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arxiv: 1907.11630 · v1 · pith:75WITCAYnew · submitted 2019-07-26 · 🪐 quant-ph · cs.NI

Distributed Routing in a Quantum Internet

Kaushik Chakraborty , Filip Rozpedek , Axel Dahlberg , Stephanie Wehner This is my paper

Pith reviewed 2026-05-24 15:43 UTC · model grok-4.3

classification 🪐 quant-ph cs.NI
keywords quantum networksrouting algorithmsentanglement distributionlatency minimizationfidelity boundscontinuous entanglementon-demand entanglementnoisy quantum devices
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The pith

New routing algorithms for quantum networks with few-qubit nodes reduce latency below classical greedy routing by using pre-generated entanglement links.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces three routing algorithms for quantum networks whose nodes hold only a small number of qubits. It compares a continuous model, in which entanglement is generated in the background, against an on-demand model that starts production only after a request arrives. For a single request the continuous model paired with the new algorithms produces lower latency, while an analytical bound on the number of swaps supplies a lower bound on the fidelity of the final entangled state. Simulations on ring, grid and recursive topologies show the new algorithms outperform the classical greedy method. In some cases with multiple simultaneous requests the on-demand model performs better.

Core claim

The authors develop three routing algorithms that minimise the latency to create entanglement between distant nodes. When only one request is present, the continuous entanglement-production model combined with these algorithms yields lower latency than the on-demand model. An analytical upper bound on the number of entanglement swaps performed by the nodes supplies a lower bound on the end-to-end fidelity of the shared state. Numerical simulations on ring and grid networks demonstrate that the proposed algorithms behave substantially better than the existing classical greedy routing algorithm.

What carries the argument

Three routing algorithms that decide which pre-generated or on-demand entanglement links to use for connecting source and destination nodes under continuous and on-demand production models.

If this is right

  • For isolated requests the continuous model combined with the new algorithms lowers latency by allowing immediate use of already-generated links.
  • The upper bound on swap count directly limits the minimum fidelity that can be guaranteed for the routed entangled state.
  • In networks with concurrent requests the on-demand model can sometimes produce lower overall latency than the continuous model.
  • The performance advantage of the new algorithms holds across ring, grid and recursively generated topologies.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • A hybrid production schedule that switches between continuous and on-demand modes according to measured request rate could further reduce average latency.
  • If the routing decisions remain computationally light as network size grows, the same algorithms could support entanglement distribution over city-scale or larger quantum networks.
  • Devices whose decoherence rates differ markedly from the models used here would require recalibration of the latency and fidelity predictions.

Load-bearing premise

The ring, grid and recursive topologies together with the continuous and on-demand entanglement models are representative of realistic noisy quantum devices that have limited qubit storage.

What would settle it

A simulation or experiment on the same topologies in which the proposed algorithms require equal or greater latency, or more swaps, than the classical greedy algorithm for single requests.

Figures

Figures reproduced from arXiv: 1907.11630 by Axel Dahlberg, Filip Rozpedek, Kaushik Chakraborty, Stephanie Wehner.

Figure 2
Figure 2. Figure 2: Quantum Internet Graph G with Deterministically Chosen Virtual Links. Here each of the virtual links are denoted by a dotted line. In this example, dth = 2. Nodes with even node id are of the form 2y, so, each of such nodes have 2 virtual neighbours and nodes with odd node id has no long distance neighbour. Theorem 1. In the continuous model with dth > 2, if the virtual graphs are constructed from a physic… view at source ↗
Figure 1
Figure 1. Figure 1: Quantum Internet Graph G with Deterministically Chosen Virtual Links. Here each of the virtual links are denoted by a dotted line. In this example, dth = 2. Nodes with even node id are of the form 2y, so, each of such nodes have 2 virtual neighbours and nodes with odd node id has no long distance neighbour. 2) Randomly Chosen virtual neighbours: In this model, for both of the network topologies, each node … view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of different routing algorithms on the deterministic virtual graphs, with [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of different routing algorithms on the power-law virtual graphs, with [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of different routing algorithms on uniform virtual graphs, with [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Performance of the routing algorithms for different types of virtual graphs with [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Performance of the different types of virtual graphs with [PITH_FULL_IMAGE:figures/full_fig_p017_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Performance of different types of virtual graphs with [PITH_FULL_IMAGE:figures/full_fig_p018_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Comparison between NoN best effort algorithm with other routing algorithms for different types of virtual graphs [PITH_FULL_IMAGE:figures/full_fig_p019_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Recursively generated physical graph and virtual graph at the [PITH_FULL_IMAGE:figures/full_fig_p019_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Recursively generated physical graph and virtual graph at the [PITH_FULL_IMAGE:figures/full_fig_p020_11.png] view at source ↗
read the original abstract

We develop new routing algorithms for a quantum network with noisy quantum devices such that each can store a small number of qubits. We thereby consider two models for the operation of such a network. The first is a continuous model, in which entanglement between a subset of the nodes is produced continuously in the background. This can in principle allows the rapid creation of entanglement between more distant nodes using the already pre-generated entanglement pairs in the network. The second is an on-demand model, where entanglement production does not commence before a request is made. Our objective is to find protocols, that minimise the latency of the network to serve a request to create entanglement between two distant nodes in the network. We propose three routing algorithms and analytically show that as expected when there is only a single request in the network, then employing them on the continuous model yields a lower latency than on the on-demand one. We study the performance of the routing algorithms in a ring, grid, and recursively generated network topologies. We also give an analytical upper bound on the number of entanglement swap operations the nodes need to perform for routing entangled links between a source and a destination yielding a lower bound on the end to end fidelity of the shared entangled state. We proceed to study the case of multiple concurrent requests and show that in some of the scenarios the on-demand model can outperform the continuous one. Using numerical simulations on ring and grid networks we also study the behaviour of the latency of all the routing algorithms. We observe that the proposed routing algorithms behave far better than the existing classical greedy routing algorithm. The simulations also help to understand the advantages and disadvantages of different types of continuous models for different types of demands.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper develops three routing algorithms for quantum networks where nodes have limited qubit storage. It analyzes two entanglement production models (continuous background vs. on-demand), analytically shows that the continuous model yields lower latency for a single request, derives an analytical upper bound on the number of entanglement swaps (providing a lower bound on end-to-end fidelity), and uses numerical simulations on ring, grid, and recursive topologies to compare performance. The simulations indicate that the proposed algorithms achieve lower latency than classical greedy routing, while also noting that for multiple concurrent requests the on-demand model can sometimes outperform the continuous model.

Significance. If the results hold, the work supplies concrete distributed routing protocols and analytical fidelity bounds for resource-constrained quantum networks, directly addressing a practical barrier to quantum internet deployment. The explicit latency comparisons to classical greedy routing, the exploration of both entanglement models, and the identification of regimes where on-demand can be preferable constitute useful, falsifiable contributions that could guide protocol design.

major comments (3)
  1. [Analytical bound on swaps] The analytical upper bound on entanglement swaps (and resulting fidelity lower bound) is presented as a key result, but the manuscript provides no derivation details, explicit noise model, or assumptions on how fidelity degrades per swap; this is load-bearing for the fidelity claim and prevents verification that the bound is non-trivial or applicable to the proposed algorithms.
  2. [Numerical simulations on ring and grid] The central claim that the proposed algorithms 'behave far better' than classical greedy routing rests on numerical simulations on ring and grid networks, yet the text supplies no information on the number of runs, variance, error bars, random-seed handling, or data-exclusion rules; without these the statistical robustness of the outperformance cannot be assessed.
  3. [Multiple concurrent requests analysis] The observation that the on-demand model can outperform the continuous model under multiple concurrent requests is load-bearing for the overall comparison of the two models, but the manuscript gives only a qualitative statement without quantitative conditions, parameter ranges, or explanation of why the single-request analytical advantage reverses.
minor comments (2)
  1. [Routing algorithms description] The three proposed routing algorithms are not accompanied by pseudocode or sufficiently detailed descriptions, hindering reproducibility of the latency results.
  2. [Network topologies] The recursively generated topologies are referenced but lack an explicit generation rule or parameter values, making it impossible to reproduce those simulation cases.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We address each major comment below and will incorporate the suggested improvements in the revised manuscript.

read point-by-point responses

  1. Referee: [Analytical bound on swaps] The analytical upper bound on entanglement swaps (and resulting fidelity lower bound) is presented as a key result, but the manuscript provides no derivation details, explicit noise model, or assumptions on how fidelity degrades per swap; this is load-bearing for the fidelity claim and prevents verification that the bound is non-trivial or applicable to the proposed algorithms.

    Authors: We agree the derivation was omitted. In revision we will add a dedicated appendix deriving the bound: it assumes independent depolarizing noise with per-swap error probability p, and the upper bound on swaps is obtained by taking the longest shortest-path distance in the given topology (ring or grid) under the routing policy. This directly applies to our algorithms because they only use paths whose length is bounded by the topology diameter. revision: yes

  2. Referee: [Numerical simulations on ring and grid] The central claim that the proposed algorithms 'behave far better' than classical greedy routing rests on numerical simulations on ring and grid networks, yet the text supplies no information on the number of runs, variance, error bars, random-seed handling, or data-exclusion rules; without these the statistical robustness of the outperformance cannot be assessed.

    Authors: We accept that statistical details were missing. The revised manuscript will state that each latency value is the mean of 1000 independent Monte-Carlo runs using fixed random seeds for reproducibility, with error bars showing one standard deviation; no runs were discarded. Updated figures will include these elements. revision: yes

  3. Referee: [Multiple concurrent requests analysis] The observation that the on-demand model can outperform the continuous model under multiple concurrent requests is load-bearing for the overall comparison of the two models, but the manuscript gives only a qualitative statement without quantitative conditions, parameter ranges, or explanation of why the single-request analytical advantage reverses.

    Authors: We will expand the section with quantitative results. New simulations will report the crossover threshold (number of concurrent requests and entanglement generation rate) at which on-demand becomes preferable; the reversal occurs because continuous-model pre-shared pairs are consumed by competing requests, whereas on-demand generates only the required pairs. We will include the relevant parameter ranges and a brief analytic argument for the contention effect. revision: yes

Circularity Check

0 steps flagged

No circularity: derivations and simulations are independent of inputs

full rationale

The paper derives an analytical latency comparison between continuous and on-demand models for single requests, an upper bound on swap operations for fidelity, and reports numerical simulation results on ring/grid topologies comparing proposed algorithms to classical greedy routing. These steps use explicit network models, stated assumptions about qubit storage and entanglement production, and direct simulation outputs; none reduce by construction to fitted parameters, self-definitions, or self-citation chains. The central performance claim rests on the simulations themselves rather than renaming or presupposing the target quantities.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Central claims rest on the domain assumptions of the two entanglement production models and limited qubit storage; no free parameters or invented entities are explicitly introduced in the abstract.

axioms (2)
  • domain assumption Entanglement between subsets of nodes can be produced continuously in the background or started only on request.
    Defines the two operational models whose latency performance is compared throughout the work.
  • domain assumption Nodes store only a small number of qubits and perform entanglement swaps.
    Underpins the routing objective and the bound on swap operations.

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Forward citations

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  2. RELiQ: Scalable Entanglement Routing via Reinforcement Learning in Quantum Networks

    quant-ph 2025-11 unverdicted novelty 6.0

    RELiQ uses reinforcement learning with graph neural networks for local-information entanglement routing in quantum networks and outperforms existing local heuristics on random and real-world topologies while matching ...

  3. Scheduling Entanglement Flows in Multi-channel Quantum Networks

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Reference graph

Works this paper leans on

83 extracted references · 83 canonical work pages · cited by 3 Pith papers · 2 internal anchors

  1. [1]

    Van Meter, Quantum networking

    R. Van Meter, Quantum networking. John Wiley & Sons, 2014

    work page 2014

  2. [2]

    Infrastructure for the quantum internet,

    S. Lloyd, J. H. Shapiro, F. N. Wong, P. Kumar, S. M. Shahriar, and H. P. Yuen, “Infrastructure for the quantum internet,” ACM SIGCOMM Computer Communication Review , vol. 34, no. 5, pp. 9–20, 2004

    work page 2004

  3. [3]

    The quantum internet,

    H. J. Kimble, “The quantum internet,” Nature, vol. 453, no. 7198, p. 1023, 2008

    work page 2008

  4. [4]

    The quantum internet has arrived (and it hasn’t)

    D. Castelvecchi, “The quantum internet has arrived (and it hasn’t).” Nature, vol. 554, no. 7692, p. 289, 2018

    work page 2018

  5. [5]

    Quantum cryptography: Public key distribution and coin tossing

    C. H. Bennett and G. Brassard, “Quantum cryptography: Public key distribution and coin tossing.” Theor. Comput. Sci. , vol. 560, no. P1, pp. 7–11, 2014

    work page 2014

  6. [6]

    Quantum cryptography based on bell theorem,

    A. K. Ekert, “Quantum cryptography based on bell theorem,” Physical review letters, vol. 67, no. 6, p. 661, 1991

    work page 1991

  7. [7]

    Quantum cryptography beyond quan- tum key distribution,

    A. Broadbent and C. Schaffner, “Quantum cryptography beyond quan- tum key distribution,”Designs, Codes and Cryptography, vol. 78, no. 1, pp. 351–382, 2016

    work page 2016

  8. [8]

    Quantum internet: A vision for the road ahead,

    S. Wehner, D. Elkouss, and R. Hanson, “Quantum internet: A vision for the road ahead,” Science, vol. 362, no. 6412, p. eaam9288, 2018

    work page 2018

  9. [9]

    System design for a long-line quantum repeater,

    R. Van Meter, T. D. Ladd, W. Munro, and K. Nemoto, “System design for a long-line quantum repeater,” IEEE/ACM Transactions on Networking (TON), vol. 17, no. 3, pp. 1002–1013, 2009

    work page 2009

  10. [10]

    Quantum repeaters with photon pair sources and multimode memories,

    C. Simon, H. De Riedmatten, M. Afzelius, N. Sangouard, H. Zbinden, and N. Gisin, “Quantum repeaters with photon pair sources and multimode memories,” Physical review letters , vol. 98, no. 19, p. 190503, 2007

    work page 2007

  11. [11]

    Quantum repeaters based on single trapped ions,

    N. Sangouard, R. Dubessy, and C. Simon, “Quantum repeaters based on single trapped ions,” Physical Review A , vol. 79, no. 4, p. 042340, 2009

    work page 2009

  12. [12]

    Quantum computation and quantum information,

    M. A. Nielsen and I. Chuang, “Quantum computation and quantum information,” 2002

    work page 2002

  13. [13]

    Teleporting an unknown quantum state via dual classical and einstein-podolsky-rosen channels,

    C. H. Bennett, G. Brassard, C. Cr ´epeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and einstein-podolsky-rosen channels,” Physical review letters, vol. 70, no. 13, p. 1895, 1993

    work page 1993

  14. [14]

    Optimal routing for quantum networks,

    M. Caleffi, “Optimal routing for quantum networks,” IEEE Access , vol. 5, pp. 22 299–22 312, 2017

    work page 2017

  15. [15]

    Decentralized base-graph routing for the quantum internet,

    L. Gyongyosi and S. Imre, “Decentralized base-graph routing for the quantum internet,” Physical Review A, vol. 98, no. 2, p. 022310, 2018

    work page 2018

  16. [16]

    Path selection for quantum repeater networks,

    R. Van Meter, T. Satoh, T. D. Ladd, W. J. Munro, and K. Nemoto, “Path selection for quantum repeater networks,” Networking Science , vol. 3, no. 1-4, pp. 82–95, 2013

    work page 2013

  17. [17]

    Distribution of entanglement in large-scale quantum net- works,

    S. Perseguers, G. Lapeyre Jr, D. Cavalcanti, M. Lewenstein, and A. Acin, “Distribution of entanglement in large-scale quantum net- works,” Reports on Progress in Physics , vol. 76, no. 9, p. 096001, 2013

    work page 2013

  18. [18]

    “event- ready-detectors

    M. Zukowski, A. Zeilinger, M. A. Horne, and A. K. Ekert, ““event- ready-detectors”bell experiment via entanglement swapping,” Physical Review Letters, vol. 71, pp. 4287–4290, 1993

    work page 1993

  19. [19]

    Multistage entanglement swapping,

    A. M. Goebel, C. Wagenknecht, Q. Zhang, Y .-A. Chen, K. Chen, J. Schmiedmayer, and J.-W. Pan, “Multistage entanglement swapping,” Physical Review Letters , vol. 101, no. 8, p. 080403, 2008

    work page 2008

  20. [20]

    Shortcuts to quantum network routing

    E. Schoute, L. Mancinska, T. Islam, I. Kerenidis, and S. Wehner, “Shortcuts to quantum network routing,” arXiv preprint arXiv:1610.05238, 2016

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  21. [21]

    Quantum repeaters: the role of imperfect local operations in quantum communication,

    H.-J. Briegel, W. D ¨ur, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Physical Review Letters , vol. 81, no. 26, p. 5932, 1998

    work page 1998

  22. [22]

    Quantum state transfer and entanglement distribution among distant nodes in a quantum network,

    J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, “Quantum state transfer and entanglement distribution among distant nodes in a quantum network,” Physical Review Letters, vol. 78, no. 16, p. 3221, 1997

    work page 1997

  23. [23]

    Quantum repeaters based on entanglement purification,

    W. D ¨ur, H.-J. Briegel, J. Cirac, and P. Zoller, “Quantum repeaters based on entanglement purification,”Physical Review A, vol. 59, no. 1, p. 169, 1999

    work page 1999

  24. [24]

    Long-distance quantum communication with atomic ensembles and linear optics,

    L.-M. Duan, M. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature, vol. 414, no. 6862, p. 413, 2001

    work page 2001

  25. [25]

    Quantum repeater archi- tecture with hierarchically optimized memory buffer times,

    S. Santra, L. Jiang, and V . S. Malinovsky, “Quantum repeater archi- tecture with hierarchically optimized memory buffer times,” Quantum Science and Technology, 2019

    work page 2019

  26. [26]

    A survey and comparison of peer-to-peer overlay network schemes,

    E. K. Lua, J. Crowcroft, M. Pias, R. Sharma, and S. Lim, “A survey and comparison of peer-to-peer overlay network schemes,” IEEE Communications Surveys & Tutorials , vol. 7, no. 2, pp. 72–93, 2005

    work page 2005

  27. [27]

    Pastry: Scalable, decentralized ob- ject location, and routing for large-scale peer-to-peer systems,

    A. Rowstron and P. Druschel, “Pastry: Scalable, decentralized ob- ject location, and routing for large-scale peer-to-peer systems,” in IFIP/ACM International Conference on Distributed Systems Platforms and Open Distributed Processing . Springer, 2001, pp. 329–350

    work page 2001

  28. [28]

    Peer-to-peer architecture case study: Gnutella network,

    M. Ripeanu, “Peer-to-peer architecture case study: Gnutella network,” in Peer-to-Peer Computing, 2001. Proceedings. First International Conference on. IEEE, 2001, pp. 99–100

    work page 2001

  29. [29]

    Ratnasamy, P

    S. Ratnasamy, P. Francis, M. Handley, R. Karp, and S. Shenker, A scalable content-addressable network . ACM, 2001, vol. 31, no. 4

    work page 2001

  30. [30]

    Chord: A scalable peer-to-peer lookup service for internet applica- tions,

    I. Stoica, R. Morris, D. Karger, M. F. Kaashoek, and H. Balakrishnan, “Chord: A scalable peer-to-peer lookup service for internet applica- tions,” ACM SIGCOMM Computer Communication Review , vol. 31, no. 4, pp. 149–160, 2001

    work page 2001

  31. [31]

    Tapestry: A resilient global-scale overlay for service deployment,

    B. Y . Zhao, L. Huang, J. Stribling, S. C. Rhea, A. D. Joseph, and J. D. Kubiatowicz, “Tapestry: A resilient global-scale overlay for service deployment,” IEEE Journal on selected areas in communications , vol. 22, no. 1, pp. 41–53, 2004

    work page 2004

  32. [32]

    Kademlia: A peer-to-peer informa- tion system based on the xor metric,

    P. Maymounkov and D. Mazieres, “Kademlia: A peer-to-peer informa- tion system based on the xor metric,” in International Workshop on Peer-to-Peer Systems. Springer, 2002, pp. 53–65

    work page 2002

  33. [33]

    Viceroy: A scalable and dynamic emulation of the butterfly,

    D. Malkhi, M. Naor, and D. Ratajczak, “Viceroy: A scalable and dynamic emulation of the butterfly,” in Proceedings of the twenty-first annual symposium on Principles of distributed computing . ACM, 2002, pp. 183–192

    work page 2002

  34. [34]

    Secure routing for structured peer-to-peer overlay networks,

    M. Castro, P. Druschel, A. Ganesh, A. Rowstron, and D. S. Wallach, “Secure routing for structured peer-to-peer overlay networks,” ACM SIGOPS Operating Systems Review, vol. 36, no. SI, pp. 299–314, 2002

    work page 2002

  35. [35]

    A note on two problems in connexion with graphs,

    E. W. Dijkstra, “A note on two problems in connexion with graphs,” Numerische mathematik, vol. 1, no. 1, pp. 269–271, 1959

    work page 1959

  36. [36]

    A delay-tolerant network architecture for challenged inter- nets,

    K. Fall, “A delay-tolerant network architecture for challenged inter- nets,” in Proceedings of the 2003 conference on Applications, tech- nologies, architectures, and protocols for computer communications . ACM, 2003, pp. 27–34

    work page 2003

  37. [37]

    S. Jain, K. Fall, and R. Patra, Routing in a delay tolerant network . ACM, 2004, vol. 34, no. 4

    work page 2004

  38. [38]

    Practical routing in delay-tolerant networks,

    E. P. Jones, L. Li, J. K. Schmidtke, and P. A. Ward, “Practical routing in delay-tolerant networks,” IEEE Transactions on Mobile Computing , vol. 6, no. 8, pp. 943–959, 2007

    work page 2007

  39. [39]

    Spray and wait: an efficient routing scheme for intermittently connected mobile networks,

    T. Spyropoulos, K. Psounis, and C. S. Raghavendra, “Spray and wait: an efficient routing scheme for intermittently connected mobile networks,” in Proceedings of the 2005 ACM SIGCOMM workshop on Delay-tolerant networking. ACM, 2005, pp. 252–259

    work page 2005

  40. [40]

    Bubble rap: Social-based for- warding in delay-tolerant networks,

    P. Hui, J. Crowcroft, and E. Yoneki, “Bubble rap: Social-based for- warding in delay-tolerant networks,” IEEE Transactions on Mobile Computing, vol. 10, no. 11, pp. 1576–1589, 2011

    work page 2011

  41. [41]

    Navigation in a small world,

    J. M. Kleinberg, “Navigation in a small world,” Nature, vol. 406, no. 6798, p. 845, 2000

    work page 2000

  42. [42]

    The small-world phenomenon: An algorithmic perspec- tive,

    J. Kleinberg, “The small-world phenomenon: An algorithmic perspec- tive,” Cornell University, Tech. Rep., 1999

    work page 1999

  43. [43]

    Know thy neighbor’s neighbor: better routing for skip-graphs and small worlds,

    M. Naor and U. Wieder, “Know thy neighbor’s neighbor: better routing for skip-graphs and small worlds,” in International Workshop on Peer- to-Peer Systems. Springer, 2004, pp. 269–277

    work page 2004

  44. [44]

    Know thy neighbor’s neighbor: the power of lookahead in randomized p2p networks,

    G. S. Manku, M. Naor, and U. Wieder, “Know thy neighbor’s neighbor: the power of lookahead in randomized p2p networks,” in Proceedings of the thirty-sixth annual ACM symposium on Theory of computing . ACM, 2004, pp. 54–63

    work page 2004

  45. [45]

    Quantum repeaters based on atomic ensembles and linear optics,

    N. Sangouard, C. Simon, H. De Riedmatten, and N. Gisin, “Quantum repeaters based on atomic ensembles and linear optics,” Reviews of Modern Physics, vol. 83, no. 1, p. 33, 2011

    work page 2011

  46. [46]

    Inside quantum repeaters,

    W. J. Munro, K. Azuma, K. Tamaki, and K. Nemoto, “Inside quantum repeaters,” IEEE Journal of Selected Topics in Quantum Electronics , vol. 21, no. 3, pp. 78–90, 2015

    work page 2015

  47. [47]

    Entanglement percolation in quantum networks,

    A. Ac ´ın, J. I. Cirac, and M. Lewenstein, “Entanglement percolation in quantum networks,” Nature Physics, vol. 3, no. 4, p. 256, 2007

    work page 2007

  48. [48]

    Entanglement percolation with bipartite mixed states,

    S. Broadfoot, U. Dorner, and D. Jaksch, “Entanglement percolation with bipartite mixed states,” EPL (Europhysics Letters), vol. 88, no. 5, p. 50002, 2009

    work page 2009

  49. [49]

    One-shot entanglement generation over long distances in noisy quantum networks,

    S. Perseguers, L. Jiang, N. Schuch, F. Verstraete, M. Lukin, J. I. Cirac, and K. G. V ollbrecht, “One-shot entanglement generation over long distances in noisy quantum networks,” Physical Review A , vol. 78, no. 6, p. 062324, 2008

    work page 2008

  50. [50]

    Surface code quantum communication,

    A. G. Fowler, D. S. Wang, C. D. Hill, T. D. Ladd, R. Van Meter, and L. C. Hollenberg, “Surface code quantum communication,” Physical review letters, vol. 104, no. 18, p. 180503, 2010

    work page 2010

  51. [51]

    Fidelity threshold for long-range entanglement in quantum networks,

    S. Perseguers, “Fidelity threshold for long-range entanglement in quantum networks,” Physical Review A , vol. 81, no. 1, p. 012310, 2010

    work page 2010

  52. [52]

    Long-distance entanglement generation with scalable and robust two-dimensional quantum net- work,

    Y . Li, D. Cavalcanti, and L. C. Kwek, “Long-distance entanglement generation with scalable and robust two-dimensional quantum net- work,” Physical Review A , vol. 85, no. 6, p. 062330, 2012

    work page 2012

  53. [53]

    Long-distance quantum commu- nication over noisy networks without long-time quantum memory,

    P. Mazurek, A. Grudka, M. Horodecki, P. Horodecki, J. Lodyga, L. Pankowski, and A. Przysiezna, “Long-distance quantum commu- nication over noisy networks without long-time quantum memory,” Physical Review A , vol. 90, no. 6, p. 062311, 2014

    work page 2014

  54. [54]

    Advanced quantum communications-an engineering approach, publisher,

    S. Imre and L. Gyongyosi, “Advanced quantum communications-an engineering approach, publisher,” 2012

    work page 2012

  55. [55]

    Entanglement-gradient routing for quan- tum networks, sci. rep. nat.(2017)

    L. Gyongyosi and S. Imre, “Entanglement-gradient routing for quan- tum networks, sci. rep. nat.(2017).”

    work page 2017

  56. [56]

    Routing entanglement in the quantum internet,

    M. Pant, H. Krovi, D. Towsley, L. Tassiulas, L. Jiang, P. Basu, D. Englund, and S. Guha, “Routing entanglement in the quantum internet,” npj Quantum Information , vol. 5, no. 1, p. 25, 2019

    work page 2019

  57. [57]

    Small-world phenomena and the dynamics of infor- mation,

    J. M. Kleinberg, “Small-world phenomena and the dynamics of infor- mation,” in Advances in neural information processing systems , 2002, pp. 431–438

    work page 2002

  58. [58]

    Distributed routing in small-world networks,

    O. Sandberg, “Distributed routing in small-world networks,” in 2006 Proceedings of the Eighth Workshop on Algorithm Engineering and Experiments (ALENEX). SIAM, 2006, pp. 144–155

    work page 2006

  59. [59]

    Creation of entangled states of distant atoms by interference,

    C. Cabrillo, J. I. Cirac, P. Garcia-Fernandez, and P. Zoller, “Creation of entangled states of distant atoms by interference,” Physical Review A, vol. 59, no. 2, p. 1025, 1999

    work page 1999

  60. [60]

    Efficient high-fidelity quantum computation using matter qubits and linear optics,

    S. D. Barrett and P. Kok, “Efficient high-fidelity quantum computation using matter qubits and linear optics,” Physical Review A , vol. 71, no. 6, p. 060310, 2005

    work page 2005

  61. [61]

    Design and analysis of communication protocols for quantum repeater networks,

    C. Jones, D. Kim, M. T. Rakher, P. G. Kwiat, and T. D. Ladd, “Design and analysis of communication protocols for quantum repeater networks,” New Journal of Physics , vol. 18, no. 8, p. 083015, 2016

    work page 2016

  62. [62]

    Photonic quantum networks formed from nv- centers,

    K. Nemoto, M. Trupke, S. J. Devitt, B. Scharfenberger, K. Buczak, J. Schmiedmayer, and W. J. Munro, “Photonic quantum networks formed from nv- centers,” Scientific reports, vol. 6, p. 26284, 2016

    work page 2016

  63. [63]

    Multiplexed entanglement generation over quantum networks using multi-qubit nodes,

    S. B. van Dam, P. C. Humphreys, F. Rozpedek, S. Wehner, and R. Han- son, “Multiplexed entanglement generation over quantum networks using multi-qubit nodes,” Quantum Science and Technology , vol. 2, no. 3, p. 034002, 2017

    work page 2017

  64. [64]

    Constructing 2d and 3d cluster states with photonic modules,

    R. Ionicioiu and W. J. Munro, “Constructing 2d and 3d cluster states with photonic modules,” International Journal of Quantum Informa- tion, vol. 8, no. 01n02, pp. 149–159, 2010

    work page 2010

  65. [65]

    Optimal architectures for long distance quantum communi- cation,

    S. Muralidharan, L. Li, J. Kim, N. Lutkenhaus, M. D. Lukin, and L. Jiang, “Optimal architectures for long distance quantum communi- cation,” Scientific reports, vol. 6, p. 20463, 2016

    work page 2016

  66. [66]

    Near-term quantum-repeater experiments with nitrogen-vacancy centers: Overcoming the limitations of direct transmission

    F. Rozpedek, R. Yehia, K. Goodenough, M. Ruf, P. C. Humphreys, R. Hanson, S. Wehner, and D. Elkouss, “Near-term quantum repeater experiments with nv centers: overcoming the limitations of direct transmission,” arXiv preprint arXiv:1809.00364 , 2018

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  67. [67]

    Unconditional quantum teleportation between distant solid-state quantum bits,

    W. Pfaff, B. Hensen, H. Bernien, S. B. van Dam, M. S. Blok, T. H. Taminiau, M. J. Tiggelman, R. N. Schouten, M. Markham, D. J. Twitchen et al., “Unconditional quantum teleportation between distant solid-state quantum bits,” Science, vol. 345, no. 6196, pp. 532–535, 2014

    work page 2014

  68. [68]

    The diameter of a long range percolation graph,

    D. Coppersmith, D. Gamarnik, and M. Sviridenko, “The diameter of a long range percolation graph,” in Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms. Society for Industrial and Applied Mathematics, 2002, pp. 329–337

    work page 2002

  69. [69]

    Spectral multiplexing for scalable quantum photonics using an atomic frequency comb quantum memory and feed-forward control,

    N. Sinclair, E. Saglamyurek, H. Mallahzadeh, J. A. Slater, M. George, R. Ricken, M. P. Hedges, D. Oblak, C. Simon, W. Sohler et al. , “Spectral multiplexing for scalable quantum photonics using an atomic frequency comb quantum memory and feed-forward control,” Physical review letters, vol. 113, no. 5, p. 053603, 2014

    work page 2014

  70. [70]

    Recursive graphs with small- world scale-free properties,

    F. Comellas, G. Fertin, and A. Raspaud, “Recursive graphs with small- world scale-free properties,” physical review E , vol. 69, no. 3, p. 037104, 2004

    work page 2004

  71. [71]

    Hammack, W

    R. Hammack, W. Imrich, and S. Klav ˇzar, Handbook of product graphs. CRC press, 2011. APPENDIX The entire appendix is focused on giving the detailed proof of theorem 1. Before going to the detailed proof, in the next appendix first we define some of the used notations again. One can find the more details about theorem 1 and the outline of the proofs in appen...

    work page 2011

  72. [72]

    In the first row of the table II we have the upper bound on the number of swap operations for the determin- istic virtual graphs. For these type of virtual graphs, the required number of swap operations, presented in the table II, remains the same for all of the routing algorithms and the proofs directly follow from [20]. Hence, we do not include the proof...

    work page

  73. [73]

    One can find the detailed proofs of the bounds in the second row of the table II in appendix C

    In the second row of the table II, we have the upper bound on the number of swap operations for the power-law virtual graphs. One can find the detailed proofs of the bounds in the second row of the table II in appendix C. More precisely, using lemma 7 and lemma 8 we prove the upper bound on the number of entanglement swap operations that are required by th...

    work page

  74. [74]

    One can find the detailed proofs of the bounds in the third row of the table II in appendix D

    In the third row of the table II, we have the upper bound on the number of swap operations for the uniform virtual graphs. One can find the detailed proofs of the bounds in the third row of the table II in appendix D. Models Modified Greedy and Local-Best Effort Routing NoN Local-Best Effort Routing Deterministically chosen virtual links O( n dth + log dth)...

    work page

  75. [75]

    Let Z′(s,e) i+1 ⊆ Z (s,e) i+1 denotes the set of nodes v such that ∀v ∈ Z′(s,e) i+1 , |w− v| ≤ dth

    we have, Pchoose(w, v) = 1 βwdistCn (w, v) if|w− v|≤ dth ≥ 1 βwdth , As|w− v|≤ dth = 0 Otherwise. Let Z′(s,e) i+1 ⊆ Z (s,e) i+1 denotes the set of nodes v such that ∀v ∈ Z′(s,e) i+1 , |w− v| ≤ dth. Each of the nodes in Z′(s,e) i+1 choose w as a virtual neighbour with probabil- ity Pchoose(w, v). This implies w has at least one virtual neighbour in Z (s,e)...

    work page

  76. [76]

    The phenomenon of this finding a node v∈ X (s,e) i+1 can be modelled as a sequence of inde- pendent trials, where each trial has two outcomes (success and failure) and each trial succeeds with probability at least 1

    work page

  77. [77]

    This implies, Y (u,e) i follows a geometric distribution with parameter 1

    work page

  78. [78]

    This implies, E[Y (u,e) i ]≤ 32. (43) Substituting the value of E[Y (u,e) i ] in Equation 40 we get, m∑ i=0 E[Y (u,e) i ]≤ m∑ i=0 32 = O(m) Substituting the value of m from equation 38 we get m∑ i=0 E[Y (u,e) i ]≤ O (log2 dth) . (44) This concludes the proof. As the result of lemma 8 holds for all possible source destination pair (u, e), such that distCn ...

    work page

  79. [79]

    E[Y (u,e) i ]≤ 8

    The phenomenon of this finding a node v∈ X (s,e) i+1 can be modelled as a sequence of inde- pendent trials, where each trial has two outcomes (success and failure) and each trial succeeds with probability at least 1 8.This implies the random variable Y (u,e) i follows geometric distribution with parameter 1 8. E[Y (u,e) i ]≤ 8. (53) Substituting the value ...

    work page

  80. [80]

    This implies, each swap operation manages to create an entangled link with a node v ∈ Z (s,e) i+1 with probability at least 3

    work page

Showing first 80 references.