Abstract
The quantum internet is envisioned as the ultimate stage of the quantum revolution, which surpasses its classical counterpart in various aspects, such as the efficiency of data transmission, the security of network services, and the capability of information processing. Given its disruptive impact on the national security and the digital economy, a global race to build scalable quantum networks has already begun. With the joint effort of national governments, industrial participants, and research institutes, the development of quantum networks has advanced rapidly in recent years, bringing the first primitive quantum networks within reach. In this work, we aim to provide an up-to-date review of the field of quantum networks from both theoretical and experimental perspectives, contributing to a better understanding of the building blocks required for the establishment of a global quantum internet. We also introduce a newly developed quantum network toolkit to facilitate the exploration and evaluation of innovative ideas. Particularly, it provides dual quantum computing engines, supporting simulations in both the quantum circuit and measurement-based models. It also includes a compilation scheme for mapping quantum network protocols onto quantum circuits, enabling their emulations on real-world quantum hardware devices. We showcase the power of this toolkit with several featured demonstrations, including a simulation of the Micius quantum satellite experiment, a testing of a four-layer quantum network architecture with resource management, and a quantum emulation of the CHSH game. We hope this work can give a better understanding of the state-of-the-art development of quantum networks and provide the necessary tools to make further contributions along the way.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Kimble H J. The quantum internet. Nature, 2008, 453: 1023–1030
Wehner S, Elkouss D, Hanson R. Quantum internet: a vision for the road ahead. Science, 2018, 362
Caleffi M, Cacciapuoti A S, Bianchi G. Quantum internet: from communication to distributed computing! In: Proceedings of the 5th ACM International Conference on Nanoscale Computing and Communication, 2018. 1–4
Castelvecchi D. The quantum internet has arrived (and it hasn’t). Nature, 2018, 554: 289–292
Kozlowski W, Wehner S. Towards large-scale quantum networks. In: Proceedings of the 6th Annual ACM International Conference on Nanoscale Computing and Communication, 2019. 1–7
Singh A, Dev K, Siljak H, et al. Quantum internet-applications, functionalities, enabling technologies, challenges, and research directions. IEEE Commun Surv Tut, 2021, 23: 2218–2247
Wei S, Jing B, Zhang X, et al. Towards real-world quantum networks: a review. Laser Photon Rev, 2022, 16: 2100219
Awschalom D, Berggren K K, Bernien H, et al. Development of quantum interconnects (QuICs) for next-generation information technologies. PRX Quantum, 2021, 2: 017002
Gyongyosi L, Imre S. Advances in the quantum internet. Commun ACM, 2022, 65: 52–63
Rohde P P. The Quantum Internet: The Second Quantum Revolution. Cambridge: Cambridge University Press, 2021
Pirandola S, Braunstein S L. Physics: unite to build a quantum internet. Nature, 2016, 532: 169–171
Ramakrishnan R K, Ravichandran A B, Kaushik I, et al. The quantum internet: a hardware review. J Ind Inst Sci, 2022, doi: https://doi.org/10.1007/s41745-022-00336-7
Bennett C, Brassard G. Quantum cryptography: public key distribution and coin tossing. In: Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing, 1984. 175–179
Ekert A K. Quantum cryptography based on Bell’s theorem. Phys Rev Lett, 1991, 67: 661–663
Broadbent A, Fitzsimons J, Kashefi E. Universal blind quantum computation. In: Proceedings of the 50th Annual IEEE Symposium on Foundations of Computer Science, 2009. 517–526
Jozsa R, Abrams D S, Dowling J P, et al. Quantum clock synchronization based on shared prior entanglement. Phys Rev Lett, 2000, 85: 2010–2013
Gottesman D, Jennewein T, Croke S. Longer-baseline telescopes using quantum repeaters. Phys Rev Lett, 2012, 109: 070503
Cirac J I, Ekert A K, Huelga S F, et al. Distributed quantum computation over noisy channels. Phys Rev A, 1999, 59: 4249–4254
Crépeau C, Gottesman D, Smith A. Secure multi-party quantum computation. In: Proceedings of the 34th Annual ACM Symposium on Theory of Computing, 2002. 643–652
Cuomo D, Caleffi M, Cacciapuoti A S. Towards a distributed quantum computing ecosystem. IET Quantum Commun, 2020, 1: 3–8
Lu C Y, Cao Y, Peng C Z, et al. Micius quantum experiments in space. Rev Mod Phys, 2022, 94: 035001
Liao S K, Cai W Q, Liu W Y, et al. Satellite-to-ground quantum key distribution. Nature, 2017, 549: 43–47
Castelvecchi D. China’s quantum satellite clears major hurdle on way to ultrasecure communications. Nature, 2017, doi: https://doi.org/10.1038/nature.2017.22142
Chen Y A, Zhang Q, Chen T Y, et al. An integrated space-to-ground quantum communication network over 4,600 kilometres. Nature, 2021, 589: 214–219
Courtland R. China’s 2,000-km quantum link is almost complete [News]. IEEE Spectr, 2016, 53: 11–12
Pompili M, Hermans S L N, Baier S, et al. Realization of a multinode quantum network of remote solid-state qubits. Science, 2021, 372: 259–264
Pirker A, Dür W. A quantum network stack and protocols for reliable entanglement-based networks. New J Phys, 2019, 21: 033003
Kozlowski W, Wehner S, Meter R V, et al. Architectural Principles for a Quantum Internet. RFC 9340. 2022
Van Meter R, Satoh R, Benchasattabuse N, et al. A quantum internet architecture. 2021. ArXiv:2112.07092
Coopmans T, Knegjens R, Dahlberg A, et al. NetSquid, a NETwork simulator for quantum information using discrete events. Commun Phys, 2021, 4: 164
Wu X, Kolar A, Chung J, et al. SeQUeNCe: a customizable discrete-event simulator of quantum networks. Quantum Sci Technol, 2021, 6: 045027
Satoh R, Hajdušek M, Benchasattabuse N, et al. QuISP: a quantum internet simulation package. 2021. ArXiv:2112.07093
Bartlett B. A distributed simulation framework for quantum networks and channels. 2018. ArXiv:1808.07047
Mailloux L O, Morris J D, Grimaila M R, et al. A modeling framework for studying quantum key distribution system implementation nonidealities. IEEE Access, 2015, 3: 110–130
Leone H, Miller N R, Singh D, et al. QuNet: cost vector analysis & multi-path entanglement routing in quantum networks. 2021. ArXiv:2105.00418
Slussarenko S, Pryde G J. Photonic quantum information processing: a concise review. Appl Phys Rev, 2019, 6: 041303
Krantz P, Kjaergaard M, Yan F, et al. A quantum engineer’s guide to superconducting qubits. Appl Phys Rev, 2019, 6: 021318
Bruzewicz C D, Chiaverini J, McConnell R, et al. Trapped-ion quantum computing: progress and challenges. Appl Phys Rev, 2019, 6: 021314
Hillery M. Coherence as a resource in decision problems: the Deutsch-Jozsa algorithm and a variation. Phys Rev A, 2016, 93: 012111
Hayashi M, Fang K, Wang K. Finite block length analysis on quantum coherence distillation and incoherent randomness extraction. IEEE Trans Inform Theory, 2021, 67: 3926–3944
Díaz M G, Fang K, Wang X, et al. Using and reusing coherence to realize quantum processes. Quantum, 2018, 2: 100
Fang K, Wang X, Lami L, et al. Probabilistic distillation of quantum coherence. Phys Rev Lett, 2018, 121: 070404
Regula B, Fang K, Wang X, et al. One-shot coherence distillation. Phys Rev Lett, 2018, 121: 010401
Ahnefeld F, Theurer T, Egloff D, et al. Coherence as a resource for Shor’s algorithm. Phys Rev Lett, 2022, 129: 120501
Bennett C H, Brassard G, Crépeau C, et al. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys Rev Lett, 1993, 70: 1895–1899
Acín A, Brunner N, Gisin N, et al. Device-independent security of quantum cryptography against collective attacks. Phys Rev Lett, 2007, 98: 230501
Bell J S. On the Einstein Podolsky Rosen paradox. Phys Phys Fizika, 1964, 1: 195–200
Freedman S J, Clauser J F. Experimental test of local hidden-variable theories. Phys Rev Lett, 1972, 28: 938–941
Aspect A, Dalibard J, Roger G. Experimental test of Bell’s inequalities using time-varying analyzers. Phys Rev Lett, 1982, 49: 1804–1807
Ou Z Y, Mandel L. Violation of Bell’s inequality and classical probability in a two-photon correlation experiment. Phys Rev Lett, 1988, 61: 50–53
Hensen B, Bernien H, Dréau A E, et al. Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres. Nature, 2015, 526: 682–686
Giustina M, Versteegh M A M, Wengerowsky S, et al. Significant-loophole-free test of Bell’s theorem with entangled photons. Phys Rev Lett, 2015, 115: 250401
Shalm L K, Meyer-Scott E, Christensen B G, et al. Strong loophole-free test of local realism. Phys Rev Lett, 2015, 115: 250402
Handsteiner J, Friedman A S, Rauch D, et al. Cosmic Bell test: measurement settings from milky way stars. Phys Rev Lett, 2017, 118: 060401
Yin J, Cao Y, Li Y H, et al. Satellite-based entanglement distribution over 1200 kilometers. Science, 2017, 356: 1140–1144
Nielsen M A, Chuang I L. Quantum Computation and Quantum Information. Cambridge: Cambridge University Press, 2012
Xiao Y, Fang K, Gour G. The complementary information principle of quantum mechanics. 2019. ArXiv:1908.07694
Briegel H J, Browne D E, Dür W, et al. Measurement-based quantum computation. Nat Phys, 2009, 5: 19–26
Wootters W K, Zurek W H. A single quantum cannot be cloned. Nature, 1982, 299: 802–803
Briegel H J, Duür W, Cirac J I, et al. Quantum repeaters: the role of imperfect local operations in quantum communication. Phys Rev Lett, 1998, 81: 5932–5935
Duan L M, Lukin M D, Cirac J I, et al. Long-distance quantum communication with atomic ensembles and linear optics. Nature, 2001, 414: 413–418
Muralidharan S, Li L, Kim J, et al. Optimal architectures for long distance quantum communication. Sci Rep, 2016, 6: 20463
Zwerger M, Pirker A, Dunjko V, et al. Long-range big quantum-data transmission. Phys Rev Lett, 2018, 120: 030503
Brand S, Coopmans T, Elkouss D. Efficient computation of the waiting time and fidelity in quantum repeater chains. IEEE J Sel Areas Commun, 2020, 38: 619–639
Li B, Coopmans T, Elkouss D. Efficient optimization of cutoffs in quantum repeater chains. IEEE Trans Quantum Eng, 2021, 2: 1–15
Rozpedek F, Noh K, Xu Q, et al. Quantum repeaters based on concatenated bosonic and discrete-variable quantum codes. npj Quantum Inf, 2021, 7: 102
Rozpędek F, Goodenough K, Ribeiro J, et al. Parameter regimes for a single sequential quantum repeater. Quantum Sci Technol, 2018, 3: 034002
Coutinho B C, Munro W J, Nemoto K, et al. Robustness of noisy quantum networks. Commun Phys, 2022, 5: 105
Zhou Z. A multiplexed quantum repeater based on absorptive quantum memories. Sci China Inf Sci, 2021, 64: 217501
Sangouard N, Simon C, de Riedmatten H, et al. Quantum repeaters based on atomic ensembles and linear optics. Rev Mod Phys, 2011, 83: 33–80
Gottesman D. An introduction to quantum error correction and fault-tolerant quantum computation. 2009. ArXiv:0904.2557
Munro W J, Azuma K, Tamaki K, et al. Inside quantum repeaters. IEEE J Sel Top Quantum Electron, 2015, 21: 78–90
Lago-Rivera D, Grandi S, Rakonjac J V, et al. Telecom-heralded entanglement between multimode solid-state quantum memories. Nature, 2021, 594: 37–40
Liu X, Hu J, Li Z F, et al. Heralded entanglement distribution between two absorptive quantum memories. Nature, 2021, 594: 41–45
Pu Y F, Zhang S, Wu Y K, et al. Experimental demonstration of memory-enhanced scaling for entanglement connection of quantum repeater segments. Nat Photon, 2021, 15: 374–378
Cao Y, Zhao Y, Wang Q, et al. The evolution of quantum key distribution networks: on the road to the qinternet. IEEE Commun Surv Tut, 2022, 24: 839–894
Sidhu J S, Joshi S K, Gündoğan M, et al. Advances in space quantum communications. IET Quantum Commun, 2021, 2: 182–217
Belenchia A, Carlesso M, Bayraktar Ö, et al. Quantum physics in space. Phys Rep, 2022, 951: 1–70
Neumann S P, Joshi S K, Fink M, et al. Q3Sat: quantum communications uplink to a 3U CubeSat-feasibility & design. EPJ Quantum Technol, 2018, 5: 4
Knips L, Auer M, Baliuka A, et al. QUBE–towards quantum key distribution with small satellites. In: Proceedings of Quantum 2.0. Optica Publishing Group, 2022
Kerstel E, Gardelein A, Barthelemy M, et al. Nanobob: a CubeSat mission concept for quantum communication experiments in an uplink configuration. EPJ Quantum Technol, 2018, 5: 6
Dalibot C, Tustain S. The preliminary thermal design for the SPEQTRE CubeSat. In: Proceedings of International Conference on Environmental Systems, 2020
Greenberger D M, Horne M A, Zeilinger A. Going beyond Bell’s theorem. In: Proceedings of Bell’s Theorem, Quantum Theory and Conceptions of the Universe, 1989. 69–72
Dai W, Rinaldi A, Towsley D. Entanglement swapping in quantum switches: protocol design and stability analysis. 2021. ArXiv:2110.04116
Nain P, Vardoyan G, Guha S, et al. On the analysis of a multipartite entanglement distribution switch. Proc ACM Meas Anal Comput Syst, 2020, 4: 1–39
Vardoyan G, Nain P, Guha S, et al. On the capacity region of bipartite and tripartite entanglement switching. 2019. ArXiv:1901.06786
Vardoyan G, Guha S, Nain P, et al. On the stochastic analysis of a quantum entanglement switch. SIGMETRICS Perform Eval Rev, 2019, 47: 27–29
Lütkenhaus N, Jahma M. Quantum key distribution with realistic states: photon-number statistics in the photon-number splitting attack. New J Phys, 2002, 4: 44
Eisaman M D, Fan J, Migdall A, et al. Invited review article: single-photon sources and detectors. Rev Sci Instrum, 2011, 82: 071101
Migdall A, Polyakov S V, Fan J, et al. Single-photon Generation and Detection: Physics and Applications. New York: Academic Press, 2013
Senellart P, Solomon G, White A. High-performance semiconductor quantum-dot single-photon sources. Nat Nanotech, 2017, 12: 1026–1039
Arakawa Y, Holmes M J. Progress in quantum-dot single photon sources for quantum information technologies: a broad spectrum overview. Appl Phys Rev, 2020, 7: 021309
Strauf S, Stoltz N G, Rakher M T, et al. High-frequency single-photon source with polarization control. Nat Photon, 2007, 1: 704–708
Shields A J. Semiconductor quantum light sources. Nat Photon, 2007, 1: 215–223
Kim J, Benson O, Kan H, et al. A single-photon turnstile device. Nature, 1999, 397: 500–503
Chu X L, Götzinger S, Sandoghdar V. A single molecule as a high-fidelity photon gun for producing intensity-squeezed light. Nat Photon, 2017, 11: 58–62
De Martini F, Di Giuseppe G, Marrocco M. Single-mode generation of quantum photon states by excited single molecules in a microcavity trap. Phys Rev Lett, 1996, 76: 900–903
Kako S, Santori C, Hoshino K, et al. A gallium nitride single-photon source operating at 200 K. Nat Mater, 2006, 5: 887–892
Kuhn A, Hennrich M, Rempe G. Deterministic single-photon source for distributed quantum networking. Phys Rev Lett, 2002, 89: 067901
Blinov B B, Moehring D L, Duan L M, et al. Observation of entanglement between a single trapped atom and a single photon. Nature, 2004, 428: 153–157
Maurer C, Becher C, Russo C, et al. A single-photon source based on a single Ca+ ion. New J Phys, 2004, 6: 94
Kurtsiefer C, Mayer S, Zarda P, et al. Stable solid-state source of single photons. Phys Rev Lett, 2000, 85: 290–293
Babinec T M, Hausmann B J M, Khan M, et al. A diamond nanowire single-photon source. Nat Nanotech, 2010, 5: 195–199
Alléaume R, Treussart F, Messin G, et al. Experimental open-air quantum key distribution with a single-photon source. New J Phys, 2004, 6: 92
Pittman T B, Franson J D, Jacobs B C. Investigation of a single-photon source based on quantum interference. New J Phys, 2007, 9: 195
Grangier P, Roger G, Aspect A. Experimental evidence for a photon anticorrelation effect on a beam splitter: a new light on single-photon interferences. Europhys Lett, 1986, 1: 173–179
Hong C K, Mandel L. Experimental realization of a localized one-photon state. Phys Rev Lett, 1986, 56: 58–60
Fasel S, Alibart O, Tanzilli S, et al. High-quality asynchronous heralded single-photon source at telecom wavelength. New J Phys, 2004, 6: 163
Meyer-Scott E, Silberhorn C, Migdall A. Single-photon sources: approaching the ideal through multiplexing. Rev Sci Instrum, 2020, 91: 041101
Wang H, Qin J, Ding X, et al. Boson sampling with 20 input photons and a 60-mode interferometer in a 60-mode interferometer in a 1014-dimensional Hilbert space. Phys Rev Lett, 2019, 123: 250503
Thomas S, Senellart P. The race for the ideal single-photon source is on. Nat Nanotechnol, 2021, 16: 367–368
Tomm N, Javadi A, Antoniadis N O, et al. A bright and fast source of coherent single photons. Nat Nanotechnol, 2021, 16: 399–403
Wei Y, Liu S, Li X, et al. Tailoring solid-state single-photon sources with stimulated emissions. Nat Nanotechnol, 2022, 17: 470–476
Hadfield R H. Single-photon detectors for optical quantum information applications. Nat Photon, 2009, 3: 696–705
Komiyama S, Astafiev O, Antonov V, et al. A single-photon detector in the far-infrared range. Nature, 2000, 403: 405–407
Cova S, Ghioni M, Lotito A, et al. Evolution and prospects for single-photon avalanche diodes and quenching circuits. J Modern Opt, 2004, 51: 1267–1288
Rosfjord K M, Yang J K W, Dauler E A, et al. Nanowire single-photon detector with an integrated optical cavity and anti-reflection coating. Opt Express, 2006, 14: 527–534
Takesue H, Diamanti E, Langrock C, et al. 1.5-µm single photon counting using polarization-independent up-conversion detector. Opt Express, 2006, 14: 13067–13072
Peacock A, Verhoeve P, Rando N, et al. Single optical photon detection with a superconducting tunnel junction. Nature, 1996, 381: 135–137
Rosenberg D, Lita A, Miller A, et al. Noise-free high-efficiency photon-number-resolving detectors. Phys Rev A, 2005, 71: 061803
Fujiwara M, Sasaki M. Direct measurement of photon number statistics at telecom wavelengths using a charge integration photon detector. Appl Opt, 2007, 46: 3069–3074
Gansen E J, Rowe M A, Greene M B, et al. Photon-number-discriminating detection using a quantum-dot, optically gated, field-effect transistor. Nat Photon, 2007, 1: 585–588
Reddy D V, Nerem R R, Nam S W, et al. Superconducting nanowire single-photon detectors with 98% system detection efficiency at 1550 nm. Optica, 2020, 7: 1649–1653
Korzh B, Zhao Q Y, Allmaras J P, et al. Demonstration of sub-3 ps temporal resolution with a superconducting nanowire single-photon detector. Nat Photon, 2020, 14: 250–255
Lu C Y, Pan J W. Push-button photon entanglement. Nat Photon, 2014, 8: 174–176
Burnham D C, Weinberg D L. Observation of simultaneity in parametric production of optical photon pairs. Phys Rev Lett, 1970, 25: 84–87
Pan J W, Chen Z B, Lu C Y, et al. Multiphoton entanglement and interferometry. Rev Mod Phys, 2012, 84: 777–838
Anwar A, Perumangatt C, Steinlechner F, et al. Entangled photon-pair sources based on three-wave mixing in bulk crystals. Rev Sci Instrum, 2021, 92: 041101
Bock M, Lenhard A, Chunnilall C, et al. Highly efficient heralded single-photon source for telecom wavelengths based on a PPLN waveguide. Opt Express, 2016, 24: 23992–24001
Aspect A, Grangier P, Roger G. Experimental tests of realistic local theories via Bell’s theorem. Phys Rev Lett, 1981, 47: 460–463
Young R J, Stevenson R M, Atkinson P, et al. Improved fidelity of triggered entangled photons from single quantum dots. New J Phys, 2006, 8: 29
Akopian N, Lindner N H, Poem E, et al. Entangled photon pairs from semiconductor quantum dots. Phys Rev Lett, 2006, 96: 130501
Wang H, Hu H, Chung T H, et al. On-demand semiconductor source of entangled photons which simultaneously has high fidelity, efficiency, and indistinguishability. Phys Rev Lett, 2019, 122: 113602
Hammerer K, Sørensen A S, Polzik E S. Quantum interface between light and atomic ensembles. Rev Mod Phys, 2010, 82: 1041–1093
Stannigel K, Rabl P, Sørensen A S, et al. Optomechanical transducers for long-distance quantum communication. Phys Rev Lett, 2010, 105: 220501
Lauk N, Sinclair N, Barzanjeh S, et al. Perspectives on quantum transduction. Quantum Sci Technol, 2020, 5: 020501
Bochmann J, Vainsencher A, Awschalom D D, et al. Nanomechanical coupling between microwave and optical photons. Nat Phys, 2013, 9: 712–716
Andrews R W, Peterson R W, Purdy T P, et al. Bidirectional and efficient conversion between microwave and optical light. Nat Phys, 2014, 10: 321–326
Jiang W, Sarabalis C J, Dahmani Y D, et al. Efficient bidirectional piezo-optomechanical transduction between microwave and optical frequency. Nature Commun, 2020, 11: 1166
Wang C H, Li F, Jiang L. Quantum capacities of transducers. Nat Commun, 2022, 13: 6698
Higginbotham A P, Burns P S, Urmey M D, et al. Harnessing electro-optic correlations in an efficient mechanical converter. Nat Phys, 2018, 14: 1038–1042
Han X, Fu W, Zou C L, et al. Microwave-optical quantum frequency conversion. Optica, 2021, 8: 1050–1064
Julsgaard B, Kozhekin A, Polzik E S. Experimental long-lived entanglement of two macroscopic objects. Nature, 2001, 413: 400–403
Chou C W, de Riedmatten H, Felinto D, et al. Measurement-induced entanglement for excitation stored in remote atomic ensembles. Nature, 2005, 438: 828–832
Vernaz-Gris P, Huang K, Cao M, et al. Highly-efficient quantum memory for polarization qubits in a spatially-multiplexed cold atomic ensemble. Nat Commun, 2018, 9: 1–6
Heller L, Farrera P, Heinze G, et al. Cold-atom temporally multiplexed quantum memory with cavity-enhanced noise suppression. Phys Rev Lett, 2020, 124: 210504
Choi K S, Deng H, Laurat J, et al. Mapping photonic entanglement into and out of a quantum memory. Nature, 2008, 452: 67–71
Usmani I, Clausen C, Bussieres F, et al. Heralded quantum entanglement between two crystals. Nat Photon, 2012, 6: 234–237
Ortu A, Holzuapfel A, Etesse J, et al. Storage of photonic time-bin qubits for up to 20 ms in a rare-earth doped crystal. npj Quantum Inf, 2022, 8: 29
Lvovsky A I, Sanders B C, Tittel W. Optical quantum memory. Nat Photon, 2009, 3: 706–714
Simon C, Afzelius M, Appel J, et al. Quantum memories. Eur Phys J D, 2010, 58: 1–22
Heshami K, England D G, Humphreys P C, et al. Quantum memories: emerging applications and recent advances. J Modern Opt, 2016, 63: 2005–2028
Bussieres F, Sangouard N, Afzelius M, et al. Prospective applications of optical quantum memories. J Modern Opt, 2013, 60: 1519–1537
Novikova I, Walsworth R L, Xiao Y. Electromagnetically induced transparency-based slow and stored light in warm atoms. Laser Photon Rev, 2012, 6: 333–353
Ma L, Slattery O, Tang X. Optical quantum memory based on electromagnetically induced transparency. J Opt, 2017, 19: 043001
Wang Y, Li J, Zhang S, et al. Efficient quantum memory for single-photon polarization qubits. Nat Photon, 2019, 13: 346–351
Ma L, Slattery O, Tang X. Optical quantum memory and its applications in quantum communication systems. J Res Natl Inst Stan, 2020, 125: 125002
Zhu T X, Liu C, Jin M, et al. On-demand integrated quantum memory for polarization qubits. Phys Rev Lett, 2022, 128: 180501
Stas P J, Huan Y Q, Machielse B, et al. Robust multi-qubit quantum network node with integrated error detection. Science, 2022, 378: 557–560
Inagaki T, Matsuda N, Tadanaga O, et al. Entanglement distribution over 300 km of fiber. Opt Express, 2013, 21: 23241
Yin H L, Chen T Y, Yu Z W, et al. Measurement-device-independent quantum key distribution over a 404 km optical fiber. Phys Rev Lett, 2016, 117: 190501
Villoresi P, Jennewein T, Tamburini F, et al. Experimental verification of the feasibility of a quantum channel between space and Earth. New J Phys, 2008, 10: 033038
Hughes R J, Nordholt J E. Quantum space race heats up. Nat Photon, 2017, 11: 456–458
Buttler W T, Hughes R J, Kwiat P G, et al. Practical free-space quantum key distribution over 1 km. Phys Rev Lett, 1998, 81: 3283–3286
Ma X S, Herbst T, Scheidl T, et al. Quantum teleportation over 143 kilometres using active feed-forward. Nature, 2012, 489: 269–273
Steinlechner F, Ecker S, Fink M, et al. Distribution of high-dimensional entanglement via an intra-city free-space link. Nat Commun, 2017, 8: 1–7
Valivarthi R, Puigibert M G, Zhou Q, et al. Quantum teleportation across a metropolitan fibre network. Nat Photon, 2016, 10: 676–680
Sun Q C, Mao Y L, Chen S J, et al. Quantum teleportation with independent sources and prior entanglement distribution over a network. Nat Photon, 2016, 10: 671–675
Pugh C J, Kaiser S, Bourgoin J P, et al. Airborne demonstration of a quantum key distribution receiver payload. Quantum Sci Technol, 2017, 2: 024009
Wang J Y, Yang B, Liao S K, et al. Direct and full-scale experimental verifications towards ground-satellite quantum key distribution. Nat Photon, 2013, 7: 387–393
Liu H Y, Tian X H, Gu C, et al. Drone-based entanglement distribution towards mobile quantum networks. Natl Sci Rev, 2020, 7: 921–928
Ren J G, Xu P, Yong H L, et al. Ground-to-satellite quantum teleportation. Nature, 2017, 549: 70–73
Liao S K, Cai W Q, Handsteiner J, et al. Satellite-relayed intercontinental quantum network. Phys Rev Lett, 2018, 120: 030501
Pirandola S, Laurenza R, Ottaviani C, et al. Fundamental limits of repeaterless quantum communications. Nat Commun, 2017, 8: 1–5
Pirandola S. Capacities of repeater-assisted quantum communications. 2016. ArXiv:1601.00966
Wang X, Fang K, Tomamichel M. On Converse bounds for classical communication over quantum channels. IEEE Trans Inform Theory, 2019, 65: 4609–4619
Wang X, Fang K, Duan R. Semidefinite programming converse bounds for quantum communication. IEEE Trans Inform Theory, 2018, 65: 2583–2592
Fang K, Fawzi H. Geometric Renyi divergence and its applications in quantum channel capacities. Commun Math Phys, 2021, 384: 1615–1677
Fang K, Gour G, Wang X. Towards the ultimate limits of quantum channel discrimination. 2021. ArXiv:2110.14842
Fawzi H, Fawzi O. Defining quantum divergences via convex optimization. Quantum, 2021, 5: 387
Fawzi O, Shayeghi A, Ta H. A hierarchy of efficient bounds on quantum capacities exploiting symmetry. IEEE Trans Inform Theory, 2022, 68: 7346–7360
Wang X, Xie W, Duan R. Semidefinite programming converse bounds for classical communication over quantum channels. In: Proceedings of IEEE International Symposium on Information Theory (ISIT), 2017. 1728–1732
Fang K, Wang X, Tomamichel M, et al. Quantum channel simulation and the channel’s smooth max-information. IEEE Trans Inform Theory, 2019, 66: 2129–2140
Fang K, Fawzi O, Renner R, et al. Chain rule for the quantum relative entropy. Phys Rev Lett, 2020, 124: 100501
Dahlberg A, Skrzypczyk M, Coopmans T, et al. A link layer protocol for quantum networks. In: Proceedings of the ACM Special Interest Group on Data Communication, 2019. 159–173
Kozlowski W, Dahlberg A, Wehner S. Designing a quantum network protocol. In: Proceedings of the 16th International Conference on Emerging Networking Experiments and Technologies, 2020. 1–16
Illiano J, Caleffi M, Manzalini A, et al. Quantum internet protocol stack: a comprehensive survey. Comput Netw, 2022, 213: 109092
DiAdamo S, Qi B, Miller G, et al. Packet switching in quantum networks: a path to quantum internet. 2022. ArXiv:2205.07507
Pirker A, Wallnoüfer J, Duür W. Modular architectures for quantum networks. New J Phys, 2018, 20: 053054
Zhang H, Li Y, Zhang C, et al. Connection-oriented and connectionless quantum internet considering quantum repeaters. 2022, ArXiv:2208.03930
Zwerger M, Duür W, Briegel H J. Measurement-based quantum repeaters. Phys Rev A, 2012, 85: 062326
Zwerger M, Briegel H J, Duür W. Measurement-based quantum communication. Appl Phys B, 2016, 122: 1–5
Cerf V, Kahn R. A protocol for packet network intercommunication. IEEE Trans Commun, 1974, 22: 637–648
Boschi D, Branca S, De Martini F, et al. Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys Rev Lett, 1998, 80: 1121–1125
Bouwmeester D, Pan J W, Mattle K, et al. Experimental quantum teleportation. Nature, 1997, 390: 575–579
Pirandola S, Eisert J, Weedbrook C, et al. Advances in quantum teleportation. Nat Photon, 2015, 9: 641–652
Liu S, Lou Y, Jing J. Orbital angular momentum multiplexed deterministic all-optical quantum teleportation. Nat Commun, 2020, 11: 3875
Ursin R, Jennewein T, Aspelmeyer M, et al. Quantum teleportation across the Danube. Nature, 2004, 430: 849
Riebe M, Hüffner H, Roos C F, et al. Deterministic quantum teleportation with atoms. Nature, 2004, 429: 734–737
Leuenberger M N, Flatte M E, Awschalom D D. Teleportation of electronic many-qubit states encoded in the electron spin of quantum dots via single photons. Phys Rev Lett, 2005, 94: 107401
Zukowski M, Zeilinger A, Horne M A, et al. ‘Event-ready-detectors’ Bell experiment via entanglement swapping. Phys Rev Lett, 1993, 71: 4287–4290
Pan J W, Bouwmeester D, Weinfurter H, et al. Experimental entanglement swapping: entangling photons that never interacted. Phys Rev Lett, 1998, 80: 3891–3894
Kaltenbaek R, Prevedel R, Aspelmeyer M, et al. High-fidelity entanglement swapping with fully independent sources. Phys Rev A, 2009, 79: 040302
Jennewein T, Weihs G, Pan J W, et al. Experimental nonlocality proof of quantum teleportation and entanglement swapping. Phys Rev Lett, 2001, 88: 017903
de Riedmatten H, Marcikic I, van Houwelingen J A W, et al. Long-distance entanglement swapping with photons from separated sources. Phys Rev A, 2005, 71: 050302
Wu Q L, Namekata N, Inoue S. High-fidelity entanglement swapping at telecommunication wavelengths. J Phys B-At Mol Opt Phys, 2013, 46: 235503
Halder M, Beveratos A, Gisin N, et al. Entangling independent photons by time measurement. Nat Phys, 2007, 3: 692–695
Xue Y, Yoshizawa A, Tsuchida H. Polarization-based entanglement swapping at the telecommunication wavelength using spontaneous parametric down-conversion photon-pair sources. Phys Rev A, 2012, 85: 032337
Takesue H, Miquel B. Entanglement swapping using telecom-band photons generated in fibers. Opt Express, 2009, 17: 10748–10756
Sun Q C, Jiang Y F, Mao Y L, et al. Field test of entanglement swapping over 100-km optical fiber with independent 1-GHz-clock sequential time-bin entangled photon-pair sources. 2017. ArXiv:1704.03960
Huang C X, Hu X M, Guo Y, et al. Entanglement swapping and quantum correlations via symmetric joint measurements. Phys Rev Lett, 2022, 129: 030502
Liu S, Lou Y, Chen Y, et al. All-optical entanglement swapping. Phys Rev Lett, 2022, 128: 060503
van Meter R, Satoh T, Ladd T D, et al. Path selection for quantum repeater networks. NetwSci, 2013, 3: 82–95
Caleffi M. Optimal routing for quantum networks. IEEE Access, 2017, 5: 22299–22312
Schoute E, Mancinska L, Islam T, et al. Shortcuts to quantum network routing. 2016. ArXiv:1610.05238
Bugalho L, Coutinho B C, Monteiro F A, et al. Distributing multipartite entanglement over noisy quantum networks. 2021. ArXiv:2103.14759
Gyongyosi L, Imre S. Decentralized base-graph routing for the quantum internet. Phys Rev A, 2018, 98: 022310
Gyongyosi L, Imre S. Entanglement-gradient routing for quantum networks. Sci Rep, 2017, 7: 14255
Chakraborty K, Rozpedek F, Dahlberg A, et al. Distributed routing in a quantum internet. 2019. ArXiv:1907.11630
Perseguers S, LapeyreJr G J, Cavalcanti D, et al. Distribution of entanglement in large-scale quantum networks. Rep Prog Phys, 2013, 76: 096001
Hahn F, Pappa A, Eisert J. Quantum network routing and local complementation. npj Quantum Inf, 2019, 5: 76
Pant M, Krovi H, Towsley D, et al. Routing entanglement in the quantum internet. npj Quantum Inf, 2019, 5: 1–9
Shi S, Qian C. Concurrent entanglement routing for quantum networks: model and designs. In: Proceedings of the Annual Conference of the ACM Special Interest Group on Data Communication on the Applications, Technologies, Architectures, and Protocols for Computer Communication, 2020. 62–65
Bennett C H, Wiesner S J. Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. Phys Rev Lett, 1992, 69: 2881–2884
Bennett C H, DiVincenzo D P, Smolin J A, et al. Mixed-state entanglement and quantum error correction. Phys Rev A, 1996, 54: 3824–3851
Bennett C H, Brassard G, Popescu S, et al. Purification of noisy entanglement and faithful teleportation via noisy channels. Phys Rev Lett, 1996, 76: 722–725
Deutsch D, Ekert A, Jozsa R, et al. Quantum privacy amplification and the security of quantum cryptography over noisy channels. Phys Rev Lett, 1996, 77: 2818–2821
Buscemi F, Datta N. Distilling entanglement from arbitrary resources. J Math Phys, 2010, 51: 102201
Brandao F G S L, Datta N. One-shot rates for entanglement manipulation under non-entangling maps. IEEE Trans Inform Theory, 2011, 57: 1754–1760
Datta N, Leditzky F. Second-order asymptotics for source coding, dense coding, and pure-state entanglement conversions. IEEE Trans Inform Theory, 2015, 61: 582–608
Rozpedek F, Schiet T, Thinh L P, et al. Optimizing practical entanglement distillation. Phys Rev A, 2018, 97: 062333
Fang K, Liu Z W. No-go theorems for quantum resource purification: new approach and channel theory. PRX Quantum, 2022, 3: 010337
Regula B, Fang K, Wang X, et al. One-shot entanglement distillation beyond local operations and classical communication. New J Phys, 2019, 21: 103017
Fang K, Wang X, Tomamichel M, et al. Non-asymptotic entanglement distillation. IEEE Trans Inform Theory, 2019, 65: 6454–6465
Zhao X, Zhao B, Wang Z, et al. Practical distributed quantum information processing with LOCCNet. npj Quantum Inf, 2021, 7: 159
Fang K, Fawzi H. The sum-of-squares hierarchy on the sphere and applications in quantum information theory. Math Program, 2021, 190: 331–360
Regula B, Takagi R. Fundamental limitations on distillation of quantum channel resources. Nat Commun, 2021, 12: 4411
Zhang H, Xu X, Zhang C, et al. Variational quantum circuit learning of entanglement purification in multi-degree-of-freedom. 2022. ArXiv:2209.08306
Fang K, Liu Z W. No-go theorems for quantum resource purification. Phys Rev Lett, 2020, 125: 060405
Kalb N, Reiserer A A, Humphreys P C, et al. Entanglement distillation between solid-state quantum network nodes. Science, 2017, 356: 928–932
Abdelkhalek D, Syllwasschy M, Cerf N J, et al. Efficient entanglement distillation without quantum memory. Nat Commun, 2016, 7: 1–7
Ecker S, Sohr P, Bulla L, et al. Experimental single-copy entanglement distillation. Phys Rev Lett, 2021, 127: 040506
Gottesman D. Stabilizer codes and quantum error correction. 1997. ArXiv:quant-ph/9705052
Gaitan F. Quantum Error Correction and Fault Tolerant Quantum Computing. Boca Raton: CRC Press, 2008
Lidar D A, Brun T A. Quantum Error Correction. Cambridge: Cambridge University Press, 2013
Terhal B M. Quantum error correction for quantum memories. Rev Mod Phys, 2015, 87: 307–346
Suter D, Álvarez G A. Colloquium: protecting quantum information against environmental noise. Rev Mod Phys, 2016, 88: 041001
Ofek N, Petrenko A, Heeres R, et al. Extending the lifetime of a quantum bit with error correction in superconducting circuits. Nature, 2016, 536: 441–445
Linke N M, Gutierrez M, Landsman K A, et al. Fault-tolerant quantum error detection. Sci Adv, 2017, 3: e1701074
Wootton J R, Loss D. Repetition code of 15 qubits. Phys Rev A, 2018, 97: 052313
Harper R, Flammia S T. Fault-tolerant logical gates in the IBM quantum experience. Phys Rev Lett, 2019, 122: 080504
Livingston W P, Blok M S, Flurin E, et al. Experimental demonstration of continuous quantum error correction. Nat Commun, 2022, 13: 2307
Rivest R L, Shamir A, Adleman L. A method for obtaining digital signatures and public-key cryptosystems. Commun ACM, 1978, 21: 120–126
Shor P. Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings of the 35th Annual Symposium on Foundations of Computer Science, 1994. 124–134
Travagnin M, Lewis A. Quantum Key Distribution In-field Implementations. EUR 29865 EN, Publications Office of the European Union. 2019
Zhang Q, Xu F, Chen Y A, et al. Large scale quantum key distribution: challenges and solutions [Invited]. Opt Express, 2018, 26: 24260
Hwang W Y. Quantum key distribution with high loss: toward global secure communication. Phys Rev Lett, 2003, 91: 057901
Wang X B. Beating the photon-number-splitting attack in practical quantum cryptography. Phys Rev Lett, 2005, 94: 230503
Lo H K, Ma X, Chen K. Decoy state quantum key distribution. Phys Rev Lett, 2005, 94: 230504
Lo H K, Curty M, Qi B. Measurement-device-independent quantum key distribution. Phys Rev Lett, 2012, 108: 130503
Zhang G W, Chen W, Fan-Yuan G J, et al. Polarization-insensitive quantum key distribution using planar lightwave circuit chips. Sci China Inf Sci, 2022, 65: 200506
Xu F, Ma X, Zhang Q, et al. Secure quantum key distribution with realistic devices. Rev Mod Phys, 2020, 92: 025002
Pirandola S, Andersen U L, Banchi L, et al. Advances in quantum cryptography. Adv Opt Photon, 2020, 12: 1012
George I, Lin J, van Himbeeck T, et al. Finite-key analysis of quantum key distribution with characterized devices using entropy accumulation. 2022. ArXiv:2203.06554
Lucamarini M, Yuan Z L, Dynes J F, et al. Overcoming the rate-distance limit of quantum key distribution without quantum repeaters. Nature, 2018, 557: 400–403
Wang S, Yin Z Q, He D Y, et al. Twin-field quantum key distribution over 830-km fibre. Nat Photon, 2022, 16: 154–161
Ren S, Wang Y, Su X. Hybrid quantum key distribution network. Sci China Inf Sci, 2022, 65: 200502
Fitzsimons J F. Private quantum computation: an introduction to blind quantum computing and related protocols. npj Quantum Inf, 2017, 3: 23
Morimae T, Koshiba T. Impossibility of perfectly-secure one-round delegated quantum computing for classical client. Quantum Inform Comput, 2019, 19: 214–221
Aaronson S, Cojocaru A, Gheorghiu A, et al. Complexity-theoretic limitations on blind delegated quantum computation. 2017. ArXiv:1704.08482
Mantri A, Demarie T F, Fitzsimons J F. Universality of quantum computation with cluster states and (X, Y)-plane measurements. Sci Rep, 2017, 7: 42861
Morimae T, Fujii K. Blind quantum computation protocol in which Alice only makes measurements. Phys Rev A, 2013, 87: 050301
Shan R T, Chen X, Yuan K G. Multi-party blind quantum computation protocol with mutual authentication in network. Sci China Inf Sci, 2021, 64: 162302
Reichardt B W, Unger F, Vazirani U. Classical command of quantum systems. Nature, 2013, 496: 456–460
McKague M. Interactive proofs for BQP via self-tested graph states. Theor Comput, 2016, 12: 1–42
Barz S, Kashefi E, Broadbent A, et al. Demonstration of blind quantum computing. Science, 2012, 335: 303–308
Huang H L, Zhao Q, Ma X, et al. Experimental blind quantum computing for a classical client. Phys Rev Lett, 2017, 119: 050503
Greganti C, Roehsner M C, Barz S, et al. Demonstration of measurement-only blind quantum computing. New J Phys, 2016, 18: 013020
Lynch N A. Distributed Algorithms. San Francisco: Morgan Kaufmann Publishers Inc., 1996
Tani S, Kobayashi H, Matsumoto K. Exact quantum algorithms for the leader election problem. ACM Trans Comput Theory, 2012, 4: 1–24
Angluin D. Local and global properties in networks of processors (extended abstract). In: Proceedings of the 12th Annual ACM Symposium on Theory of Computing, 1980. 82–83
Itai A, Rodeh M. Symmetry breaking in distributed networks. Inf Comput, 1990, 88: 60–87
Yamashita M, Kameda T. Computing on anonymous networks. I. Characterizing the solvable cases. IEEE Trans Parallel Distrib Syst, 1996, 7: 69–89
Kobayashi H, Matsumoto K, Tani S. Simpler exact leader election via quantum reduction. Chicago J Theor Comp Sci, 2014, 20: 1–31
Okubo Y, Wang X B, Jiang Y K, et al. Experimental demonstration of quantum leader election in linear optics. Phys Rev A, 2008, 77: 032343
van Meter R, Nemoto K, Munro W. Communication links for distributed quantum computation. IEEE Trans Comput, 2007, 56: 1643–1653
Buhrman H, Ruohrig H. Distributed quantum computing. In: Mathematical Foundations of Computer Science. Berlin: Springer, 2003
van Meter R, Devitt S J. The path to scalable distributed quantum computing. Computer, 2016, 49: 31–42
Beals R, Brierley S, Gray O, et al. Efficient distributed quantum computing. Proc R Soc A, 2013, 469: 20120686
Bravyi S, Dial O, Gambetta J M, et al. The future of quantum computing with superconducting qubits. J Appl Phys, 2022, 132: 160902
Piveteau C, Sutter D. Circuit knitting with classical communication. 2022. ArXiv:2205.00016
DiAdamo S, Ghibaudi M, Cruise J. Distributed quantum computing and network control for accelerated VQE. IEEE Trans Quantum Eng, 2021, 2: 1–21
Parekh R, Ricciardi A, Darwish A, et al. Quantum algorithms and simulation for parallel and distributed quantum computing. 2022. ArXiv:2106.06841
Haner T, Steiger D S, Hoefler T, et al. Distributed quantum computing with QMPI. In: Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, 2021. 1–13
Ferrari D, Cacciapuoti A S, Amoretti M, et al. Compiler design for distributed quantum computing. IEEE Trans Quantum Eng, 2021, 2: 1–20
Eisert J, Jacobs K, Papadopoulos P, et al. Optimal local implementation of nonlocal quantum gates. Phys Rev A, 2000, 62: 052317
Gottesman D, Chuang I L. Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations. Nature, 1999, 402: 390–393
Chou K S, Blumoff J Z, Wang C S, et al. Deterministic teleportation of a quantum gate between two logical qubits. Nature, 2018, 561: 368–373
Wan Y, Kienzler D, Erickson S D, et al. Quantum gate teleportation between separated qubits in a trapped-ion processor. Science, 2019, 364: 875–878
Daiss S, Langenfeld S, Welte S, et al. A quantum-logic gate between distant quantum-network modules. Science, 2021, 371: 614–617
Cleve R, Dam W V, Nielsen M, et al. Quantum entanglement and the communication complexity of the inner product function. In: Proceedings of NASA International Conference on Quantum Computing and Quantum Communications, 1998. 61–74
Buhrman H, Cleve R, Wigderson A. Quantum vs. classical communication and computation. In: Proceedings of the 30th Annual ACM Symposium on Theory of Computing, 1998. 63–68
Anshu A, Touchette D, Yao P, et al. Exponential separation of quantum communication and classical information. In: Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing, 2017. 277–288
Brukner C, Zukowski M, Pan J W, et al. Bell’s inequalities and quantum communication complexity. Phys Rev Lett, 2004, 92: 127901
Wei K, Tischler N, Zhao S R, et al. Experimental quantum switching for exponentially superior quantum communication complexity. Phys Rev Lett, 2019, 122: 120504
Buhrman H, Cleve R, Watrous J, et al. Quantum fingerprinting. Phys Rev Lett, 2001, 87: 167902
Zhong X, Xu F, Lo H K, et al. Efficient experimental quantum fingerprinting with channel multiplexing and simultaneous detection. Nat Commun, 2021, 12: 4464
Einstein A. Zur elektrodynamik bewegter Kuorper. Ann Phys, 1905, 322: 891–921
Eddington A S. The Mathematical Theory of Relativity. Cambridge: Cambridge University Press, 1923
Yurtsever U, Dowling J P. Lorentz-invariant look at quantum clock-synchronization protocols based on distributed entanglement. Phys Rev A, 2002, 65: 052317
Krčo M, Paul P. Quantum clock synchronization: multiparty protocol. Phys Rev A, 2002, 66: 024305
Ben-Av R, Exman I. Optimized multiparty quantum clock synchronization. Phys Rev A, 2011, 84: 014301
Kómár P, Kessler E M, Bishof M, et al. A quantum network of clocks. Nat Phys, 2014, 10: 582–587
Quan R, Zhai Y, Wang M, et al. Demonstration of quantum synchronization based on second-order quantum coherence of entangled photons. Sci Rep, 2016, 6: 30453
Giovannetti V, Lloyd S, Maccone L. Quantum-enhanced positioning and clock synchronization. Nature, 2001, 412: 417–419
Valencia A, Scarcelli G, Shih Y. Distant clock synchronization using entangled photon pairs. Appl Phys Lett, 2004, 85: 2655–2657
Kong X, Xin T, Wei S, et al. Implementation of multiparty quantum clock synchronization. 2017. ArXiv:1708.06050
Lee J, Shen L, Cere A, et al. Symmetrical clock synchronization with time-correlated photon pairs. Appl Phys Lett, 2019, 114: 101102
Troupe J, Haldar S, Agullo I, et al. Quantum clock synchronization for future NASA deep space quantum links and fundamental science. 2022. ArXiv:2209.15122
Lawson P. Principles of long baseline stellar interferometry. JPL, 2000. https://hdl.handle.net/1813/41240
Zernike F. The concept of degree of coherence and its application to optical problems. Physica, 1938, 5: 785–795
Khabiboulline E T, Borregaard J, De Greve K, et al. Optical interferometry with quantum networks. Phys Rev Lett, 2019, 123: 070504
Khabiboulline E T, Borregaard J, De Greve K, et al. Quantum-assisted telescope arrays. Phys Rev A, 2019, 100: 022316
Cacciapuoti A S, Caleffi M, Tafuri F, et al. Quantum internet: networking challenges in distributed quantum computing. IEEE Netw, 2020, 34: 137–143
Satoh T, Nagayama S, Suzuki S, et al. Attacking the quantum internet. IEEE Trans Quantum Eng, 2021, 2: 1–17
Bernstein D J, Lange T. Post-quantum cryptography. Nature, 2017, 549: 188–194
Wang J, Liu L, Lyu S, et al. Quantum-safe cryptography: crossroads of coding theory and cryptography. Sci China Inf Sci, 2022, 65: 111301
Huang Y, Zhang F, Liu Z, et al. Pseudorandom number generator based on supersingular elliptic curve isogenies. Sci China Inf Sci, 2022, 65: 159101
Tao Y, Ji Y, Zhang R. Generalizing Lyubashevsky-Wichs trapdoor sampler for NTRU lattices. Sci China Inf Sci, 2022, 65: 159103
Liu J, Yu Y, Bi H, et al. Post quantum secure fair data trading with deterability based on machine learning. Sci China Inf Sci, 2022, 65: 170308
Bavdekar R, Chopde E J, Agrawal A, et al. Post quantum cryptography: a review of techniques, challenges and standardizations. In: Proceedings of International Conference on Information Networking (ICOIN), 2023. 146–151
Wehrle K, Günes M, Gross J. Modeling and Tools for Network Simulation. Berlin: Springer, 2010
Baidu Quantum. QNET. 2022. Official website at https://quantum-hub.baidu.com/qnet/, Source code available at https://github.com/baidu/QCompute/tree/master/Extensions/QuantumNetwork
Deutsch D E. Quantum computational networks. Proc Royal Soc London A, 1989, 425: 73–90
Barenco A, Bennett C H, Cleve R, et al. Elementary gates for quantum computation. Phys Rev A, 1995, 52: 3457–3467
Morimae T. Verification for measurement-only blind quantum computing. Phys Rev A, 2014, 89: 060302
Li X, Fang K. Methods, devices and electronic apparatus for quantum computing. Patent No. CN202210324719.5, 2022
Fang K, Li X. Method and device for operating quantum system of one-way quantum computer calculation model. Patent No. CN202210858691.3, 2022
Fang K, Zhao J. Methods, devices and electronic apparatus for simulating quantum network protocols. Patent No. CN202210885409.0, 2022
Dahlberg A, van der Vecht B, Donne C D, et al. NetQASM-a low-level instruction set architecture for hybrid quantum-classical programs in a quantum internet. Quantum Sci Technol, 2022, 7: 035023
Fang K, Li Y. Request processing methods, apparatus and electronic device. Patent No. CN2022114860192, 2022
Fang K, Li Y. Quantum key distribution method, apparatus and electronic device. Patent No. CN2022114862164, 2022
Clauser J F, Horne M A, Shimony A, et al. Proposed experiment to test local hidden-variable theories. Phys Rev Lett, 1969, 23: 880–884
Montanaro A, de Wolf R. A survey of quantum property testing. 2013. ArXiv:1310.2035
Acknowledgements
We would like to thank Yu-Ao CHEN, Shusen LIU, Jingbo WANG, Kun WANG, Xin WANG, and Zihe WANG for discussions on the development of QNET. We also thank Jie LIN for suggesting relevant references on single-photon sources and detectors.
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
Fang, K., Zhao, J., Li, X. et al. Quantum NETwork: from theory to practice. Sci. China Inf. Sci. 66, 180509 (2023). https://doi.org/10.1007/s11432-023-3773-4
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11432-023-3773-4