Complex Networks from Classical to Quantum
arXiv:1702.08459 · doi:10.1038/s42005-019-0152-6
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
References in corpus (73)
- Emergence of scaling in random networks
- Statistical mechanics of complex networks
- The structure and function of complex networks
- Community detection in graphs
- Error and attack tolerance of complex networks
- The Quantum Internet
- Uncovering the overlapping community structure of complex networks in nature and society
- Quantum Machine Learning
- Catastrophic cascade of failures in interdependent networks
- Functional cartography of complex metabolic networks
- Multilayer Networks
- The structure and dynamics of multilayer networks
- Network robustness and fragility: Percolation on random graphs
- Critical phenomena in complex networks
- Quantum state transfer and entanglement distribution among distant nodes in a quantum network
- Self-similarity of complex networks
- String-net condensation: A physical mechanism for topological phases
- A Quantum Random Walk Search Algorithm
- Silica-on-Silicon Waveguide Quantum Circuits
- Detecting rich-club ordering in complex networks
- Mathematical Formulation of Multi-Layer Networks
- An Elementary Quantum Network of Single Atoms in Optical Cavities
- Bose-Einstein condensation in complex networks
- Towards Quantum Chemistry on a Quantum Computer
- Storage and retrieval of single photons transmitted between remote quantum memories
- Cascade control and defense in complex networks
- A quantum network of clocks
- The physics of spreading processes in multilayer networks
- Layer aggregation and reducibility of multilayer interconnected networks
- Detecting fuzzy community structures in complex networks with a Potts model
- Random Walks on Multiplex Networks
- Navigability of Complex Networks
- Limits on Fundamental Limits to Computation
- An example of the difference between quantum and classical random walks
- Emergence of a 4D World from Causal Quantum Gravity
- Abrupt transition in the structural formation of interconnected networks
- The multilayer connectome of Caenorhabditis elegans
- Entanglement Percolation in Quantum Networks
- Random Quantum Circuits and Pseudo-Random Operators: Theory and Applications
- Quantum Graphity: a model of emergent locality
- Localization of maximal entropy random walk
- Spatial search by quantum walk is optimal for almost all graphs
- Mapping multiplex hubs in human functional brain network
- Network geometry with flavor: from complexity to quantum geometry
- Generalized Bose-Fermi statistics and structural correlations in weighted networks
- The Shannon and the Von Neumann entropy of random networks with heterogeneous expected degree
- The laplacian of a graph as a density matrix: a basic combinatorial approach to separability of mixed states
- Quantum complex networks
- Quantum stochastic walks: A generalization of classical random walks and quantum walks
- Google in a Quantum Network
- Quantum Navigation and Ranking in Complex Networks
- Interdisciplinary and physics challenges of Network Theory
- Adiabatic quantum algorithm for search engine ranking
- Convergence rates for arbitrary statistical moments of random quantum circuits
- Entanglement percolation in quantum complex networks
- On the geometry of loop quantum gravity on a graph
- Experimental non-locality in a quantum network
- Symmetry and the thermodynamics of currents in open quantum systems
- Quantum Transport Enhancement by Time-Reversal Symmetry Breaking
- Chiral Quantum Walks
- Magnetic eigenmaps for community detection in directed networks
- Dynamic quantum clustering: a method for visual exploration of structures in data
- Optimal quantum spatial search on random temporal networks
- Magnetic Eigenmaps for the Visualization of Directed Networks
- Complex Quantum Networks: From Universal Breakdown to Optimal Transport
- Thermodynamic formalism for dissipative quantum walks
- Quantum-Classical Transitions in Complex Networks
- Quantized recurrence time in iterated open quantum dynamics
- Quantum walks on complex networks with connection instabilities and community structure
- Information sharing in Quantum Complex Networks
- Irreconcilable Difference Between Quantum Walks and Adiabatic Quantum Computing
- Continuous-Time Quantum Walks on Directed Bipartite Graphs
- Random Walks on Complex Networks
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- Towards quantum advantage via topological data analysis
- Symmetries in quantum networks lead to no-go theorems for entanglement distribution and to verification techniques
- Complex Quantum Networks: a Topical Review
- The topological Dirac equation of networks and simplicial complexes
- Concurrence Percolation in Quantum Networks
- Multilayer Network Science: from Cells to Societies
- Unraveling the effects of multiscale network entanglement on disintegration of empirical systems
- Complex networks with complex weights
- Quantum communication capacity transition of complex quantum networks
- From classical to quantum walks with stochastic resetting on networks
- Controlled State Reconstruction and Quantum Secret Sharing
- Entanglement in highly symmetric multipartite quantum states
- Analytical Methods for High-Rate Global Quantum Networks
- Pairwise tomography networks for many-body quantum systems
- Entanglement-assisted capacity regions and protocol designs for quantum multiple-access channels
- Multimode Squeezed State for Reconfigurable Quantum Networks at Telecommunication Wavelengths
- Entanglement formation in continuous-variable random quantum networks
- Continuous-time quantum walk spatial search on the Bollobás scale-free network
- Teleportation of quantum coherence
- Generalized network density matrices for analysis of multiscale functional diversity
- The mass of simple and higher-order networks
- Quantivine: A Visualization Approach for Large-scale Quantum Circuit Representation and Analysis
- Atomic Quantum Technologies for Quantum Matter and Fundamental Physics Applications
- Dirac gauge theory for topological spinors in 3+1 dimensional networks
- Deterministic Entanglement Distribution on Series-Parallel Quantum Networks
- Quantum walks defined by digraphs and generalized Hermitian adjacency matrices
- Complex quantum network models from spin clusters
- Highly Clustered Complex Networks in the Configuration Model: Random Regular Small-World Network
- Floquet engineering of continuous-time quantum walks: towards the simulation of complex and next-to-nearest neighbor couplings
- Quantum Internet under random breakdowns and intentional attacks
- Continuous variables graph states shaped as complex networks: optimization and manipulation
- Energy-dependent barren plateau in bosonic variational quantum circuits
- Emergent entanglement structures and self-similarity in quantum spin chains
- 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
- Network architecture of energy landscapes in mesoscopic quantum systems
- Discovering hidden layers in quantum graphs
- Entanglement percolation in random quantum networks
- Three Party Quantum Networks Created by Quantum Cloning
- Universal scaling hypothesis of quantum spatial search in complex networks
- Unveiling hidden features of the Kitaev model through a complex-network analysis
- Quantum community detection via deterministic elimination
- Directionality and quantum backfire in continuous-time quantum walks from delocalized states: Exact results
- Noncooperative Quantum Networks