Complex Quantum Networks: a Topical Review
arXiv:2311.16265 · doi:10.1088/1751-8121/ad41a6
Abstract
These are exciting times for quantum physics as new quantum technologies are expected to soon transform computing at an unprecedented level. Simultaneously network science is flourishing proving an ideal mathematical and computational framework to capture the complexity of large interacting systems. Here we provide a comprehensive and timely review of the rising field of complex quantum networks. On one side, this subject is key to harness the potential of complex networks in order to provide design principles to boost and enhance quantum algorithms and quantum technologies. On the other side this subject can provide a new generation of quantum algorithms to infer significant complex network properties. The field features fundamental research questions as diverse as designing networks to shape Hamiltonians and their corresponding phase diagram, taming the complexity of many-body quantum systems with network theory, revealing how quantum physics and quantum algorithms can predict novel network properties and phase transitions, and studying the interplay between architecture, topology and performance in quantum communication networks. Our review covers all of these multifaceted aspects in a self-contained presentation aimed both at network-curious quantum physicists and at quantum-curious network theorists. We provide a framework that unifies the field of quantum complex networks along four main research lines: network-generalized, quantum-applied, quantum-generalized and quantum-enhanced. Finally we draw attention to the connections between these research lines, which can lead to new opportunities and new discoveries at the interface between quantum physics and network science.
94 pages + 25 pages of references, 26 figures. Updated to accepted version
References in corpus (121)
- Fast unfolding of communities in large networks
- Modularity and community structure in networks
- The Quantum Internet
- Maps of random walks on complex networks reveal community structure
- Synchronization in complex networks
- Benchmark graphs for testing community detection algorithms
- The structure and dynamics of multilayer networks
- Critical phenomena in complex networks
- Multi-party entanglement in graph states
- Universal computation by quantum walk
- The physics of higher-order interactions in complex systems
- Dephasing assisted transport: Quantum networks and biomolecules
- Exponential algorithmic speedup by quantum walk
- Quantum technologies with hybrid systems
- Spatial search by quantum walk
- Layer aggregation and reducibility of multilayer interconnected networks
- Topological fault-tolerance in cluster state quantum computation
- Perfect Transfer of Arbitrary States in Quantum Spin Networks
- Quantum Communication through Spin Chain Dynamics: an Introductory Overview
- Progress in satellite quantum key distribution
- Recent progress in many-body localization
- Experimental quantum key distribution beyond the repeaterless secret key capacity
- The entropy of network ensembles
- Quantum chaos and the complexity of spread of states
- Direct and Reverse Secret-Key Capacities of a Quantum Channel
- The entropy of randomized network ensembles
- Towards real-world quantum networks: a review
- Graphical calculus for Gaussian pure states
- Fractal properties of quantum spacetime
- Fast simulation of stabilizer circuits using a graph state representation
- Spectral entropies as information-theoretic tools for complex network comparison
- Quantum synchronization of two Van der Pol oscillators
- Generalized Bose-Fermi statistics and structural correlations in weighted networks
- Recent advances on integrated quantum communications
- Generalized Flow and Determinism in Measurement-based Quantum Computation
- Quantum repeaters with imperfect memories: cost and scalability
- A random walk approach to quantum algorithms
- Network Cosmology
- Dynamics, Synchronization and Quantum Phase Transitions of Two Dissipative Spins
- Field test of a practical secure communication network with decoy-state quantum cryptography
- Ultracompact Generation of Continuous-Variable Cluster States
- Entanglement Distribution in Pure-State Quantum Networks
- Quantum transport on small-world networks: A continuous-time quantum walk approach
- Current status of the DARPA Quantum Network
- Satellite-based Quantum Information Networks: Use cases, Architecture, and Roadmap
- On the role of memory errors in quantum repeaters
- Tools for quantum network design
- Weighted simplicial complexes and their representation power of higher-order network data and topology
- Indirect Hamiltonian Identification through a small gateway
- Quantum synchronization and quantum state sharing in irregular complex network
- Quantum Technologies in Space
- Indirect Quantum Tomography of Quadratic Hamiltonians
- Entanglement and nonclassical properties of hypergraph states
- Quantum chaos and random matrix theoryfor fidelity decay in quantum computationswith static imperfections
- Probing the spectral density of a dissipative qubit via quantum synchronization
- Global topological synchronization on simplicial and cell complexes
- Network Quantum Steering
- Simulating quantum repeater strategies for multiple satellites
- Quantum annealing: the fastest route to quantum computation?
- Magnetic eigenmaps for community detection in directed networks
- Centrality measure based on continuous-time quantum walks and experimental realization
- Experimental Quantum Network Coding
- Transport properties of continuous-time quantum walks on Sierpinski fractals
- On the optimality of spatial search by continuous-time quantum walk
- Characterization of qubit chains by Feynman probes
- Symmetries in quantum networks lead to no-go theorems for entanglement distribution and to verification techniques
- Satellite-based photonic quantum networks are small-world
- Coherent transport on Apollonian networks and continuous-time quantum walks
- The topological Dirac equation of networks and simplicial complexes
- Laplacian paths in complex networks: information core emerges from entropic transitions
- Multi-User Entanglement Distribution in Quantum Networks Using Multipath Routing
- Persistent Dirac for molecular representation
- Complex networks with complex weights
- Versatile relative entropy bounds for quantum networks
- Gapped Two-Body Hamiltonian for continuous-variable quantum computation
- Dirac signal processing of higher-order topological signals
- Limited path entanglement percolation in quantum complex networks
- Dirac synchronization is rhythmic and explosive
- Minimal model for spontaneous quantum synchronization
- Diffusion-driven instability of topological signals coupled by the Dirac operator
- Self-Assembly of Geometric Space from Random Graphs
- Lectures on Quantum Tensor Networks
- Phase transition of light on complex quantum networks
- Fingerprint and universal Markovian closure of structured bosonic environments
- Continuous-time quantum walks on dynamical percolation graphs
- Local Dirac Synchronization on Networks
- Energy backflow in strongly coupled non-Markovian continuous-variables systems
- Influence of noise in entanglement-based quantum networks
- Continuous Time Quantum Walks in finite Dimensions
- Satellite Relayed Global Quantum Communication without Quantum Memory
- Continuous-Time Quantum Walks on Dynamic Graphs
- Achieving the ultimate end-to-end rates of lossy quantum communication networks
- The mass of simple and higher-order networks
- Quantum-classical distance as a tool to design optimal chiral quantum walk
- Dirac gauge theory for topological spinors in 3+1 dimensional networks
- End-to-End Capacities of Hybrid Quantum Networks
- Deterministic Entanglement Distribution on Series-Parallel Quantum Networks
- The Quantum Internet: A Hardware Review
- Complex quantum network models from spin clusters
- Dynamics of condensation in growing complex networks
- Rate limits in quantum networks with lossy repeaters
- Characterization and comparison of large directed graphs through the spectra of the magnetic Laplacian
- Statistical mechanics of graph models and their implications for emergent spacetime manifolds
- Noisy Stabilizer Formalism
- Field operator transformations in Quantum Optics using a novel graphical method with applications to beam splitters and interferometers
- Extended-range percolation in complex networks
- Swift chiral quantum walks
- Continuous variables graph states shaped as complex networks: optimization and manipulation
- Grand canonical ensembles of sparse networks and Bayesian inference
- The quantum optical description of three experiments involving non-linear optics using a graphical method
- Low-Dissipation Data Bus via Coherent Quantum Dynamics
- Network science Ising states of matter
- Perfect transfer of quantum states in a network of harmonic oscillators
- Optimal quantum key distribution networks: capacitance versus security
- Physics in non-fixed spatial dimensions via random networks
- Emergent spacetime from purely random structures
- Continuum limit for a discrete Hodge-Dirac operator on square lattices
- Dissipative Quantum Hopfield Network: A numerical analysis
- A sprinkling of hybrid-signature discrete spacetimes in real-world networks
- Practical limitations on robustness and scalability of quantum Internet
- Non-Markovianity over ensemble averages in quantum complex networks
Cited by in corpus (21)
- Path Percolation in Quantum Communication Networks
- Unveiling the Importance of Nonshortest Paths in Quantum Networks
- Optimal quantum key distribution networks: capacitance versus security
- Quantum entropy couples matter with geometry
- General theory for extended-range percolation on simple and multiplex networks
- Quantum Communication Networks Enhanced by Distributed Quantum Memories
- Discrete-Time Open Quantum Walks for Vertex Ranking in Graphs
- Exploring the Non-Markovian Dynamics in Depolarizing Maps
- Triadic percolation on multilayer networks
- Dynamical processes on metric networks
- Control of Overfitting with Physics
- Clustering-induced localization of quantum walks on networks
- Neural networks with quantum states of light
- Experimental Phase-Matching Quantum Cryptographic Conferencing in Symmetric and Asymmetric Fiber Channels
- Shaping Magnetic Order by Local Frustration for Itinerant Fermions on a Graph
- Perfect Wave Transfer in Continuous Quantum Systems
- Unsupervised Techniques to Detect Quantum Chaos
- Quantum HodgeRank: Topology-Based Rank Aggregation on Quantum Computers
- Noncooperative Quantum Networks
- Unveiling hidden features of the Kitaev model through a complex-network analysis
- Local-available quantum correlation swapping in one-parameter X states