Complex Networks from Classical to Quantum

Abstract

Recent progress in applying complex network theory to problems in quantum information has resulted in a beneficial crossover. Complex network methods have successfully been applied to transport and entanglement models while information physics is setting the stage for a theory of complex systems with quantum information-inspired methods. Novel quantum induced effects have been predicted in random graphs---where edges represent entangled links---and quantum computer algorithms have been proposed to offer enhancement for several network problems. Here we review the results at the cutting edge, pinpointing the similarities and the differences found at the intersection of these two fields.

12 pages, 4 figures, REVTeX 4-1, accepted version

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• Teleportation of quantum coherence
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• Spatial search by continuous-time quantum walks on renormalized Internet networks
• Construction of genuinely entangled multipartite subspaces from bipartite ones by reducing the total number of separated parties
• Measuring dynamical systems on directed hyper-graphs
• Thermal state entanglement entropy on a quantum graph
• Lightcone Bounds for Quantum Circuit Mapping via Uncomplexity
• Characterising heavy-tailed networks using q-generalised entropy and q-adjacency kernels
• Network structure and dynamics of effective models of non-equilibrium quantum transport
• Random Apollonian networks with tailored clustering coefficient
• Quantum simulations of complex systems
• Quantum transfer through small networks coupled to phonons: effects of topology vs phonons
• Entangled quantum cellular automata, physical complexity, and Goldilocks rules
• Absence of small-world effects at the quantum level and stability of the quantum critical point
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• Entanglement percolation in random quantum networks
• Three Party Quantum Networks Created by Quantum Cloning
• Universal scaling hypothesis of quantum spatial search in complex networks
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