with, e.g., the study of the Ising model and Bose Einstein condensation [31][32][33][34][35][36][37]. More recently the study of complex networks has become relevant for quantum systems and procedures employed in quantum information technologies [24,25,[38][39][40][41][42] indicating that a dedicated theory of quantum complex networks needs to be built, especially for networks with no classical equivalent, like those based on quantum correlations or quantum mutual information. In particular, emergent complex networks based on quantum mutual information have determined critical points for quantum phase transitions [36,43].…”

Entanglement trimming in stabilizer formalism

“…Introduction.-Distributed quantum architecture has been recently proposed for various quantum enhanced applications, e.g., quantum metrology, quantum communication and quantum computation [1][2][3][4]. These quantum enhancements usually require efficiently generating and distributing entanglement between different quantum nodes in a network through connected quantum channels [5].…”