Concurrence percolation threshold of large-scale quantum networks

Omar Malik; Xiangyi Meng; Shlomo Havlin; Gyorgy Korniss; Boleslaw Karol Szymanski; Jianxi Gao

doi:10.1038/s42005-022-00958-4

Concurrence percolation threshold of large-scale quantum networks

Omar Malik
, Xiangyi Meng
, Shlomo Havlin
, Gyorgy Korniss
, Boleslaw Karol Szymanski
, Jianxi Gao

Department of Physics - at Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

Abstract

Quantum networks describe communication networks that are based on quantum entanglement. A concurrence percolation theory has been recently developed to determine the required entanglement to enable communication between two distant stations in an arbitrary quantum network. Unfortunately, concurrence percolation has been calculated only for very small networks or large networks without loops. Here, we develop a set of mathematical tools for approximating the concurrence percolation threshold for unprecedented large-scale quantum networks by estimating the path-length distribution, under the assumption that all paths between a given pair of nodes have no overlap. We show that our approximate method agrees closely with analytical results from concurrence percolation theory. The numerical results we present include 2D square lattices of 200² nodes and complex networks of up to 10⁴ nodes. The entanglement percolation threshold of a quantum network is a crucial parameter for constructing a real-world communication network based on entanglement, and our method offers a significant speed-up for the intensive computations involved.

Original language	English
Article number	193
Number of pages	11
Journal	Communications Physics
Volume	5
Issue number	1
DOIs	https://doi.org/10.1038/s42005-022-00958-4
State	Published - 29 Jul 2022

Bibliographical note

Publisher Copyright:
© 2022, The Author(s).

Funding

O.M., G.K., and B.K.S. were supported in part by the Defense Advanced Research Projects Agency (DARPA) and the Army Research Office (ARO) under Contract No. W911NF-17-C-0099. B.K.S. was also supported by ARO under Contract No. W911NF-16-1-05241. J.G. acknowledges the support of National Science Foundation under Grant No. 2047488, and the Rensselaer-IBM AI Research Collaboration. X.M. was supported by the NetSeed: Seedling Research Award of Northeastern University. S.H. thanks the Israel Science Foundation, the Binational Israel-China Science Foundation (Grant No. 3132/19), the BIU Center for Research in Applied Cryptography and Cyber Security, NSF-BSF (Grant No. 2019740) and DTRA (Grant No. HDTRA1-19-1-0016) for financial support. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies either expressed or implied by the U.S. Government.

Funders	Funder number
Binational Israel-China Science Foundation	3132/19
NSF-BSF	2019740, HDTRA1-19-1-0016
National Science Foundation	2047488
Army Research Office	W911NF-17-C-0099, W911NF-16-1-05241
Defense Advanced Research Projects Agency
Northeastern University
Israel Science Foundation

Access to Document

10.1038/s42005-022-00958-4

Cite this

@article{e1c8916eded64ff79fb79c5ce3ccc7b4,

title = "Concurrence percolation threshold of large-scale quantum networks",

abstract = "Quantum networks describe communication networks that are based on quantum entanglement. A concurrence percolation theory has been recently developed to determine the required entanglement to enable communication between two distant stations in an arbitrary quantum network. Unfortunately, concurrence percolation has been calculated only for very small networks or large networks without loops. Here, we develop a set of mathematical tools for approximating the concurrence percolation threshold for unprecedented large-scale quantum networks by estimating the path-length distribution, under the assumption that all paths between a given pair of nodes have no overlap. We show that our approximate method agrees closely with analytical results from concurrence percolation theory. The numerical results we present include 2D square lattices of 2002 nodes and complex networks of up to 104 nodes. The entanglement percolation threshold of a quantum network is a crucial parameter for constructing a real-world communication network based on entanglement, and our method offers a significant speed-up for the intensive computations involved.",

author = "Omar Malik and Xiangyi Meng and Shlomo Havlin and Gyorgy Korniss and Szymanski, \{Boleslaw Karol\} and Jianxi Gao",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s).",

year = "2022",

month = jul,

day = "29",

doi = "10.1038/s42005-022-00958-4",

language = "אנגלית",

volume = "5",

journal = "Communications Physics",

issn = "2399-3650",

publisher = "Springer Nature",

number = "1",

}

TY - JOUR

T1 - Concurrence percolation threshold of large-scale quantum networks

AU - Malik, Omar

AU - Meng, Xiangyi

AU - Havlin, Shlomo

AU - Korniss, Gyorgy

AU - Szymanski, Boleslaw Karol

AU - Gao, Jianxi

PY - 2022/7/29

Y1 - 2022/7/29

N2 - Quantum networks describe communication networks that are based on quantum entanglement. A concurrence percolation theory has been recently developed to determine the required entanglement to enable communication between two distant stations in an arbitrary quantum network. Unfortunately, concurrence percolation has been calculated only for very small networks or large networks without loops. Here, we develop a set of mathematical tools for approximating the concurrence percolation threshold for unprecedented large-scale quantum networks by estimating the path-length distribution, under the assumption that all paths between a given pair of nodes have no overlap. We show that our approximate method agrees closely with analytical results from concurrence percolation theory. The numerical results we present include 2D square lattices of 2002 nodes and complex networks of up to 104 nodes. The entanglement percolation threshold of a quantum network is a crucial parameter for constructing a real-world communication network based on entanglement, and our method offers a significant speed-up for the intensive computations involved.

AB - Quantum networks describe communication networks that are based on quantum entanglement. A concurrence percolation theory has been recently developed to determine the required entanglement to enable communication between two distant stations in an arbitrary quantum network. Unfortunately, concurrence percolation has been calculated only for very small networks or large networks without loops. Here, we develop a set of mathematical tools for approximating the concurrence percolation threshold for unprecedented large-scale quantum networks by estimating the path-length distribution, under the assumption that all paths between a given pair of nodes have no overlap. We show that our approximate method agrees closely with analytical results from concurrence percolation theory. The numerical results we present include 2D square lattices of 2002 nodes and complex networks of up to 104 nodes. The entanglement percolation threshold of a quantum network is a crucial parameter for constructing a real-world communication network based on entanglement, and our method offers a significant speed-up for the intensive computations involved.

UR - https://www.scopus.com/pages/publications/85135159491

U2 - 10.1038/s42005-022-00958-4

DO - 10.1038/s42005-022-00958-4

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85135159491

SN - 2399-3650

VL - 5

JO - Communications Physics

JF - Communications Physics

IS - 1

M1 - 193

ER -

Concurrence percolation threshold of large-scale quantum networks

Abstract

Bibliographical note

Funding

Access to Document

Other files and links

Fingerprint

Cite this