1. Introducing complex networks into quantum regime
魏宗文
导师：汪秉宏 教授
中国科学技术大学 近代物理系

2. outline
Brief introduction of the joint study of quantum information and complex networks
Entanglement-based percolation
Classical and quantum entanglement percolation
Limited-path-length entanglement percolation
Quantum random networks
Small-world model of quantum repeater networks
Summary and outlook
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3. Joint study of complex networks and quantum information
Growth of graph states in quantum networks. PRA (2012)
Bipartite quantum states and random complex networks. New J. Phys (2012).
Encoding graphs into quantum states: an axiomatic approach. PRA (2012).
Synchronization, quantum correlations and entanglement in oscillator networks. Sci. Rep. (2013)
Adiabatic quantum algorithm for search engine ranking. PRL (2012).
Google in a quantum network. Sci. Rep. (2012)
Quantum navigation and ranking in complex networks. Sci. Rep. (2012).
featured progress
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4. Quantum networks provide access to exchange of quantum information.
Entanglement percolation in quantum networks. Nature physics. (2007)
Entanglement Percolation in Quantum Complex Networks. PRL (2009)
Quantum random networks. Nature physics. (2010)
Limited-path-length entanglement percolation in quantum complex networks. PRA (2011)
Renormalization and small-world model of fractal quantum repeater networks. Sci. Rep. (2013)
Quantum networks provide access to exchange of quantum information.
The primary task of quantum networks is to distribute entanglement between remote nodes.
Complex networks provide conceptual and mathematical preparation for design of quantum networks.
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5. Entanglement—assisted quantum communication
Quantum Teleportation
Teleportation
Quantum cryptograph (Ekert 91)
Dense coding
Entangled link
Entanglement Swapping
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7. outline
Brief introduction of the joint study of quantum information and complex networks
Entanglement-based percolation
Classical and quantum entanglement percolation
Limited-path-length entanglement percolation
Quantum random networks
Small-world model of quantum repeater networks
Summary and outlook
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8. From bond percolation to entanglement percolation
Classical entanglement percolation
Quantum entanglement percolation
Singlet conversion probability
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9. Trick of QEP: change topology and decrease threshold
Q-Swap:
Trick of QEP: change topology and decrease threshold
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10. Advantage of scale-free networks
Does QEP necessarily outperform CEP strategy?
How do you like entanglement percolation ?
Is entanglement percolation a new strategy ?
Topology is essential for entanglement distribution.
A trivial strategy
Advantage of scale-free networks
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11. Significance of small-world for quantum networks
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12. outline
Brief introduction of the joint study of quantum information and complex networks
Entanglement-based percolation
Classical and quantum entanglement percolation
Limited-path-length entanglement percolation
Quantum random networks
Small-world model of quantum repeater networks
Summary and outlook
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13. Beyond classical random networks model
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14. Threshold at which the giant connected cluster emerges?
A surprising result that goes beyond classical model
Collapse of critical exponents ～
Quantum:
Classical:
Threshold at which the giant connected cluster emerges?
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15. outline
Brief introduction of the joint study of quantum information and complex networks
Entanglement-based percolation
Classical and quantum entanglement percolation
Limited-path-length entanglement percolation
Quantum random networks
Small-world model of quantum repeater networks
Summary and outlook
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17. Possible topology of quantum repeater networks
Principle of quantum repeater protocols
Possible topology of quantum repeater networks
Quantum repeater networks are fractal.
Small-world effect could reinforce scalability.
Scale-free networks are robust to channel noise.
Generalize 1D quantum repeaters to high dimension:
Coupled renormalization
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18. Box-covering technique: maximum-excluded-mass-burning algorithm
Brief introduction to renormalization
Nature, 433, 392 (2005).
Box-covering technique: maximum-excluded-mass-burning algorithm
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19. Coupled Renormalization and high dimensional quantum repeaters
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20. Corresponding relationships
Renormalization and its relationship with quantum repeaters
Corresponding relationships
1D chain configuration
Scale-free fractal network
Length N
Segmentation: grouped into units
Box-covering : divided into boxes
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21. Application to a scale-free fractal network
Nature Phys. 2, 275 (2006).
Minimal Model
Parameters: n, s, a,e
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22. Proofs(1)—renormalization flow
Is there a critical nesting level n
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23. Proofs(2) definition
Hierarchical routing method
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24. Criterion and direct evidence
Recursive Derivation
Critical Condition
Critical Nesting Level
Diameter
Relevant comment on the simultaneous logarithmical behavior
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25. Statistical properties of coupled networks
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26. summary outlook Percolation phenomena in quantum networks.
Quantum random networks.
High fractal dimensional quantum repeaters: coupled renormalization.
The first scalable small-world model of quantum networks.
outlook
Introducing complex networks into quantum regime and search for quantum effect .
Does it make a difference? Is it complete?
Design of quantum internet.
Apart from quantum networks, there are a wide range of topics deserving pursuits for the joint study.
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27. Thanks for your attention!
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