Near-deterministic hybrid generation of arbitrary photonic graph states using a single quantum emitter and linear optics

Paul Hilaire1,2, Leonid Vidro3, Hagai S. Eisenberg3, and Sophia E. Economou1

1Department of Physics, Virginia Tech, Blacksburg, Virginia 24061, USA
2Huygens-Kamerlingh Onnes Laboratory, Leiden University
3Racah Institute of Physics, Hebrew University of Jerusalem, 91904 Jerusalem, Israel

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

Abstract

Since linear-optical two-photon gates are inherently probabilistic, measurement-based implementations are particularly well suited for photonic platforms: a large highly-entangled photonic resource state, called a graph state, is consumed through measurements to perform a computation. The challenge is thus to produce these graph states. Several generation procedures, which use either interacting quantum emitters or efficient spin-photon interface, have been proposed to create these photonic graph states deterministically. Yet, these solutions are still out of reach experimentally since the state-of-the-art is the generation of a linear graph state. Here, we introduce near-deterministic solutions for the generation of graph states using the current quantum emitter capabilities. We propose hybridizing quantum-emitter-based graph state generation with all-photonic fusion gates to produce graph states of complex topology near-deterministically. Our results should pave the way towards the practical implementation of resource-efficient quantum information processing, including measurement-based quantum communication and quantum computing.

Creating large entangled states of photonic qubits is critical for quantum communications and for building a large photonic quantum computer.
Unfortunately, we cannot easily create entanglement between photonic qubits. Using linear-optical processing, the "easy way" to manipulate photons, entanglement can only be created probabilistically using, for example, the so-called "fusion gates". Yet, the success rate of building larger photonic states leads to either vanishingly small success probability or daunting resource overhead.

An alternative to creating photonic entanglement is to build it "at creation" from quantum emitters, i.e., by using atoms with the correct level structure that can sequentially emit photons entangled with the atomic qubit. Recent works have experimentally demonstrated such sources of entangled photons using natural atoms or quantum dots.

Yet, the entanglement structure of the photonic state that a single atom can produce is not universal for quantum computing and thus cannot create the types of photonic states that are useful for quantum technology applications. To circumvent this limitation, we propose a hybrid approach, combining these sources of photons and linear optics building a large class of photonic entangled states called graph states (including universal resource states for quantum computing). We show how we can create these graph states near-deterministically by proposing a variant of the initial fusion gates compatible with these sources of entangled photons.

► BibTeX data

► References

[1] Han-Sen Zhong, Hui Wang, Yu-Hao Deng, Ming-Cheng Chen, Li-Chao Peng, Yi-Han Luo, Jian Qin, Dian Wu, Xing Ding, Yi Hu, et al. Quantum computational advantage using photons. Science, 370 (6523): 1460–1463, 2020. 10.1126/​science.abe8770.
https:/​/​doi.org/​10.1126/​science.abe8770

[2] Han-Sen Zhong, Yu-Hao Deng, Jian Qin, Hui Wang, Ming-Cheng Chen, Li-Chao Peng, Yi-Han Luo, Dian Wu, Si-Qiu Gong, Hao Su, et al. Phase-programmable gaussian boson sampling using stimulated squeezed light. Physical review letters, 127 (18): 180502, 2021. 10.1103/​PhysRevLett.127.180502.
https:/​/​doi.org/​10.1103/​PhysRevLett.127.180502

[3] Frank Arute, Kunal Arya, Ryan Babbush, Dave Bacon, Joseph C Bardin, Rami Barends, Rupak Biswas, Sergio Boixo, Fernando GSL Brandao, David A Buell, et al. Quantum supremacy using a programmable superconducting processor. Nature, 574 (7779): 505–510, 2019. 10.1038/​s41586-019-1666-5.
https:/​/​doi.org/​10.1038/​s41586-019-1666-5

[4] Emanuel Knill, Raymond Laflamme, and Gerald J Milburn. A scheme for efficient quantum computation with linear optics. Nature, 409 (6816): 46–52, 2001. 10.1038/​35051009.
https:/​/​doi.org/​10.1038/​35051009

[5] Robert Raussendorf and Hans J Briegel. A one-way quantum computer. Physical Review Letters, 86 (22): 5188, 2001. 10.1103/​PhysRevLett.86.5188.
https:/​/​doi.org/​10.1103/​PhysRevLett.86.5188

[6] Robert Raussendorf, Jim Harrington, and Kovid Goyal. A fault-tolerant one-way quantum computer. Annals of physics, 321 (9): 2242–2270, 2006. 10.1016/​j.aop.2006.01.012.
https:/​/​doi.org/​10.1016/​j.aop.2006.01.012

[7] Koji Azuma, Kiyoshi Tamaki, and Hoi-Kwong Lo. All-photonic quantum repeaters. Nature communications, 6: 6787, 2015. 10.1038/​ncomms7787.
https:/​/​doi.org/​10.1038/​ncomms7787

[8] Fabian Ewert, Marcel Bergmann, and Peter van Loock. Ultrafast long-distance quantum communication with static linear optics. Physical review letters, 117 (21): 210501, 2016. 10.1103/​PhysRevLett.117.210501.
https:/​/​doi.org/​10.1103/​PhysRevLett.117.210501

[9] Seung-Woo Lee, Timothy C Ralph, and Hyunseok Jeong. Fundamental building block for all-optical scalable quantum networks. Physical Review A, 100 (5): 052303, 2019a. 10.1103/​PhysRevA.100.052303.
https:/​/​doi.org/​10.1103/​PhysRevA.100.052303

[10] Paul Hilaire, Edwin Barnes, Sophia E. Economou, and Frédéric Grosshans. Error-correcting entanglement swapping using a practical logical photon encoding. Phys. Rev. A, 104: 052623, Nov 2021a. 10.1103/​PhysRevA.104.052623. URL https:/​/​doi.org/​10.1103/​PhysRevA.104.052623.
https:/​/​doi.org/​10.1103/​PhysRevA.104.052623

[11] Paul Hilaire, Edwin Barnes, and Sophia E Economou. Resource requirements for efficient quantum communication using all-photonic graph states generated from a few matter qubits. Quantum, 5: 397, 2021b. 10.22331/​q-2021-02-15-397.
https:/​/​doi.org/​10.22331/​q-2021-02-15-397

[12] Donovan Buterakos, Edwin Barnes, and Sophia E Economou. Deterministic generation of all-photonic quantum repeaters from solid-state emitters. Physical Review X, 7 (4): 041023, 2017. 10.1103/​PhysRevX.7.041023.
https:/​/​doi.org/​10.1103/​PhysRevX.7.041023

[13] Ming Lai Chan. Optimized protocol to create repeater graph states for all-photonic quantum repeater. arXiv preprint arXiv:1811.10214, 2018. 10.48550/​arXiv.1811.10214.
https:/​/​doi.org/​10.48550/​arXiv.1811.10214
arXiv:1811.10214

[14] Antonio Russo, Edwin Barnes, and Sophia E Economou. Photonic graph state generation from quantum dots and color centers for quantum communications. Physical Review B, 98 (8): 085303, 2018. 10.1103/​PhysRevB.98.085303.
https:/​/​doi.org/​10.1103/​PhysRevB.98.085303

[15] Yuan Zhan and Shuo Sun. Deterministic generation of loss-tolerant photonic cluster states with a single quantum emitter. Physical Review Letters, 125 (22): 223601, 2020. 10.1103/​PhysRevLett.125.223601.
https:/​/​doi.org/​10.1103/​PhysRevLett.125.223601

[16] Daniel E Browne and Terry Rudolph. Resource-efficient linear optical quantum computation. Physical Review Letters, 95 (1): 010501, 2005. 10.1103/​PhysRevLett.95.010501.
https:/​/​doi.org/​10.1103/​PhysRevLett.95.010501

[17] Terry Rudolph. Why i am optimistic about the silicon-photonic route to quantum computing. APL Photonics, 2 (3): 030901, 2017. 10.1063/​1.4976737.
https:/​/​doi.org/​10.1063/​1.4976737

[18] Sara Bartolucci, Patrick Birchall, Hector Bombin, Hugo Cable, Chris Dawson, Mercedes Gimeno-Segovia, Eric Johnston, Konrad Kieling, Naomi Nickerson, Mihir Pant, et al. Fusion-based quantum computation. Nature Communications, 14 (1): 912, 2023. 10.1038/​s41467-023-36493-1.
https:/​/​doi.org/​10.1038/​s41467-023-36493-1

[19] Michael Varnava, Daniel E. Browne, and Terry Rudolph. How good must single photon sources and detectors be for efficient linear optical quantum computation? Physical Review Letters, 100: 060502, Feb 2008. 10.1103/​PhysRevLett.100.060502. URL http:/​/​doi.org/​10.1103/​PhysRevLett.100.060502.
https:/​/​doi.org/​10.1103/​PhysRevLett.100.060502

[20] C Greganti, TF Demarie, M Ringbauer, JA Jones, V Saggio, I Alonso Calafell, LA Rozema, A Erhard, M Meth, L Postler, et al. Cross-verification of independent quantum devices. Physical Review X, 11 (3): 031049, 2021. 10.1103/​PhysRevX.11.031049.
https:/​/​doi.org/​10.1103/​PhysRevX.11.031049

[21] Alberto Peruzzo, Jarrod McClean, Peter Shadbolt, Man-Hong Yung, Xiao-Qi Zhou, Peter J Love, Alán Aspuru-Guzik, and Jeremy L O’brien. A variational eigenvalue solver on a photonic quantum processor. Nature communications, 5 (1): 1–7, 2014. 10.1038/​ncomms5213.
https:/​/​doi.org/​10.1038/​ncomms5213

[22] Ryan R Ferguson, Luca Dellantonio, Abdulrahim Al Balushi, Karl Jansen, Wolfgang Dür, and Christine A Muschik. Measurement-based variational quantum eigensolver. Physical review letters, 126 (22): 220501, 2021. 10.1103/​PhysRevLett.126.220501.
https:/​/​doi.org/​10.1103/​PhysRevLett.126.220501

[23] Christian Schön, Enrique Solano, Frank Verstraete, J Ignacio Cirac, and Michael M Wolf. Sequential generation of entangled multiqubit states. Physical review letters, 95 (11): 110503, 2005. 10.1103/​PhysRevLett.95.110503.
https:/​/​doi.org/​10.1103/​PhysRevLett.95.110503

[24] Netanel H Lindner and Terry Rudolph. Proposal for pulsed on-demand sources of photonic cluster state strings. Physical Review Letters, 103 (11): 113602, 2009. 10.1103/​PhysRevLett.103.113602.
https:/​/​doi.org/​10.1103/​PhysRevLett.103.113602

[25] Sophia E Economou, Netanel Lindner, and Terry Rudolph. Optically generated 2-dimensional photonic cluster state from coupled quantum dots. Physical review letters, 105 (9): 093601, 2010. 10.1103/​PhysRevLett.105.093601.
https:/​/​doi.org/​10.1103/​PhysRevLett.105.093601

[26] Antonio Russo, Edwin Barnes, and Sophia E Economou. Generation of arbitrary all-photonic graph states from quantum emitters. New Journal of Physics, 21 (5): 055002, 2019. 10.1088/​1367-2630/​ab193d.
https:/​/​doi.org/​10.1088/​1367-2630/​ab193d

[27] Mercedes Gimeno-Segovia, Terry Rudolph, and Sophia E Economou. Deterministic generation of large-scale entangled photonic cluster state from interacting solid state emitters. Physical review letters, 123 (7): 070501, 2019. 10.1103/​PhysRevLett.123.070501.
https:/​/​doi.org/​10.1103/​PhysRevLett.123.070501

[28] Cathryn P Michaels, Jesús Arjona Martínez, Romain Debroux, Ryan A Parker, Alexander M Stramma, Luca I Huber, Carola M Purser, Mete Atatüre, and Dorian A Gangloff. Multidimensional cluster states using a single spin-photon interface coupled strongly to an intrinsic nuclear register. Quantum, 5: 565, 2021. 10.22331/​q-2021-10-19-565.
https:/​/​doi.org/​10.22331/​q-2021-10-19-565

[29] Bikun Li, Sophia E Economou, and Edwin Barnes. Photonic resource state generation from a minimal number of quantum emitters. npj Quantum Information, 8 (1): 1–7, 2022. 10.1038/​s41534-022-00522-6.
https:/​/​doi.org/​10.1038/​s41534-022-00522-6

[30] Hannes Pichler, Soonwon Choi, Peter Zoller, and Mikhail D Lukin. Universal photonic quantum computation via time-delayed feedback. Proceedings of the National Academy of Sciences, 114 (43): 11362–11367, 2017. 10.1073/​pnas.1711003114.
https:/​/​doi.org/​10.1073/​pnas.1711003114

[31] Kianna Wan, Soonwon Choi, Isaac H Kim, Noah Shutty, and Patrick Hayden. Fault-tolerant qubit from a constant number of components. PRX Quantum, 2 (4): 040345, 2021. 10.1103/​PRXQuantum.2.040345.
https:/​/​doi.org/​10.1103/​PRXQuantum.2.040345

[32] Yu Shi and Edo Waks. Deterministic generation of multidimensional photonic cluster states using time-delay feedback. Physical Review A, 104 (1): 013703, 2021. 10.1103/​PhysRevA.104.013703.
https:/​/​doi.org/​10.1103/​PhysRevA.104.013703

[33] Han-Sen Zhong, Yuan Li, Wei Li, Li-Chao Peng, Zu-En Su, Yi Hu, Yu-Ming He, Xing Ding, Weijun Zhang, Hao Li, et al. 12-photon entanglement and scalable scattershot boson sampling with optimal entangled-photon pairs from parametric down-conversion. Physical review letters, 121 (25): 250505, 2018. 10.1103/​PhysRevLett.121.250505.
https:/​/​doi.org/​10.1103/​PhysRevLett.121.250505

[34] D Istrati, Y Pilnyak, JC Loredo, C Antón, N Somaschi, P Hilaire, H Ollivier, M Esmann, L Cohen, L Vidro, et al. Sequential generation of linear cluster states from a single photon emitter. Nature communications, 11 (1): 1–8, 2020. 10.1038/​s41467-020-19341-4.
https:/​/​doi.org/​10.1038/​s41467-020-19341-4

[35] Rui Zhang, Li-Zheng Liu, Zheng-Da Li, Yue-Yang Fei, Xu-Fei Yin, Li Li, Nai-Le Liu, Yingqiu Mao, Yu-Ao Chen, and Jian-Wei Pan. Loss-tolerant all-photonic quantum repeater with generalized shor code. Optica, 9 (2): 152–158, 2022. 10.1364/​OPTICA.439170.
https:/​/​doi.org/​10.1364/​OPTICA.439170

[36] Ido Schwartz, Dan Cogan, Emma R Schmidgall, Yaroslav Don, Liron Gantz, Oded Kenneth, Netanel H Lindner, and David Gershoni. Deterministic generation of a cluster state of entangled photons. Science, 354: 434–437, 2016. 10.1126/​science.aah4758.
https:/​/​doi.org/​10.1126/​science.aah4758

[37] Jean-Claude Besse, Kevin Reuer, Michele C Collodo, Arne Wulff, Lucien Wernli, Adrian Copetudo, Daniel Malz, Paul Magnard, Abdulkadir Akin, Mihai Gabureac, et al. Realizing a deterministic source of multipartite-entangled photonic qubits. Nature communications, 11 (1): 1–6, 2020. 10.1038/​s41467-020-18635-x.
https:/​/​doi.org/​10.1038/​s41467-020-18635-x

[38] Dan Cogan, Zu-En Su, Oded Kenneth, and David Gershoni. Deterministic generation of indistinguishable photons in a cluster state. Nature Photonics, pages 1–6, 2023. 10.1038/​s41566-022-01152-2.
https:/​/​doi.org/​10.1038/​s41566-022-01152-2

[39] Philip Thomas, Leonardo Ruscio, Olivier Morin, and Gerhard Rempe. Efficient generation of entangled multiphoton graph states from a single atom. Nature, 608 (7924): 677–681, 2022. 10.1038/​s41566-022-01152-2.
https:/​/​doi.org/​10.1038/​s41566-022-01152-2

[40] Pascale Senellart, Glenn Solomon, and Andrew White. High-performance semiconductor quantum-dot single-photon sources. Nature nanotechnology, 12 (11): 1026, 2017. 10.1038/​nnano.2017.218.
https:/​/​doi.org/​10.1038/​nnano.2017.218

[41] Daniel M Jackson, Dorian A Gangloff, Jonathan H Bodey, Leon Zaporski, Clara Bachorz, Edmund Clarke, Maxime Hugues, Claire Le Gall, and Mete Atatüre. Quantum sensing of a coherent single spin excitation in a nuclear ensemble. Nature Physics, pages 1–6, 2021. 10.1038/​s41567-020-01161-4.
https:/​/​doi.org/​10.1038/​s41567-020-01161-4

[42] Andreas Reiserer, Norbert Kalb, Machiel S Blok, Koen JM van Bemmelen, Tim H Taminiau, Ronald Hanson, Daniel J Twitchen, and Matthew Markham. Robust quantum-network memory using decoherence-protected subspaces of nuclear spins. Physical Review X, 6 (2): 021040, 2016. 10.1103/​PhysRevX.6.021040.
https:/​/​doi.org/​10.1103/​PhysRevX.6.021040

[43] Daniel Gottesman. Stabilizer codes and quantum error correction. arXiv preprint quant-ph/​9705052, 1997. 10.48550/​arXiv.quant-ph/​9705052.
https:/​/​doi.org/​10.48550/​arXiv.quant-ph/​9705052
arXiv:quant-ph/9705052

[44] Michael A. Nielsen and Isaac L. Chuang. Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, 2010. 10.1017/​CBO9780511976667.
https:/​/​doi.org/​10.1017/​CBO9780511976667

[45] JP Lee, B Villa, AJ Bennett, RM Stevenson, DJP Ellis, I Farrer, DA Ritchie, and AJ Shields. A quantum dot as a source of time-bin entangled multi-photon states. Quantum Science and Technology, 4 (2): 025011, 2019b. 10.1088/​2058-9565/​ab0a9b.
https:/​/​doi.org/​10.1088/​2058-9565/​ab0a9b

[46] Konstantin Tiurev, Martin Hayhurst Appel, Pol Llopart Mirambell, Mikkel Bloch Lauritzen, Alexey Tiranov, Peter Lodahl, and Anders Søndberg Sørensen. High-fidelity multiphoton-entangled cluster state with solid-state quantum emitters in photonic nanostructures. Physical Review A, 105 (3): L030601, 2022. 10.1103/​PhysRevA.105.L030601.
https:/​/​doi.org/​10.1103/​PhysRevA.105.L030601

[47] Konstantin Tiurev, Pol Llopart Mirambell, Mikkel Bloch Lauritzen, Martin Hayhurst Appel, Alexey Tiranov, Peter Lodahl, and Anders Søndberg Sørensen. Fidelity of time-bin-entangled multiphoton states from a quantum emitter. Physical Review A, 104 (5): 052604, 2021. 10.1103/​PhysRevA.104.052604.
https:/​/​doi.org/​10.1103/​PhysRevA.104.052604

[48] Sara Bartolucci, Patrick M Birchall, Mercedes Gimeno-Segovia, Eric Johnston, Konrad Kieling, Mihir Pant, Terry Rudolph, Jake Smith, Chris Sparrow, and Mihai D Vidrighin. Creation of entangled photonic states using linear optics. arXiv preprint arXiv:2106.13825, 2021. 10.48550/​arXiv.2106.13825.
https:/​/​doi.org/​10.48550/​arXiv.2106.13825
arXiv:2106.13825

[49] Jian-Wei Pan, Zeng-Bing Chen, Chao-Yang Lu, Harald Weinfurter, Anton Zeilinger, and Marek Żukowski. Multiphoton entanglement and interferometry. Reviews of Modern Physics, 84 (2): 777, 2012. 10.1103/​RevModPhys.84.777.
https:/​/​doi.org/​10.1103/​RevModPhys.84.777

[50] Warren P Grice. Arbitrarily complete bell-state measurement using only linear optical elements. Physical Review A, 84 (4): 042331, 2011. 10.1103/​PhysRevA.84.042331.
https:/​/​doi.org/​10.1103/​PhysRevA.84.042331

[51] Fabian Ewert and Peter van Loock. 3/​4-efficient bell measurement with passive linear optics and unentangled ancillae. Physical review letters, 113 (14): 140403, 2014. 10.1103/​PhysRevLett.113.140403.
https:/​/​doi.org/​10.1103/​PhysRevLett.113.140403

[52] Andrea Olivo and Frédéric Grosshans. Ancilla-assisted linear optical bell measurements and their optimality. Physical Review A, 98 (4): 042323, 2018. 10.1103/​PhysRevA.98.042323.
https:/​/​doi.org/​10.1103/​PhysRevA.98.042323

[53] Yuan Liang Lim, Almut Beige, and Leong Chuan Kwek. Repeat-until-success linear optics distributed quantum computing. Physical review letters, 95 (3): 030505, 2005. 10.1103/​PhysRevLett.95.030505.
https:/​/​doi.org/​10.1103/​PhysRevLett.95.030505

[54] Sean D Barrett and Pieter Kok. Efficient high-fidelity quantum computation using matter qubits and linear optics. Physical Review A, 71 (6): 060310, 2005. 10.1103/​PhysRevA.71.060310.
https:/​/​doi.org/​10.1103/​PhysRevA.71.060310

[55] Yuan Liang Lim, Sean D Barrett, Almut Beige, Pieter Kok, and Leong Chuan Kwek. Repeat-until-success quantum computing using stationary and flying qubits. Physical Review A, 73 (1): 012304, 2006. 10.1103/​PhysRevA.73.012304.
https:/​/​doi.org/​10.1103/​PhysRevA.73.012304

[56] Mihir Pant, Hari Krovi, Dirk Englund, and Saikat Guha. Rate-distance tradeoff and resource costs for all-optical quantum repeaters. Physical Review A, 95 (1): 012304, 2017. 10.1103/​PhysRevA.95.012304.
https:/​/​doi.org/​10.1103/​PhysRevA.95.012304

[57] Michael Varnava, Daniel E Browne, and Terry Rudolph. Loss tolerance in one-way quantum computation via counterfactual error correction. Physical review letters, 97 (12): 120501, 2006. 10.1103/​PhysRevLett.97.120501.
https:/​/​doi.org/​10.1103/​PhysRevLett.97.120501

[58] Tom J Bell, Love A Pettersson, and Stefano Paesani. Optimising graph codes for measurement-based loss tolerance. arXiv preprint arXiv:2212.04834, 2022. 10.48550/​arXiv.2212.04834.
https:/​/​doi.org/​10.48550/​arXiv.2212.04834
arXiv:2212.04834

[59] Benjamin Kambs and Christoph Becher. Limitations on the indistinguishability of photons from remote solid state sources. New Journal of Physics, 20 (11): 115003, 2018. 10.1088/​1367-2630/​aaea99.
https:/​/​doi.org/​10.1088/​1367-2630/​aaea99

[60] Jones Beugnon, Matthew PA Jones, Jos Dingjan, Benoı̂t Darquié, Gaëtan Messin, Antoine Browaeys, and Philippe Grangier. Quantum interference between two single photons emitted by independently trapped atoms. Nature, 440 (7085): 779–782, 2006. 10.1038/​nature04628.
https:/​/​doi.org/​10.1038/​nature04628

[61] Peter Maunz, DL Moehring, S Olmschenk, KC Younge, DN Matsukevich, and C Monroe. Quantum interference of photon pairs from two remote trapped atomic ions. Nature Physics, 3 (8): 538–541, 2007. 10.1038/​nphys644.
https:/​/​doi.org/​10.1038/​nphys644

[62] Raj B Patel, Anthony J Bennett, Ian Farrer, Christine A Nicoll, David A Ritchie, and Andrew J Shields. Two-photon interference of the emission from electrically tunable remote quantum dots. Nature photonics, 4 (9): 632–635, 2010. 10.1038/​nphoton.2010.161.
https:/​/​doi.org/​10.1038/​nphoton.2010.161

[63] V Giesz, SL Portalupi, T Grange, C Antón, L De Santis, J Demory, N Somaschi, I Sagnes, A Lemaı̂tre, L Lanco, et al. Cavity-enhanced two-photon interference using remote quantum dot sources. Physical Review B, 92 (16): 161302, 2015. 10.1103/​PhysRevB.92.161302.
https:/​/​doi.org/​10.1103/​PhysRevB.92.161302

[64] P Gold, A Thoma, S Maier, S Reitzenstein, C Schneider, S Höfling, and M Kamp. Two-photon interference from remote quantum dots with inhomogeneously broadened linewidths. Physical Review B, 89 (3): 035313, 2014. 10.1103/​PhysRevB.89.035313.
https:/​/​doi.org/​10.1103/​PhysRevB.89.035313

[65] Hannes Bernien, Lilian Childress, Lucio Robledo, Matthew Markham, Daniel Twitchen, and Ronald Hanson. Two-photon quantum interference from separate nitrogen vacancy centers in diamond. Physical Review Letters, 108 (4): 043604, 2012. 10.1103/​PhysRevLett.108.043604.
https:/​/​doi.org/​10.1103/​PhysRevLett.108.043604

[66] Hannes Bernien, Bas Hensen, Wolfgang Pfaff, Gerwin Koolstra, Machiel S Blok, Lucio Robledo, Tim H Taminiau, Matthew Markham, Daniel J Twitchen, Lilian Childress, et al. Heralded entanglement between solid-state qubits separated by three metres. Nature, 497 (7447): 86–90, 2013. 10.1038/​nature12016.
https:/​/​doi.org/​10.1038/​nature12016

[67] Alp Sipahigil, Kay D Jahnke, Lachlan J Rogers, Tokuyuki Teraji, Junichi Isoya, Alexander S Zibrov, Fedor Jelezko, and Mikhail D Lukin. Indistinguishable photons from separated silicon-vacancy centers in diamond. Physical review letters, 113 (11): 113602, 2014. 10.1103/​PhysRevLett.113.113602.
https:/​/​doi.org/​10.1103/​PhysRevLett.113.113602

[68] Robert Stockill, MJ Stanley, Lukas Huthmacher, E Clarke, M Hugues, AJ Miller, C Matthiesen, Claire Le Gall, and Mete Atatüre. Phase-tuned entangled state generation between distant spin qubits. Physical review letters, 119 (1): 010503, 2017. 10.1103/​PhysRevLett.119.010503.
https:/​/​doi.org/​10.1103/​PhysRevLett.119.010503

[69] Aymeric Delteil, Zhe Sun, Wei-bo Gao, Emre Togan, Stefan Faelt, and Ataç Imamoğlu. Generation of heralded entanglement between distant hole spins. Nature Physics, 12 (3): 218–223, 2016. 10.1038/​nphys3605.
https:/​/​doi.org/​10.1038/​nphys3605

[70] Niccolo Somaschi, Valerian Giesz, Lorenzo De Santis, JC Loredo, Marcelo P Almeida, Gaston Hornecker, S Luca Portalupi, Thomas Grange, Carlos Anton, Justin Demory, et al. Near-optimal single-photon sources in the solid state. Nature Photonics, 10 (5): 340–345, 2016. 10.1038/​nphoton.2016.23.
https:/​/​doi.org/​10.1038/​nphoton.2016.23

[71] Xing Ding, Yu He, Z-C Duan, Niels Gregersen, M-C Chen, S Unsleber, Sebastian Maier, Christian Schneider, Martin Kamp, Sven Höfling, et al. On-demand single photons with high extraction efficiency and near-unity indistinguishability from a resonantly driven quantum dot in a micropillar. Physical review letters, 116 (2): 020401, 2016. 10.1103/​PhysRevLett.116.020401.
https:/​/​doi.org/​10.1103/​PhysRevLett.116.020401

[72] Ravitej Uppu, Freja T Pedersen, Ying Wang, Cecilie T Olesen, Camille Papon, Xiaoyan Zhou, Leonardo Midolo, Sven Scholz, Andreas D Wieck, Arne Ludwig, et al. Scalable integrated single-photon source. Science advances, 6 (50): eabc8268, 2020. 10.1126/​sciadv.abc8268.
https:/​/​doi.org/​10.1126/​sciadv.abc8268

[73] Natasha Tomm, Alisa Javadi, Nadia Olympia Antoniadis, Daniel Najer, Matthias Christian Löbl, Alexander Rolf Korsch, Rüdiger Schott, Sascha René Valentin, Andreas Dirk Wieck, Arne Ludwig, et al. A bright and fast source of coherent single photons. Nature Nanotechnology, pages 1–5, 2021. 10.1038/​s41565-020-00831-x.
https:/​/​doi.org/​10.1038/​s41565-020-00831-x

[74] N Coste, DA Fioretto, N Belabas, SC Wein, P Hilaire, R Frantzeskakis, M Gundin, B Goes, N Somaschi, M Morassi, et al. High-rate entanglement between a semiconductor spin and indistinguishable photons. Nature Photonics, pages 1–6, 2023. 10.1038/​s41566-023-01186-0.
https:/​/​doi.org/​10.1038/​s41566-023-01186-0

[75] Daniel Riedel, Immo Söllner, Brendan J Shields, Sebastian Starosielec, Patrick Appel, Elke Neu, Patrick Maletinsky, and Richard J Warburton. Deterministic enhancement of coherent photon generation from a nitrogen-vacancy center in ultrapure diamond. Physical Review X, 7 (3): 031040, 2017. 10.1103/​PhysRevX.7.031040.
https:/​/​doi.org/​10.1103/​PhysRevX.7.031040

[76] Jingyuan Linda Zhang, Shuo Sun, Michael J Burek, Constantin Dory, Yan-Kai Tzeng, Kevin A Fischer, Yousif Kelaita, Konstantinos G Lagoudakis, Marina Radulaski, Zhi-Xun Shen, et al. Strongly cavity-enhanced spontaneous emission from silicon-vacancy centers in diamond. Nano letters, 18 (2): 1360–1365, 2018. 10.1021/​acs.nanolett.7b05075.
https:/​/​doi.org/​10.1021/​acs.nanolett.7b05075

[77] Erik N Knall, Can M Knaut, Rivka Bekenstein, Daniel R Assumpcao, Pavel L Stroganov, Wenjie Gong, Yan Qi Huan, P-J Stas, Bartholomeus Machielse, Michelle Chalupnik, et al. Efficient source of shaped single photons based on an integrated diamond nanophotonic system. Physical Review Letters, 129 (5): 053603, 2022. 10.1103/​PhysRevLett.129.053603.
https:/​/​doi.org/​10.1103/​PhysRevLett.129.053603

[78] Feng Liu, Alistair J Brash, John O’Hara, Luis MPP Martins, Catherine L Phillips, Rikki J Coles, Benjamin Royall, Edmund Clarke, Christopher Bentham, Nikola Prtljaga, et al. High purcell factor generation of indistinguishable on-chip single photons. Nature nanotechnology, 13 (9): 835–840, 2018. 10.1038/​s41565-018-0188-x.
https:/​/​doi.org/​10.1038/​s41565-018-0188-x

[79] Timothy C Ralph, AJF Hayes, and Alexei Gilchrist. Loss-tolerant optical qubits. Physical review letters, 95 (10): 100501, 2005. 10.1103/​PhysRevLett.95.100501.
https:/​/​doi.org/​10.1103/​PhysRevLett.95.100501

[80] Nicolas Heurtel, Andreas Fyrillas, Grégoire de Gliniasty, Raphaël Le Bihan, Sébastien Malherbe, Marceau Pailhas, Eric Bertasi, Boris Bourdoncle, Pierre-Emmanuel Emeriau, Rawad Mezher, Luka Music, Nadia Belabas, Benoît Valiron, Pascale Senellart, Shane Mansfield, and Jean Senellart. Perceval: A Software Platform for Discrete Variable Photonic Quantum Computing. Quantum, 7: 931, February 2023. ISSN 2521-327X. 10.22331/​q-2023-02-21-931. URL https:/​/​doi.org/​10.22331/​q-2023-02-21-931.
https:/​/​doi.org/​10.22331/​q-2023-02-21-931

[81] Marc Hein, Jens Eisert, and Hans J Briegel. Multiparty entanglement in graph states. Physical Review A, 69 (6): 062311, 2004. 10.1103/​PhysRevA.69.062311.
https:/​/​doi.org/​10.1103/​PhysRevA.69.062311

[82] Marc Hein, Wolfgang Dür, Jens Eisert, Robert Raussendorf, M Nest, and H-J Briegel. Entanglement in graph states and its applications. arXiv preprint quant-ph/​0602096, 2006. 10.48550/​arXiv.quant-ph/​0602096.
https:/​/​doi.org/​10.48550/​arXiv.quant-ph/​0602096
arXiv:quant-ph/0602096

Cited by

[1] Philip Thomas, Leonardo Ruscio, Olivier Morin, and Gerhard Rempe, "Fusion of deterministically generated photonic graph states", Nature 629 8012, 567 (2024).

[2] Ben Bartlett, Olivia Y. Long, Avik Dutt, and Shanhui Fan, "Programmable photonic system for quantum simulation in arbitrary topologies", APL Quantum 1 1, 016102 (2024).

[3] Martin Esmann, Stephen C. Wein, and Carlos Antón‐Solanas, "Solid‐State Single‐Photon Sources: Recent Advances for Novel Quantum Materials", Advanced Functional Materials 2315936 (2024).

[4] Jiahui Huang, Wei Liu, Xiang Cheng, Alessio Miranda, Benjamin Dwir, Alok Rudra, Eli Kapon, and Chee Wei Wong, "Single site-controlled inverted pyramidal InGaAs QD–nanocavity operating at the onset of the strong coupling regime", Journal of Applied Physics 134 22, 223103 (2023).

[5] Koji Azuma, Sophia E. Economou, David Elkouss, Paul Hilaire, Liang Jiang, Hoi-Kwong Lo, and Ilan Tzitrin, "Quantum repeaters: From quantum networks to the quantum internet", Reviews of Modern Physics 95 4, 045006 (2023).

[6] Shahar Silberstein and Rotem Arnon-Friedman, "Robustness of Bell violation of graph states to qubit loss", Physical Review Research 5 4, 043099 (2023).

[7] Daoheng Niu, Yuxuan Zhang, Alireza Shabani, and Hassan Shapourian, "All-photonic one-way quantum repeaters with measurement-based error correction", npj Quantum Information 9 1, 106 (2023).

[8] H. Cao, L. M. Hansen, F. Giorgino, L. Carosini, P. Zahálka, F. Zilk, J. C. Loredo, and P. Walther, "Photonic Source of Heralded Greenberger-Horne-Zeilinger States", Physical Review Letters 132 13, 130604 (2024).

[9] Thomas J. Bell, Love A. Pettersson, and Stefano Paesani, "Optimizing Graph Codes for Measurement-Based Loss Tolerance", PRX Quantum 4 2, 020328 (2023).

[10] Naphan Benchasattabuse, Michal Hajdušek, and Rodney Van Meter, "Architecture and protocols for all-photonic quantum repeaters", arXiv:2306.03748, (2023).

The above citations are from Crossref's cited-by service (last updated successfully 2024-05-24 18:56:26) and SAO/NASA ADS (last updated successfully 2024-05-24 18:56:27). The list may be incomplete as not all publishers provide suitable and complete citation data.