Silicon photonic devices for scalable quantum information applications

Lantian Feng; Ming Zhang; Jianwei Wang; Xiaoqi Zhou; Xiaogang Qiang; Guangcan Guo; Xifeng Ren

doi:10.1364/PRJ.464808

[1] C. H. Bennett, G. Brassard. Quantum cryptography: public key distribution and coin tossing. Proceedings of the International Conference on Computers, Systems and Signal Processing, 175-179(1984).

[2] N. Gisin, G. Ribordy, W. Tittel, H. Zbinden. Quantum cryptography. Rev. Mod. Phys., 74, 145-195(2002).

[3] P. W. Shor. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev., 41, 303-332(1999).

[4] L. K. Grover. Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett., 79, 325-328(1997).

[5] R. P. Feynman. Simulating physics with computers. Int. J. Theor. Phys., 21, 467-488(1982).

[6] V. Giovannetti, S. Lloyd, L. Maccone. Advances in quantum metrology. Nat. Photonics, 5, 222-229(2011).

[7] F. Arute, K. Arya, R. Babbush. Quantum supremacy using a programmable superconducting processor. Nature, 574, 505-510(2019).

[8] H.-S. Zhong, H. Wang, Y. H. Deng, M.-C. Chen, L.-C. Peng, Y.-H. Luo, J. Qin, D. Wu, X. Ding, Y. Hu, P. Hu, X.-Y. Yang, W.-J. Zhang, H. Li, Y. Li, X. Jiang, L. Gan, G. Yang, L. You, H. Wang, L. Li, N.-L. Liu, C.-Y. Lu, J.-W. Pan. Quantum computational advantage using photons. Science, 370, 1460-1463(2020).

[9] Y. Wu, W. S. Bao, S. Cao, F. Chen, M.-C. Chen, X. Chen, T.-H. Chung, H. Deng, Y. Du, D. Fan, M. Gong, C. Guo, C. Guo, S. Guo, L. Han, L. Hong, H.-L. Huang, Y.-H. Huo, L. Li, N. Li, S. Li, Y. Li, F. Liang, C. Lin, J. Lin, H. Qian, D. Qiao, H. Rong, H. Su, L. Sun, L. Wang, S. Wang, D. Wu, Y. Xu, K. Yan, W. Yang, Y. Yang, Y. Ye, J. Yin, C. Ying, J. Yu, C. Zha, C. Zhang, H. Zhang, K. Zhang, Y. Zhang, H. Zhao, Y. Zhao, L. Zhou, Q. Zhu, C.-Y. Lu, C.-Z. Peng, X. Zhu, J.-W. Pan. Strong quantum computational advantage using a superconducting quantum processor. Phys. Rev. Lett., 127, 180501(2021).

[10] S. K. Liao, W. Q. Cai, W. Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, J.-W. Pan. Satellite-to-ground quantum key distribution. Nature, 549, 43-47(2017).

[11] B. P. Abbott, R. Abbott, T. D. Abbott. Observation of gravitational waves from a binary black hole merger. Phys. Rev. Lett., 116, 061102(2016).

[12] J. M. Boss, K. S. Cujia, J. Zopes, C. L. Degen. Quantum sensing with arbitrary frequency resolution. Science, 356, 837-840(2017).

[13] Y. Zheng, L. M. Zhou, Y. Dong, C. W. Qiu, X. D. Chen, G. C. Guo, F. W. Sun. Robust optical-levitation-based metrology of nanoparticle’s position and mass. Phys. Rev. Lett., 124, 223603(2020).

[14] J. L. O’Brien, A. Furusawa, J. Vučković. Photonic quantum technologies. Nat. Photonics, 3, 687-695(2009).

[15] F. Flamini, N. Spagnolo, F. Sciarrino. Photonic quantum information processing: a review. Rep. Prog. Phys., 82, 016001(2018).

[16] S. Slussarenko, G. J. Pryde. Photonic quantum information processing: a concise review. Appl. Phys. Rev., 6, 041303(2019).

[17] J. Wang, F. Sciarrino, A. Laing, M. G. Thompson. Integrated photonic quantum technologies. Nat. Photonics, 14, 273-284(2020).

[18] L. Lu, X. Zheng, Y. Lu, S. Zhu, X. S. Ma. Advances in chip-scale quantum photonic technologies. Adv. Quantum Technol., 4, 2100068(2021).

[19] A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, J. L. O’Brien. Silica-on-silicon waveguide quantum circuits. Science, 320, 646-649(2008).

[20] X. Jiang, L. Shao, S. X. Zhang, X. Yi, J. Wiersig, L. Wang, Q. Gong, M. Lončar, L. Yang, Y. F. Xiao. Chaos-assisted broadband momentum transformation in optical microresonators. Science, 358, 344-347(2017).

[21] X. Zhang, Q. T. Cao, Z. Wang, Y. X. Liu, C. W. Qiu, L. Yang, Q. Gong, Y. F. Xiao. Symmetry-breaking-induced nonlinear optics at a microcavity surface. Nat. Photonics, 13, 21-24(2019).

[22] M. Li, C. Li, Y. Chen, L. T. Feng, L. Yan, Q. Zhang, J. Bao, B. H. Liu, X. F. Ren, J. Wang, S. Wang, Y. Gao, X. Hu, Q. Gong, Y. Li. On-chip path encoded photonic quantum Toffoli gate. Photon. Res., 10, 1533-1542(2022).

[23] J. W. Silverstone, D. Bonneau, J. L. O’Brien, M. G. Thompson. Silicon quantum photonics. IEEE J. Sel. Top. Quantum Electron., 22, 390-402(2016).

[24] X. Zhang, B. A. Bell, A. Mahendra, C. Xiong, P. H. W. Leong, B. J. Eggleton. Integrated silicon nitride time-bin entanglement circuits. Opt. Lett., 43, 3469-3472(2018).

[25] X. Lu, Q. Li, D. A. Westly, G. Moille, A. Singh, V. Anant, K. Srinivasan. Chip-integrated visible-telecom entangled photon pair source for quantum communication. Nat. Phys., 15, 373-381(2019).

[26] C. Taballione, R. van der Meer, H. J. Snijders, P. Hooijschuur, J. P. Epping, M. de Goede, B. Kassenberg, P. Venderbosch, C. Toebes, H. van den Vlekkert, P. W. H. Pinkse, J. J. Renema. A universal fully reconfigurable 12-mode quantum photonic processor. Mater. Quantum. Technol., 1, 035002(2021).

[27] S. Y. Ren, W. Yan, L. T. Feng, Y. Chen, Y. K. Wu, X. Z. Qi, X. J. Liu, Y. J. Cheng, B. Y. Xu, L. J. Deng, G. C. Guo, L. Bi, X. F. Ren. Single-photon nonreciprocity with an integrated magneto-optical isolator. Laser Photon. Rev., 16, 2100595(2022).

[28] H. Jin, F. M. Liu, P. Xu, J. L. Xia, M. L. Zhong, Y. Yuan, J. W. Zhou, Y. X. Gong, W. Wang, S. N. Zhu. On-chip generation and manipulation of entangled photons based on reconfigurable lithium-niobate waveguide circuits. Phys. Rev. Lett., 113, 103601(2014).

[29] C. Wang, X. Xiong, N. Andrade, V. Venkataraman, X. F. Ren, G. C. Guo, M. Lončar. Second harmonic generation in nano-structured thin-film lithium niobate waveguides. Opt. Express, 25, 6963-6973(2017).

[30] B. Y. Xu, L. Chen, J. Lin, L. T. Feng, R. Niu, Z. Y. Zhou, R. Gao, C. Dong, G. Guo, Q. Gong, Y. Cheng, Y. F. Xiao, X. F. Ren. Spectrally multiplexed and bright entangled photon pairs in a lithium niobate microresonator. Sci. China, 65, 294262(2022).

[31] R. J. Bojko, J. Li, L. He, T. Baehr-Jones, M. Hochberg. Electron beam lithography writing strategies for low loss, high confinement silicon optical waveguides. J. Vac. Sci. Technol. B, 29, 06F309(2011).

[32] K. Sugioka, Y. Cheng. Ultrafast lasers-reliable tools for advanced materials processing. Light Sci. Appl., 3, e149(2014).

[33] T. Rudolph. Why I am optimistic about the silicon-photonic route to quantum computing. APL Photon., 2, 030901(2017).

[34] D. Thomson, A. Zilkie, J. E. Bowers, T. Komljenovic, G. T. Reed, L. Vivien, D. Marris-Morini, E. Cassan, L. Virot, J. M. Fédéli, J. M. Hartmann, J. H. Schmid, D. X. Xu, F. Boeuf, P. O’Brien, G. Z. Mashanovich, M. Nedeljkovic. Roadmap on silicon photonics. J. Opt., 18, 073003(2016).

[35] G. Son, S. Han, J. Park, K. Kwon, K. Yu. High-efficiency broadband light coupling between optical fibers and photonic integrated circuits. Nanophotonics, 7, 1845-1864(2018).

[36] N. C. Harris, D. Bunandar, M. Pant, G. R. Steinbrecher, J. Mower, M. Prabhu, T. Baehr-Jones, M. Hochberg, D. Englund. Large-scale quantum photonic circuits in silicon. Nanophotonics, 5, 456-468(2016).

[37] W. H. Pernice, C. Schuck, O. Minaeva, M. Li, G. N. Goltsman, A. V. Sergienko, H. X. Tang. High-speed and high-efficiency travelling wave single-photon detectors embedded in nanophotonic circuits. Nat. Commun., 3, 1325(2012).

[38] L. T. Feng, G. C. Guo, X. F. Ren. Progress on integrated quantum photonic sources with silicon. Adv. Quantum Technol., 3, 1900058(2020).

[39] X. Chen, Z. Fu, Q. Gong, J. Wang. Quantum entanglement on photonic chips: a review. Adv. Photon., 3, 064002(2021).

[40] J. C. Adcock, J. Bao, Y. Chi, X. Chen, D. Bacco, Q. Gong, L. K. Oxenløwe, J. Wang, Y. Ding. Advances in silicon quantum photonics. IEEE J. Sel. Top. Quantum Electron., 27, 6700224(2020).

[41] A. W. Elshaari, W. Pernice, K. Srinivasan, O. Benson, V. Zwiller. Hybrid integrated quantum photonic circuits. Nat. Photonics, 14, 285-298(2020).

[42] J. H. Kim, S. Aghaeimeibodi, J. Carolan, D. Englund, E. Waks. Hybrid integration methods for on-chip quantum photonics. Optica, 7, 291-308(2020).

[43] Y. H. Li, Z. Y. Zhou, L. T. Feng, W. T. Fang, S. L. Liu, S. K. Liu, K. Wang, X. F. Ren, D. S. Ding, L. X. Xu, B. S. Shi. On-chip multiplexed multiple entanglement sources in a single silicon nanowire. Phys. Rev. Appl., 7, 064005(2017).

[44] C. Ma, X. Wang, V. Anant, A. D. Beyer, M. D. Shaw, S. Mookherjea. Silicon photonic entangled photon-pair and heralded single photon generation with CAR > 12,000 and g²(0) < 0.006. Opt. Express, 25, 32995-33006(2017).

[45] Y. Liu, C. Wu, X. Gu, Y. Kong, X. Yu, R. Ge, X. Cai, X. Qiang, J. Wu, X. Yang, P. Xu. High-spectral-purity photon generation from a dual-interferometer-coupled silicon microring. Opt. Lett., 45, 73-76(2020).

[46] B. M. Burridge, I. I. Faruque, J. G. Rarity, J. Barreto. High spectro-temporal purity single-photons from silicon micro-racetrack resonators using a dual-pulse configuration. Opt. Lett., 45, 4048-4051(2020).

[47] S. Paesani, M. Borghi, S. Signorini, A. Maïnos, L. Pavesi, A. Laing. Near-ideal spontaneous photon sources in silicon quantum photonics. Nat. Commun., 11, 2505(2020).

[48] Y. Zhou, Z. Wang, A. Rasmita, S. Kim, A. Berhane, Z. Bodrog, G. Adamo, A. Gali, I. Aharonovich, W. B. Gao. Room temperature solid-state quantum emitters in the telecom range. Sci. Adv., 4, eaar3580(2018).

[49] H. Zhao, M. T. Pettes, Y. Zheng, H. Htoon. Site-controlled telecom-wavelength single-photon emitters in atomically-thin MoTe₂. Nat. Commun., 12, 6753(2021).

[50] M. Hollenbach, Y. Berencén, U. Kentsch, M. Helm, G. V. Astakhov. Engineering telecom single-photon emitters in silicon for scalable quantum photonics. Opt. Express, 28, 26111-26121(2020).

[51] D. B. Higginbottom, A. T. K. Kurkjian, C. Chartrand, M. Kazemi, N. A. Brunelle, E. R. MacQuarrie, J. R. Klein, N. R. Lee-Hone, J. Stacho, M. Ruether, C. Bowness, L. Bergeron, A. DeAbreu, S. R. Harrigan, J. Kanaganayagam, D. W. Marsden, T. S. Richards, L. A. Stott, S. Roorda, K. J. Morse, M. L. W. Thewalt, S. Simmons. Optical observation of single spins in silicon. Nature, 607, 266-270(2022).

[52] M. J. Collins, C. Xiong, I. H. Rey, T. D. Vo, J. He, S. Shahnia, C. Reardon, T. F. Krauss, M. J. Steel, A. S. Clark, B. J. Eggleton. Integrated spatial multiplexing of heralded single-photon sources. Nat. Commun., 4, 2582(2013).

[53] X. Zhang, I. Jizan, J. He, A. S. Clark, D.-Y. Choi, C. J. Chae, B. J. Eggleton, C. Xiong. Enhancing the heralded single-photon rate from a silicon nanowire by time and wavelength division multiplexing pump pulses. Opt. Lett., 40, 2489-2492(2015).

[54] C. Xiong, X. Zhang, Z. Liu, M. J. Collins, A. Mahendra, L. G. Helt, M. J. Steel, D.-Y. Choi, C. J. Chae, P. H. W. Leong, B. J. Eggleton. Active temporal multiplexing of indistinguishable heralded single photons. Nat. Commun., 7, 10853(2016).

[55] F. Kaneda, P. G. Kwiat. High-efficiency single-photon generation via large-scale active time multiplexing. Sci. Adv., 5, eaaw8586(2019).

[56] H. Lee, T. Chen, J. Li, O. Painter, K. J. Vahala. Ultra-low-loss optical delay line on a silicon chip. Nat. Commun., 3, 867(2012).

[57] M. He, M. Xu, Y. Ren, J. Jian, Z. Ruan, Y. Xu, S. Gao, S. Sun, X. Wen, L. Zhou, L. Liu, C. Guo, H. Chen, S. Yu, L. Liu, X. Cai. High-performance hybrid silicon and lithium niobate Mach–Zehnder modulators for 100 Gbit s^-1 and beyond. Nat. Photonics, 13, 359-364(2019).

[58] S. Haffouz, K. D. Zeuner, D. Dalacu, P. J. Poole, J. Lapointe, D. Poitras, K. Mnaymneh, X. Wu, M. Couillard, M. Korkusinski, E. Schöll, K. D. Jöns, V. Zwiller, R. L. Williams. Bright single InAsP quantum dots at telecom wavelengths in position-controlled InP nanowires: the role of the photonic waveguide. Nano Lett., 18, 3047-3052(2018).

[59] J. H. Kim, S. Aghaeimeibodi, C. J. Richardson, R. P. Leavitt, D. Englund, E. Waks. Hybrid integration of solid-state quantum emitters on a silicon photonic chip. Nano Lett., 17, 7394-7400(2017).

[60] T. Müller, J. Skiba-Szymanska, A. B. Krysa, J. Huwer, M. Felle, M. Anderson, R. M. Stevenson, J. Heffernan, D. A. Ritchie, A. J. Shields. A quantum light-emitting diode for the standard telecom window around 1,550 nm. Nat. Commun., 9, 862(2018).

[61] R. Katsumi, Y. Ota, M. Kakuda, S. Iwamoto, Y. Arakawa. Transfer-printed single-photon sources coupled to wire waveguides. Optica, 5, 691-694(2018).

[62] R. Katsumi, Y. Ota, A. Osada, T. Yamaguchi, T. Tajiri, M. Kakuda, S. Iwamoto, H. Akiyama, Y. Arakawa. Quantum-dot single-photon source on a CMOS silicon photonic chip integrated using transfer printing. APL Photon., 4, 036105(2019).

[63] W. Redjem, A. Durand, T. Herzig, A. Benali, S. Pezzagna, J. Meijer, A. Y. Kuznetsov, H. S. Nguyen, S. Cueff, J.-M. Gérard, I. Robert-Philip, B. Gil, D. Caliste, P. Pochet, M. Abbarchi, V. Jacques, A. Dréau, G. Cassabois. Single artificial atoms in silicon emitting at telecom wavelengths. Nat. Electron., 3, 738-743(2020).

[64] M. Hollenbach, N. S. Jagtap, C. Fowley, J. Baratech, V. Guardia-Arce, U. Kentsch, A. Eichler-Volf, N. V. Abrosimov, A. Erbe, C. Shin, H. Kim, M. Helm, W. Lee, G. V. Astakhov, Y. Berencén. A photonic platform hosting telecom photon emitters in silicon(2021).

[65] M. Prabhu, C. Errando-Herranz, L. D. Santis, I. Christen, C. Chen, D. R. Englund. Individually addressable artificial atoms in silicon photonics(2022).

[66] L. Bergeron, C. Chartrand, A. T. K. Kurkjian, K. J. Morse, H. Riemann, N. V. Abrosimov, P. Becker, H. J. Pohl, M. L. W. Thewalt, S. Simmons. Silicon-integrated telecommunications photon-spin interface. PRX Quantum, 1, 020301(2020).

[67] S. Liu, K. Srinivasan, J. Liu. Nanoscale positioning approaches for integrating single solid-state quantum emitters with photonic nanostructures. Laser Photon. Rev., 15, 2100223(2021).

[68] P. Peng, Y. C. Liu, D. Xu, Q. T. Cao, G. Lu, Q. Gong, Y. F. Xiao. Enhancing coherent light-matter interactions through microcavity-engineered plasmonic resonances. Phys. Rev. Lett., 119, 233901(2017).

[69] S. Liu, Y. Wei, X. Li, Y. Yu, J. Liu, S. Yu, X. Wang. Dual-resonance enhanced quantum light-matter interactions in deterministically coupled quantum-dot-micropillars. Light Sci. Appl., 10, 158(2021).

[70] Y. Wei, S. Liu, X. Li, Y. Yu, X. Su, S. Li, X. Shang, H. Liu, H. Hao, H. Ni, S. Yu, Z. Niu, J. Iles-Smith, J. Liu, X. Wang. Tailoring solid-state single-photon sources with stimulated emissions. Nat. Nanotechnol., 17, 470-476(2022).

[71] R. B. Patel, A. J. Bennett, I. Farrer, C. A. Nicoll, D. A. Ritchie, A. J. Shields. Two-photon interference of the emission from electrically tunable remote quantum dots. Nat. Photonics, 4, 632-635(2010).

[72] E. B. Flagg, A. Muller, S. V. Polyakov, A. Ling, A. Migdall, G. S. Solomon. Interference of single photons from two separate semiconductor quantum dots. Phys. Rev. Lett., 104, 137401(2010).

[73] A. W. Elshaari, E. Büyüközer, I. E. Zadeh, T. Lettner, P. Zhao, E. Schöll, S. Gyger, M. E. Reimer, D. Dalacu, P. J. Poole, K. D. Jöns, V. Zwiller. Strain-tunable quantum integrated photonics. Nano Lett., 18, 7969-7976(2018).

[74] B. Machielse, S. Bogdanovic, S. Meesala, S. Gauthier, M. J. Burek, G. Joe, M. Chalupnik, Y. I. Sohn, J. Holzgrafe, R. E. Evans, C. Chia, H. Atikian, M. K. Bhaskar, D. D. Sukachev, L. Shao, S. Maity, M. D. Lukin, M. Lončar. Quantum interference of electromechanically stabilized emitters in nanophotonic devices. Phys. Rev. X, 9, 031022(2019).

[75] R. Katsumi, Y. Ota, A. Osada, T. Tajiri, T. Yamaguchi, M. Kakuda, S. Iwamoto, H. Akiyama, Y. Arakawa. In situ wavelength tuning of quantum-dot single-photon sources integrated on a CMOS-processed silicon waveguide. Appl. Phys. Lett., 116, 041103(2020).

[76] L. Zhai, G. N. Nguyen, C. Spinnler, J. Ritzmann, M. C. Löbl, A. D. Wieck, A. Ludwig, A. Javadi, R. J. Warburton. Quantum interference of identical photons from remote GaAs quantum dots. Nat. Nanotechnol., 17, 829-833(2022).

[77] N. H. Wan, T.-J. Lu, K. C. Chen, M. P. Walsh, M. E. Trusheim, L. D. Santis, E. A. Bersin, I. B. Harris, S. L. Mouradian, I. R. Christen, E. S. Bielejec, D. Englund. Large-scale integration of artificial atoms in hybrid photonic circuits. Nature, 583, 226-231(2020).

[78] D. Benedikovic, L. Virot, G. Aubin, F. Amar, B. Szelag, B. Karakus, J.-M. Hartmann, C. Alonso-Ramos, X. L. Roux, P. Crozat, E. Cassan, D. Marris-Morini, C. Baudot, F. Boeuf, J.-M. Fédéli, C. Kopp, L. Vivien. 25 Gbps low-voltage hetero-structured silicon-germanium waveguide pin photodetectors for monolithic on-chip nanophotonic architectures. Photon. Res., 7, 437-444(2019).

[79] F. Raffaelli, G. Ferranti, D. H. Mahler, P. Sibson, J. E. Kennard, A. Santamato, G. Sinclair, D. Bonneau, M. G. Thompson, J. C. F. Matthews. A homodyne detector integrated onto a photonic chip for measuring quantum states and generating random numbers. Quantum Sci. Technol., 3, 025003(2018).

[80] J. F. Tasker, J. Frazer, G. Ferranti, E. J. Allen, L. F. Brunel, S. Tanzilli, V. D’Auria, J. C. F. Matthews. Silicon photonics interfaced with integrated electronics for 9 GHz measurement of squeezed light. Nat. Photonics, 15, 11-15(2021).

[81] C. Bruynsteen, M. Vanhoecke, J. Bauwelinck, X. Yin. Integrated balanced homodyne photonic-electronic detector for beyond 20 GHz shot-noise-limited measurements. Optica, 8, 1146-1152(2021).

[82] D. V. Reddy, R. R. Nerem, S. W. Nam, R. P. Mirin, V. B. Verma. Superconducting nanowire single-photon detectors with 98% system detection efficiency at 1550 nm. Optica, 7, 1649-1653(2020).

[83] B. Korzh, Q. Y. Zhao, J. P. Allmaras, S. Frasca, T. M. Autry, E. A. Bersin, A. D. Beyer, R. M. Briggs, B. Bumble, M. Colangelo, A. E. Dane, T. Gerrits, A. E. Lita, F. Marsili, G. Moody, C. Peña, E. Ramirez, J. D. Rezac, N. Sinclair, M. J. Stevens, A. E. Velasco, V. B. Verma, E. E. Wollman, S. Xie, D. Zhu, P. D. Hale, M. Spiropulu, K. L. Silverman, R. P. Mirin, S. W. Nam, A. G. Kozorezov, M. D. Shaw, K. K. Berggren. Demonstration of sub-3 ps temporal resolution with a superconducting nanowire single-photon detector. Nat. Photonics, 14, 250-255(2020).

[84] M. Akhlaghi, E. Schelew, J. Young. Waveguide integrated superconducting single-photon detectors implemented as near-perfect absorbers of coherent radiation. Nat. Commun., 6, 8233(2015).

[85] J. Li, R. A. Kirkwood, L. J. Baker, D. Bosworth, K. Erotokritou, A. Banerjee, R. M. Heath, C. M. Natarajan, Z. H. Barber, M. Sorel, R. H. Hadfield. Nano-optical single-photon response mapping of waveguide integrated molybdenum silicide (MoSi) superconducting nanowires. Opt. Express, 24, 13931-13938(2016).

[86] S. Buckley, J. Chiles, A. N. McCaughan, G. Moody, K. L. Silverman, M. J. Stevens, R. P. Mirin, S. W. Nam, J. M. Shainline. All-silicon light-emitting diodes waveguide-integrated with superconducting single-photon detectors. Appl. Phys. Lett., 111, 141101(2017).

[87] A. Vetter, S. Ferrari, P. Rath, R. Alaee, O. Kahl, V. Kovalyuk, S. Diewald, G. N. Goltsman, A. Korneev, C. Rockstuhl, W. H. P. Pernice. Cavity-enhanced and ultrafast superconducting single-photon detectors. Nano Lett., 16, 7085-7092(2016).

[88] J. Münzberg, A. Vetter, F. Beutel, W. Hartmann, S. Ferrari, W. H. P. Pernice, C. Rockstuhl. Superconducting nanowire single-photon detector implemented in a 2D photonic crystal cavity. Optica, 5, 658-665(2018).

[89] D. Zhu, Q. Y. Zhao, H. Choi, T. J. Lu, A. E. Dane, D. Englund, K. K. Berggren. A scalable multi-photon coincidence detector based on superconducting nanowires. Nat. Nanotechnol., 13, 596-601(2018).

[90] C. Cahall, K. L. Nicolich, N. T. Islam, G. P. Lafyatis, A. J. Miller, D. J. Gauthier, J. Kim. Multi-photon detection using a conventional superconducting nanowire single-photon detector. Optica, 4, 1534-1535(2017).

[91] D. Zhu, M. Colangelo, C. Chen, B. A. Korzh, F. N. C. Wong, M. D. Shaw, K. K. Berggren. Resolving photon numbers using a superconducting nanowire with impedance-matching taper. Nano Lett., 20, 3858-3863(2020).

[92] Q. Y. Zhao, D. Zhu, N. Calandri, A. E. Dane, A. N. McCaughan, F. Bellei, H. Z. Wang, D. F. Santavicca, K. K. Berggren. Single-photon imager based on a superconducting nanowire delay line. Nat. Photonics, 11, 247-251(2017).

[93] E. E. Wollman, V. B. Verma, A. E. Lita, W. H. Farr, M. D. Shaw, R. P. Mirin, S. W. Nam. Kilopixel array of superconducting nanowire single-photon detectors. Opt. Express, 27, 35279-35289(2019).

[94] R. Cheng, C. L. Zou, X. Guo, S. Wang, X. Han, H. X. Tang. Broadband on-chip single-photon spectrometer. Nat. Commun., 10, 4104(2019).

[95] F. Beutel, H. Gehring, M. A. Wolff, C. Schuck, W. Pernice. Detector-integrated on-chip QKD receiver for GHz clock rates. NPJ Quantum Inf., 7, 40(2021).

[96] X. Zheng, P. Zhang, R. Ge, L. Lu, G. He, Q. Chen, F. Qu, L. Zhang, X. Cai, Y. Lu, S. N. Zhu, P. Wu, X. Ma. Heterogeneously integrated, superconducting silicon-photonic platform for measurement-device-independent quantum key distribution. Adv. Photon., 3, 055002(2021).

[97] P. Vines, K. Kuzmenko, J. Kirdoda, D. C. S. Dumas, M. M. Mirza, R. W. Millar, D. J. Paul, G. S. Buller. High performance planar germanium-on-silicon single-photon avalanche diode detectors. Nat. Commun., 10, 1086(2019).

[98] L. F. Llin, J. Kirdoda, F. Thorburn, L. L. Huddleston, Z. M. Greener, K. Kuzmenko, P. Vines, D. C. S. Dumas, R. W. Millar, G. S. Buller, D. J. Paul. High sensitivity Ge-on-Si single-photon avalanche diode detectors. Opt. Lett., 45, 6406-6409(2020).

[99] J. Zhang, M. A. Itzler, H. Zbinden, J. W. Pan. Advances in InGaAs/InP single-photon detector systems for quantum communication. Light Sci. Appl., 4, e286(2015).

[100] Y. Q. Fang, W. Chen, T. H. Ao, C. Liu, L. Wang, X. J. Gao, J. Zhang, J. W. Pan. InGaAs/InP single-photon detectors with 60% detection efficiency at 1550 nm. Rev. Sci. Instrum., 91, 083102(2020).

[101] H. Wang, J. Guo, J. Miao, W. Luo, Y. Gu, R. Xie, F. Wang, L. Zhang, P. Wang, W. Hu. Emerging single-photon detectors based on low-dimensional materials. Small, 18, 2103963(2022).

[102] W. Song, R. Gatdula, S. Abbaslou, M. Lu, A. Stein, W. Y.-C. Lai, J. Provine, R. F. W. Pease, D. N. Christodoulides, W. Jiang. High-density waveguide superlattices with low crosstalk. Nat. Commun., 6, 7027(2015).

[103] M. Zhang, L. T. Feng, M. Li, Y. Chen, L. Zhang, D. He, G. Guo, G. Guo, X. Ren, D. Dai. Supercompact photonic quantum logic gate on a silicon chip. Phys. Rev. Lett., 126, 130501(2021).

[104] H. Zhou, Y. Wang, X. Gao, D. Gao, J. Dong, D. Huang, F. Li, P. A. Wai, X. Zhang. Dielectric metasurfaces enabled ultradensely integrated multidimensional optical system. Laser Photon. Rev., 16, 2100521(2022).

[105] F. Horst, W. M. J. Green, S. Assefa, S. M. Shank, Y. A. Vlasov, B. J. Offrein. Cascaded Mach-Zehnder wavelength filters in silicon photonics for low loss and flat pass-band WDM (de-)multiplexing. Opt. Express, 21, 11652-11658(2013).

[106] S. Cheung, T. H. Su, K. Okamoto, S. J. B. Yoo. Ultra-compact silicon photonic 512×512 25 GHz arrayed waveguide grating router. IEEE J. Sel. Top. Quantum Electron., 20, 310-316(2014).

[107] D. T. H. Tan, A. Grieco, Y. Fainman. Towards 100 channel dense wavelength division multiplexing with 100 GHz spacing on silicon. Opt. Express, 22, 10408-10415(2014).

[108] S. T. Chen, X. Fu, J. Wang, Y. C. Shi, S. L. He, D. X. Dai. Compact dense wavelength-division (de)multiplexer utilizing a bidirectional arrayed-waveguide grating integrated with a Mach–Zehnder interferometer. J. Lightwave Technol., 33, 2279-2285(2015).

[109] D. Munk, M. Katzman, Y. Kaganovskii, N. Inbar, A. Misra, M. Hen, M. Priel, M. Feldberg, M. Tkachev, A. Bergman, M. Vofsi, M. Rosenbluh, T. Schneider, A. Zadok. Eight-channel silicon-photonic wavelength division multiplexer with 17 GHz spacing. IEEE J. Sel. Top. Quantum Electron., 25, 8300310(2019).

[110] Z. Liu, J. Zhang, X. Li, L. Wang, J. Li, C. Xue, J. An, B. Cheng. 25×50 Gbps wavelength division multiplexing silicon photonics receiver chip based on a silicon nanowire-arrayed waveguide grating. Photon. Res., 7, 659-663(2019).

[111] J. R. Ong, R. Kumar, S. Mookherjea. Ultra-high-contrast and tunable-bandwidth filter using cascaded high-order silicon micro-ring filters. IEEE Photon. Technol. Lett., 25, 1543-1546(2013).

[112] H. Qiu, J. Jiang, T. Hu, P. Yu, J. Yang, X. Jiang, H. Yu. Silicon add-drop filter based on multimode Bragg sidewall gratings and adiabatic couplers. J. Lightwave Technol., 35, 1705-1709(2017).

[113] A. B. Price, P. Sibson, C. Erven, J. G. Rarity, M. G. Thompson. High-speed quantum key distribution with wavelength-division multiplexing on integrated photonic devices. Conference on Lasers and Electro-Optics, JTh2A.24(2018).

[114] D. Liu, H. Xu, Y. Tan, Y. Shi, D. Dai. Silicon photonic filters. Microw. Opt. Technol. Lett., 63, 2252-2268(2021).

[115] S. Liao, Y. Ding, C. Peucheret, T. Yang, J. Dong, X. Zhang. Integrated programmable photonic filter on the silicon-on-insulator platform. Opt. Express, 22, 31993-31998(2014).

[116] F. Xia, M. Rooks, L. Sekaric, Y. Vlasov. Ultra-compact high order ring resonator filters using submicron silicon photonic wires for on-chip optical interconnects. Opt. Express, 15, 11934-11941(2007).

[117] P. Chen, S. Chen, X. Guan, Y. Shi, D. Dai. High-order microring resonators with bent couplers for a box-like filter response. Opt. Lett., 39, 6304-6307(2014).

[118] D. Liu, C. Zhang, D. Liang, D. Dai. Submicron-resonator-based add-drop optical filter with an ultra-large free spectral range. Opt. Express, 27, 416-422(2019).

[119] N. C. Harris, D. Grassani, A. Simbula, M. Pant, M. Galli, T. Baehr-Jones, M. Hochberg, D. Englund, D. Bajoni, C. Galland. Integrated source of spectrally filtered correlated photons for large-scale quantum photonic systems. Phys. Rev. X, 4, 041047(2014).

[120] D. Oser, S. Tanzilli, F. Mazeas, C. Alonso-Ramos, X. L. Roux, G. Sauder, X. Hua, O. Alibart, L. Vivien, É. Cassan, L. Labonté. High-quality photonic entanglement out of a stand-alone silicon chip. NPJ Quantum Inf., 6, 31(2020).

[121] C. Li, D. Liu, D. Dai. Multimode silicon photonics. Nanophotonics, 8, 227-247(2019).

[122] L. W. Luo, N. Ophir, C. P. Chen, L. H. Gabrielli, C. B. Poitras, K. Bergmen, M. Lipson. WDM-compatible mode-division multiplexing on a silicon chip. Nat. Commun., 5, 3069(2014).

[123] D. Dai, J. Wang, S. Chen, S. Wang, S. He. Monolithically integrated 64-channel silicon hybrid demultiplexer enabling simultaneous wavelength- and mode-division-multiplexing. Laser Photon. Rev., 9, 339-344(2015).

[124] S. Wang, X. Feng, S. Gao, Y. Shi, T. Dai, H. Yu, H.-K. Tsang, D. Dai. On-chip reconfigurable optical add-drop multiplexer for hybrid wavelength/mode-division-multiplexing systems. Opt. Lett., 42, 2802-2805(2017).

[125] D. Guo, T. Chu. Silicon mode (de)multiplexers with parameters optimized using shortcuts to adiabaticity. Opt. Express, 25, 9160-9170(2017).

[126] D. Dai, C. Li, S. Wang, H. Wu, Y. Shi, Z. Wu, S. Gao, T. Dai, H. Yu, H. K. Tsang. 10-channel mode (de)multiplexer with dual polarizations. Laser Photon. Rev., 12, 1700109(2018).

[127] H. Xu, Y. Shi. Metamaterial-based Maxwell’s fisheye lens for multimode waveguide crossing. Laser Photon. Rev., 12, 1800094(2018).

[128] Y. Liu, K. Xu, S. Wang, W. Shen, H. Xie, Y. Wang, S. Xiao, Y. Yao, J. Du, Z. He, Q. Song. Arbitrarily routed mode-division multiplexed photonic circuits for dense integration. Nat. Commun., 10, 3263(2019).

[129] Y. Xiong, R. Priti, O. Ladouceur. High-speed two-mode switch for mode-division multiplexing optical networks. Optica, 4, 1098-1102(2017).

[130] D. Dai, J. Wang, Y. Shi. Silicon mode (de)multiplexer enabling high capacity photonic networks-on-chip with a single-wavelength-carrier light. Opt. Lett., 38, 1422-1424(2013).

[131] Y. Lai, Y. Yu, S. Fu, J. Xu, P. P. Shum, X. Zhang. Compact double-part grating coupler for higher-order mode coupling. Opt. Lett., 43, 3172-3175(2018).

[132] S. Li, Y. Zhou, J. Dong, X. Zhang, E. Cassan, J. Hou, C. Yang, S. Chen, D. Gao, H. Chen. Universal multimode waveguide crossing based on transformation optics. Optica, 5, 1549-1556(2018).

[133] L. T. Feng, M. Zhang, Z. Y. Zhou, M. Li, X. Xiong, L. Yu, B. S. Shi, G. P. Guo, D. X. Dai, X. F. Ren, G. C. Guo. On-chip coherent conversion of photonic quantum entanglement between different degrees of freedom. Nat. Commun., 7, 11985(2016).

[134] A. Mohanty, M. Zhang, A. Dutt, S. Ramelow, P. Nussenzveig, M. Lipson. Quantum interference between transverse spatial waveguide modes. Nat. Commun., 8, 14010(2017).

[135] L. T. Feng, M. Zhang, X. Xiong, D. Liu, Y. J. Cheng, F. M. Jing, X. Z. Qi, Y. Chen, D. Y. He, G. P. Guo, G. C. Guo, D. X. Dai, X. F. Ren. Transverse mode-encoded quantum gate on a silicon photonic chip. Phys. Rev. Lett., 128, 060501(2022).

[136] L. T. Feng, M. Zhang, X. Xiong, Y. Chen, H. Wu, M. Li, G. P. Guo, G. C. Guo, D. X. Dai, X. F. Ren. On-chip transverse-mode entangled photon pair source. NPJ Quantum Inf., 5, 2(2019).

[137] J. Komma, C. Schwarz, G. Hofmann, D. Heinert, R. Nawrodt. Thermo-optic coefficient of silicon at 1550 nm and cryogenic temperatures. Appl. Phys. Lett., 101, 041905(2012).

[138] M. Gehl, C. Long, D. Trotter, A. Starbuck, A. Pomerene, J. B. Wright, S. Melgaard, J. Siirola, A. L. Lentine, C. DeRose. Operation of high-speed silicon photonic micro-disk modulators at cryogenic temperatures. Optica, 4, 374-382(2017).

[139] F. Eltes, G. E. Villarreal-Garcia, D. Caimi, H. Siegwart, A. A. Gentile, A. Hart, P. Stark, G. D. Marshall, M. G. Thompson, J. Barreto, J. Fompeyrine, S. Abel. An integrated optical modulator operating at cryogenic temperatures. Nat. Mater., 19, 1164-1168(2020).

[140] U. Chakraborty, J. Carolan, G. Clark, D. Bunandar, G. Gilbert, J. Notaros, M. R. Watts, D. R. Englund. Cryogenic operation of silicon photonic modulators based on the DC Kerr effect. Optica, 7, 1385-1390(2020).

[141] M. Dong, G. Clark, A. J. Leenheer, M. Zimmermann, D. Dominguez, A. J. Menssen, D. Heim, G. Gilbert, D. Englund, M. Eichenfield. High-speed programmable photonic circuits in a cryogenically compatible, visible-near-infrared 200 mm CMOS architecture. Nat. Photonics, 16, 59-65(2022).

[142] W. H. P. Pernice, C. Schuck, M. Li, H. X. Tang. Carrier and thermal dynamics of silicon photonic resonators at cryogenic temperatures. Opt. Express, 19, 3290-3296(2011).

[143] X. Sun, X. Zhang, C. Schuck, H. X. Tang. Nonlinear optical effects of ultrahigh-Q silicon photonic nanocavities immersed in superfluid helium. Sci. Rep., 3, 1436(2013).

[144] G. F. Sinclair, N. A. Tyler, D. Sahin, J. Barreto, M. G. Thompson. Temperature dependence of the Kerr nonlinearity and two-photon absorption in a silicon waveguide at 1.55 μm. Phys. Rev. Appl., 11, 044084(2019).

[145] D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Dale, I. Moerman, S. Verstuyft, K. De Mesel, R. Baets. An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers. IEEE J. Quantum Electron., 38, 949-955(2002).

[146] F. V. Laere, T. Claes, J. Schrauwen, S. Scheerlinck, W. Bogaerts, D. Taillaert, L. O’Faolain, D. V. Thourhout, R. Baets. Compact focusing grating couplers for silicon-on-insulator integrated circuits. IEEE Photon. Technol. Lett., 19, 1919-1921(2007).

[147] C. Li, H. Zhang, M. Yu, G. Lo. CMOS-compatible high efficiency double-etched apodized waveguide grating coupler. Opt. Express, 21, 7868-7874(2013).

[148] N. Hoppe, W. S. Zaoui, L. Rathgeber, Y. Wang, R. H. Klenk, W. Vogel, M. Kaschel, S. L. Portalupi, J. Burghartz, M. Berroth. Ultra-efficient silicon-on-insulator grating couplers with backside metal mirrors. IEEE J. Sel. Top. Quantum Electron., 26, 8200206(2020).

[149] Q. Fang, J. Song, X. Luo, M. Yu, G. Lo, Y. Liu. Mode-size converter with high coupling efficiency and broad bandwidth. Opt. Express, 19, 21588-21594(2011).

[150] H. Luo, F. Xie, Y. Cao, S. Yu, L. Chen, X. Cai. Low-loss and broadband fiber-to-chip coupler by 3D fabrication on a silicon photonic platform. Opt. Lett., 45, 1236-1239(2020).

[151] M. Trappen, M. Blaicher, P. I. Dietrich, C. Dankwart, Y. Xu, T. Hoose, M. R. Billah, A. Abbasi, R. Baets, U. Troppenz, M. Theurer, K. Wörhoff, M. Seyfried, W. Freude, C. Koos. 3D-printed optical probes for wafer-level testing of photonic integrated circuits. Opt. Express, 28, 37996-38007(2020).

[152] N. Lindenmann, S. Dottermusch, M. L. Goedecke, T. Hoose, M. R. Billah, T. P. Onanuga, A. Hofmann, W. Freude, C. Koos. Connecting silicon photonic circuits to multicore fibers by photonic wire bonding. J. Lightwave Technol., 33, 755-760(2015).

[153] P. I. Dietrich, M. Blaicher, I. Reuter, M. Billah, T. Hoose, A. Hofmann, C. Caer, R. Dangel, B. Offrein, U. Troppenz, M. Moehrle, W. Freude, C. Koos. In situ 3D nanoprinting of free-form coupling elements for hybrid photonic integration. Nat. Photonics, 12, 241-247(2018).

[154] Y. Tang, Z. Wang, L. Wosinski, U. Westergren, S. He. Highly efficient nonuniform grating coupler for silicon-on-insulator nanophotonic circuits. Opt. Lett., 35, 1290-1292(2010).

[155] D. Benedikovic, P. Cheben, J. H. Schmid, D. X. Xu, J. Lapointe, S. Wang, R. Halir, A. Monux, S. Janz, M. Dad. High-efficiency single etch step apodized surface grating coupler using subwavelength structure. Laser Photon. Rev., 8, L93-L97(2014).

[156] C. Li, K. S. Chee, J. Tao, H. Zhang, M. Yu, G. Q. Lo. Silicon photonics packaging with lateral fiber coupling to apodized grating coupler embedded circuit. Opt. Express, 22, 24235-24240(2014).

[157] R. Marchetti, C. Lacava, A. Khokhar, X. Chen, I. Cristiani, D. J. Richardson, G. T. Reed, P. Petropoulos, P. Minzioni. High-efficiency grating-couplers: demonstration of a new design strategy. Sci. Rep., 7, 16670(2017).

[158] D. Vermeulen, S. Selvaraja, P. Verheyen, G. Lepage, W. Bogaerts, P. Absil, D. Van Thourhout, G. Roelkens. High-efficiency fiber-to-chip grating couplers realized using an advanced CMOS-compatible silicon-on-insulator platform. Opt. Express, 18, 18278-18283(2010).

[159] D. Taillaert, P. Bienstman, R. Baets. Compact efficient broadband grating coupler for silicon-on-insulator waveguides. Opt. Lett., 29, 2749-2751(2004).

[160] Y. Ding, C. Peucheret, H. Ou, K. Yvind. Fully etched apodized grating coupler on the SOI platform with −0.58 dB coupling efficiency. Opt. Lett., 39, 5348-5350(2014).

[161] S. Paesani, Y. Ding, R. Santagati, L. Chakhmakhchyan, C. Vigliar, K. Rottwitt, L. K. Oxenløwe, J. Wang, M. G. Thompson, A. Laing. Generation and sampling of quantum states of light in a silicon chip. Nat. Phys., 15, 925-929(2019).

[162] D. Llewellyn, Y. Ding, I. I. Faruque. Chip-to-chip quantum teleportation and multi-photon entanglement in silicon. Nat. Phys., 16, 148-153(2020).

[163] C. Vigliar, S. Paesani, Y. Ding, J. C. Adcock, J. Wang, S. Morley-Short, D. Bacco, L. K. Oxenløwe, M. G. Thompson, J. G. Rarity, A. Laing. Error-protected qubits in a silicon photonic chip. Nat. Phys., 17, 1137-1143(2021).

[164] Y. Xue, H. Chen, Y. Bao, J. Dong, X. Zhang. Two-dimensional silicon photonic grating coupler with low polarization-dependent loss and high tolerance. Opt. Express, 27, 22268-22274(2019).

[165] M. Pu, L. Liu, H. Ou, K. Yvind, J. M. Hvam. Ultra-low-loss inverted taper coupler for silicon-on-insulator ridge waveguide. Opt. Commun., 283, 3678-3682(2010).

[166] L. Jia, C. Li, T. Y. Liow, G. Q. Lo. Efficient suspended coupler with loss less than −1.4 dB between Si-photonic waveguide and cleaved single mode fiber. J. Lightwave Technol., 36, 239-244(2018).

[167] N. Lindenmann, G. Balthasar, D. Hillerkuss, R. Schmogrow, M. Jordan, J. Leuthold, W. Freude, C. Koos. Photonic wire bonding: a novel concept for chip-scale interconnects. Opt. Express, 20, 17667-17677(2012).

[168] M. R. Billah, M. Blaicher, T. Hoose, P. I. Dietrich, P. Marin-Palomo, N. Lindenmann, A. Nesic, A. Hofmann, U. Troppenz, M. Moehrle, S. Randel, W. Freude, C. Koos. Hybrid integration of silicon photonics circuits and InP lasers by photonic wire bonding. Optica, 5, 876-883(2018).

[169] Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, M. Soljačić. Deep learning with coherent nanophotonic circuits. Nat. Photonics, 11, 441-446(2017).

[170] N. C. Harris, G. R. Steinbrecher, M. Prabhu, Y. Lahini, J. Mower, D. Bunandar, C. Chen, F. N. C. Wong, T. Baehr-Jones, M. Hochberg, S. Lloyd, D. Englund. Quantum transport simulations in a programmable nanophotonic processor. Nat. Photonics, 11, 447-452(2017).

[171] H. W. Rhee, J. Shim, J. Y. Kim, D. J. Bang, H. Yoon, M. Kim, C. C. Kim, J. B. You, H. H. Park. Direct optical wire bonding through open-to-air polymerization for silicon photonic chips. Opt. Lett., 47, 714-717(2022).

[172] D. Istrati, Y. Pilnyak, J. C. Loredo, C. Antón, N. Somaschi, P. Hilaire, H. Ollivier, M. Esmann, L. Cohen, L. Vidro, C. Millet, A. Lemaître, I. Sagnes, A. Harouri, L. Lanco, P. Senellart, H. S. Eisenberg. Sequential generation of linear cluster states from a single photon emitter. Nat. Commun., 11, 5501(2020).

[173] H. Wang, Y. He, Y. H. Li, Z. E. Su, B. Li, H. L. Huang, X. Ding, M. C. Chen, C. Liu, J. Qin, J. P. Li, Y. M. He, C. Schneider, M. Kamp, C. Z. Peng, S. Höfling, C. Y. Lu, J. W. Pan. High-efficiency multiphoton Boson sampling. Nat. Photonics, 11, 361-365(2017).

[174] H. Takesue, Y. Tokura, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, S. Itabashi. Entanglement generation using silicon wire waveguide. Appl. Phys. Lett., 91, 201108(2007).

[175] H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, S. Itabashi. Generation of polarization entangled photon pairs using silicon wire waveguide. Opt. Express, 16, 5721-5727(2008).

[176] N. Matsuda, H. L. Jeannic, H. Fukuda, T. Tsuchizawa, W. J. Munro, K. Shimizu, K. Yamada, Y. Tokura, H. Takesue. A monolithically integrated polarization entangled photon pair source on a silicon chip. Sci. Rep., 2, 817(2012).

[177] J. W. Silverstone, R. Santagati, D. Bonneau, M. J. Strain, M. Sorel, J. L. O’Brien, M. G. Thompson. Qubit entanglement between ring-resonator photon-pair sources on a silicon chip. Nat. Commun., 6, 7948(2015).

[178] J. Wang, S. Paesani, R. Santagati, S. Knauer, A. A. Gentile, N. Wiebe, M. Petruzzella, J. L. O’Brien, J. G. Rarity, A. Laing, M. G. Thompson. Experimental quantum Hamiltonian learning. Nat. Phys., 13, 551-555(2017).

[179] S. Paesani, A. A. Gentile, R. Santagati, J. Wang, N. Wiebe, D. P. Tew, J. L. O’Brien, M. G. Thompson. Experimental Bayesian quantum phase estimation on a silicon photonic chip. Phys. Rev. Lett., 118, 100503(2017).

[180] X. Qiang, X. Zhou, J. Wang, C. M. Wilkes, T. Loke, S. O’Gara, L. Kling, G. D. Marshall, R. Santagati, T. C. Ralph, J. B. Wang, J. L. O’Brien, M. G. Thompson, J. C. F. Matthews. Large-scale silicon quantum photonics implementing arbitrary two-qubit processing. Nat. Photonics, 12, 534-539(2018).

[181] X. Qiang, Y. Wang, S. Xue, R. Ge, L. Chen, Y. Liu, A. Huang, X. Fu, P. Xu, T. Yi, F. Xu, M. Deng, J. B. Wang, J. D. A. Meinecke, J. C. F. Matthews, X. Cai, X. Yang, J. Wu. Implementing graph-theoretic quantum algorithms on a silicon photonic quantum walk processor. Sci. Adv., 7, eabb8375(2021).

[182] K. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, S. Itabashi. Indistinguishable photon pair generation using two independent silicon wire waveguides. New J. Phys., 13, 065005(2011).

[183] I. I. Faruque, G. F. Sinclair, D. Bonneau, J. G. Rarity, M. G. Thompson. On-chip quantum interference with heralded photons from two independent micro-ring resonator sources in silicon photonics. Opt. Express, 26, 20379-20395(2018).

[184] M. Zhang, L. T. Feng, Z. Y. Zhou, Y. Chen, H. Wu, M. Li, S. M. Gao, G. P. Guo, G. C. Guo, D. X. Dai, X. F. Ren. Generation of multiphoton quantum states on silicon. Light Sci. Appl., 8, 41(2019).

[185] L. T. Feng, M. Zhang, Z. Y. Zhou, Y. Chen, M. Li, D. X. Dai, H. L. Ren, G. P. Guo, G. C. Guo, M. Tame, X. F. Ren. Generation of a frequency-degenerate four-photon entangled state using a silicon nanowire. NPJ Quantum Inf., 5, 90(2019).

[186] J. C. Adcock, C. Vigliar, R. Santagati, J. W. Silverstone, M. G. Thompson. Programmable four-photon graph states on a silicon chip. Nat. Commun., 10, 3528(2019).

[187] Y. Ding, D. Bacco, K. Dalgaard, X. Cai, X. Zhou, K. Rottwitt, L. K. Oxenløwe. High-dimensional quantum key distribution based on multicore fiber using silicon photonic integrated circuits. NPJ Quantum Inf., 3, 25(2017).

[188] J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acín, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, M. G. Thompson. Multidimensional quantum entanglement with large-scale integrated optics. Science, 360, 285-291(2018).

[189] Y. Chi, J. Huang, Z. Zhang. A programmable qudit-based quantum processor. Nat. Commun., 13, 1166(2022).

[190] L. T. Feng, M. Zhang, D. Liu, Y. J. Cheng, G. P. Guo, D. X. Dai, G. C. Guo, M. Krenn, X. F. Ren. Observation of nonlocal quantum interference between the origins of a four-photon state in a silicon chip(2021).

[191] X. M. Hu, Y. Guo, B. H. Liu, Y. F. Huang, C. F. Li, G. C. Guo. Beating the channel capacity limit for superdense coding with entangled ququarts. Sci. Adv., 4, eaat9304(2018).

[192] B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, A. G. White. Simplifying quantum logic using higher-dimensional Hilbert spaces. Nat. Phys., 5, 134-140(2009).

[193] L. Lu, L. Xia, Z. Chen, L. Chen, T. Yu, T. Tao, W. Ma, Y. Pan, X. Cai, Y. Lu, S. Zhu, X. S. Ma. Three-dimensional entanglement on a silicon chip. NPJ Quantum Inf., 6, 30(2020).

[194] C. M. Wilkes, X. Qiang, J. Wang, R. Santagati, S. Paesani, X. Zhou, D. A. B. Miller, G. D. Marshall, M. G. Thompson, J. L. O’Brien. 60 dB high-extinction auto-configured Mach–Zehnder interferometer. Opt. Lett., 41, 5318-5321(2016).

[195] X. C. Yao, T. X. Wang, H. Z. Chen, W. B. Gao, A. G. Fowler, R. Raussendorf, Z. B. Chen, N. L. Liu, C. Y. Lu, Y. J. Deng, Y. A. Chen, J. W. Pan. Experimental demonstration of topological error correction. Nature, 482, 489-494(2012).

[196] M. V. Larsen, X. Guo, C. R. Breum, J. S. Neergaard-Nielsen, U. L. Andersen. Deterministic generation of a two-dimensional cluster state. Science, 366, 369-392(2019).

[197] W. Asavanant, Y. Shiozawa, S. Yokoyama, B. Charoensombutamon, H. Emura, R. N. Alexander, S. Takeda, J. Yoshikawa, N. C. Menicucci, H. Yonezawa, A. Furusawa. Generation of time-domain-multiplexed two-dimensional cluster state. Science, 366, 373-376(2019).

[198] M. Hein, W. Dür, J. Eisert, R. Raussendorf, M. Van den Nest, H. J. Briegel. Entanglement in graph states and its applications(2006).

[199] N. Shettell, D. Markham. Graph states as a resource for quantum metrology. Phys. Rev. Lett., 124, 110502(2020).

[200] S. Bartolucci, P. Birchall, H. Bombin, H. Cable, C. Dawson, M. Gimeno-Segovia, E. Johnston, K. Kieling, N. Nickerson, M. Pant, F. Pastawski, T. Rudolph, C. Sparrow. Fusion-based quantum computation(2021).

[201] H. Bombin, I. H. Kim, D. Litinski, N. Nickerson, M. Pant, F. Pastawski, S. Roberts, T. Rudolph. Interleaving: modular architectures for fault-tolerant photonic quantum computing(2021).

[202] J. W. Pan, S. Gasparoni, R. Ursin, G. Weihs, A. Zeilinger. Experimental entanglement purification of arbitrary unknown states. Nature, 423, 417-422(2003).

[203] S. Mittal, E. A. Goldschmidt, M. Hafezi. A topological source of quantum light. Nature, 561, 502-506(2018).

[204] M. Wang, C. Doyle, B. Bell, M. J. Collins, E. Magi, B. J. Eggleton, M. Segev, A. Blanco-Redondo. Topologically protected entangled photonic states. Nanophotonics, 8, 1327-1335(2019).

[205] T. Dai, Y. Ao, J. Bao, J. Mao, Y. Chi, Z. Fu, Y. You, X. Chen, C. Zhai, B. Tang, Y. Yang, Z. Li, L. Yuan, F. Gao, X. Lin, M. G. Thompson, J. L. O’Brien, Y. Li, X. Hu, Q. Gong, J. Wang. Topologically protected quantum entanglement emitters. Nat. Photonics, 16, 248-257(2022).

[206] Y. Chen, X. T. He, Y. J. Cheng, H. Y. Qiu, L. T. Feng, M. Zhang, D. X. Dai, G. C. Guo, J. W. Dong, X. F. Ren. Topologically protected valley-dependent quantum photonic circuits. Phys. Rev. Lett., 126, 230503(2021).

[207] S. Wang, Z. Q. Yin, D. Y. He, W. Chen, R. Q. Wang, P. Ye, Y. Zhou, G. J. Fan-Yuan, F. X. Wang, W. Chen, Y. G. Zhu, P. V. Morozov, A. V. Divochiy, Z. Zhou, G. C. Guo, Z. F. Han. Twin-field quantum key distribution over 830-km fibre. Nat. Photonics, 16, 154-161(2022).

[208] Q. Wang, Y. Zheng, C. Zhai, X. Li, Q. Gong, J. Wang. Chip-based quantum communications. J. Semicond., 42, 091901(2021).

[209] P. Sibson, J. E. Kennard, S. Stanisic, C. Erven, J. L. O’Brien, M. G. Thompson. Integrated silicon photonics for high-speed quantum key distribution. Optica, 4, 172-177(2017).

[210] D. Bacco, Y. Ding, K. Dalgaard, K. Rottwitt, L. K. Oxenløwe. Space division multiplexing chip-to-chip quantum key distribution. Sci. Rep., 7, 12459(2017).

[211] D. Bunandar, A. Lentine, C. Lee, H. Cai, C. M. Long, N. Boynton, N. Martinez, C. DeRose, C. Chen, M. Grein, D. Trotter, A. Starbuck, A. Pomerene, S. Hamilton, F. N. C. Wong, R. Camacho, P. Davids, J. Urayama, D. Englund. Metropolitan quantum key distribution with silicon photonics. Phys. Rev. X, 8, 021009(2018).

[212] M. Avesani, L. Calderaro, M. Schiavon, A. Stanco, C. Agnesi, A. Santamato, M. Zahidy, A. Scriminich, G. Foletto, G. Contestabile, M. Chiesa, D. Rotta, M. Artiglia, A. Montanaro, M. Romagnoli, V. Sorianello, F. Vedovato, G. Vallone, P. Villoresi. Full daylight quantum-key-distribution at 1550 nm enabled by integrated silicon photonics. NPJ Quantum Inf., 7, 93(2019).

[213] W. Geng, C. Zhang, Y. Zheng, J. He, C. Zhou, Y. Kong. Stable quantum key distribution using a silicon photonic transceiver. Opt. Express, 27, 29045-29054(2019).