{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,26]],"date-time":"2025-10-26T15:12:00Z","timestamp":1761491520833,"version":"3.37.3"},"reference-count":96,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2023,1,18]],"date-time":"2023-01-18T00:00:00Z","timestamp":1674000000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,1,18]],"date-time":"2023-01-18T00:00:00Z","timestamp":1674000000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"crossref","award":["61901420"],"award-info":[{"award-number":["61901420"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Shanxi Province Foundation for Youths","award":["201901D211235"],"award-info":[{"award-number":["201901D211235"]}]},{"name":"Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi","award":["2019L0507"],"award-info":[{"award-number":["2019L0507"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"DOI":"10.1007\/s11128-022-03801-5","type":"journal-article","created":{"date-parts":[[2023,1,18]],"date-time":"2023-01-18T14:03:07Z","timestamp":1674050587000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Implementations of heralded quantum Toffoli and Fredkin gates assisted by waveguide-mediated photon scattering"],"prefix":"10.1007","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1213-3041","authenticated-orcid":false,"given":"Fang-Fang","family":"Du","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gang","family":"Fan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yi-Ming","family":"Wu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,1,18]]},"reference":[{"key":"3801_CR1","doi-asserted-by":"crossref","first-page":"558","DOI":"10.1119\/1.1463744","volume":"70","author":"MA Nielsen","year":"2002","unstructured":"Nielsen, M.A., Chuang, I.L.: Quantum computation and quantum information. Am. J. Phys. 70, 558 (2002)","journal-title":"Am. J. Phys."},{"key":"3801_CR2","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1007\/s11128-021-03191-0","volume":"20","author":"SM Moein","year":"2021","unstructured":"Moein, S.M., Mariam, Z.: A general protocol for distributed quantum gates. Quantum Inf. Process. 20, 265 (2021)","journal-title":"Quantum Inf. Process."},{"key":"3801_CR3","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1007\/s11128-021-03031-1","volume":"20","author":"ZW Song","year":"2021","unstructured":"Song, Z.W., Chen, L., Hu, M.Y.: Constructing three-qubit unitary gates in terms of Schmidt rank and CNOT gates. Quantum Inf. Process. 20, 96 (2021)","journal-title":"Quantum Inf. Process."},{"key":"3801_CR4","doi-asserted-by":"crossref","first-page":"370","DOI":"10.1007\/s11128-021-03292-w","volume":"20","author":"D Kheirandish","year":"2021","unstructured":"Kheirandish, D., Haghparast, M., Reshadi, M., Hosseinzadeh, M.: Efficient techniques for fault detection and location of multiple controlled Toffoli-based reversible circuit. Quantum Inf. Process. 20, 370 (2021)","journal-title":"Quantum Inf. Process."},{"key":"3801_CR5","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1007\/s43673-022-00043-6","volume":"32","author":"GF Xu","year":"2022","unstructured":"Xu, G.F., Tong, D.M.: Realizing multi-qubit controlled nonadiabatic holonomic gates with connecting systems. AAPPS Bull. 32, 13 (2022)","journal-title":"AAPPS Bull."},{"key":"3801_CR6","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1007\/s11128-022-03415-x","volume":"21","author":"RC Souza","year":"2022","unstructured":"Souza, R.C., Balthazar, W.F., Huguenin, J.A.O.: Universal quantum gates for path photonic qubit. Quantum Inf. Process. 21, 68 (2022)","journal-title":"Quantum Inf. Process."},{"key":"3801_CR7","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1007\/s43673-021-00017-0","volume":"31","author":"LC Kwek","year":"2021","unstructured":"Kwek, L.C., Cao, L., Luo, W., Wang, Y.X., Sun, S.H., Wang, X.B., Liu, A.Q.: Chip-based quantum key distribution. AAPPS Bull. 31, 15 (2021)","journal-title":"AAPPS Bull."},{"key":"3801_CR8","volume":"3","author":"GZ Tang","year":"2021","unstructured":"Tang, G.Z., Li, C.Y., Wang, M.: Polarization discriminated time-bin phase-encoding measurement-device-independent quantum key distribution. Quantum Eng. 3, e79 (2021)","journal-title":"Quantum Eng."},{"key":"3801_CR9","doi-asserted-by":"publisher","DOI":"10.1088\/1674-1056\/aca395","author":"FF Du","year":"2022","unstructured":"Du, F.F., Fan, G., Wu, Y.M.: Faithful and efficient hyperentanglement purification for spatial-polarization-time-bin photon system. Chin. Phys. B (2022). https:\/\/doi.org\/10.1088\/1674-1056\/aca395","journal-title":"Chin. Phys. B"},{"key":"3801_CR10","first-page":"2200092","volume":"5","author":"YT Liu","year":"2022","unstructured":"Liu, Y.T., Wu, Y.M., Du, F.F.: Self-error-rejecting multipartite entanglement purification for electron systems assisted by quantum-dot spins in optical microcavities. Chin. Phys. B 5, 2200092 (2022)","journal-title":"Chin. Phys. B"},{"key":"3801_CR11","doi-asserted-by":"crossref","first-page":"27046","DOI":"10.1364\/OE.27.027046","volume":"27","author":"FF Du","year":"2019","unstructured":"Du, F.F., Liu, Y.T., Shi, Z.R., Liang, Y.X., Tang, J., Liu, J.: Efficient hyperentanglement purification for three-photon systems with the fidelity-robust quantum gates and hyperentanglement link. Opt. Express 27, 27046 (2019)","journal-title":"Opt. Express"},{"key":"3801_CR12","doi-asserted-by":"crossref","first-page":"17493","DOI":"10.1364\/OE.27.017493","volume":"27","author":"FF Du","year":"2019","unstructured":"Du, F.F., Shi, Z.R.: Robust hybrid hyper-controlled-not gates assisted by an input-output process of low-Q cavities. Opt. Express 27, 17493 (2019)","journal-title":"Opt. Express"},{"key":"3801_CR13","doi-asserted-by":"crossref","first-page":"31501","DOI":"10.1007\/s11467-021-1120-7","volume":"17","author":"P Wang","year":"2022","unstructured":"Wang, P., Yu, C.Q., Wang, Z.X., Yuan, R.Y., Du, F.F., Ren, B.C.: Hyperentanglement-assisted hyperdistillation for hyper-encoding photon system. Front. Phys. 17, 31501 (2022)","journal-title":"Front. Phys."},{"key":"3801_CR14","volume-title":"Quantum Computation and Quantum Information","author":"MA Nielsen","year":"2000","unstructured":"Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)"},{"key":"3801_CR15","volume":"63","author":"HS Li","year":"2020","unstructured":"Li, H.S., Fan, P., Xia, H.Y., Peng, H.L., Long, G.L.: Efficient quantum arithmetic operation circuits for quantum image processing. Sci. China Phys. Mech. 63, 280311 (2020)","journal-title":"Sci. China Phys. Mech."},{"key":"3801_CR16","first-page":"1486935","volume":"2020","author":"SJ Wei","year":"2020","unstructured":"Wei, S.J., Li, H., Long, G.L.: A full quantum eigensolver for quantum chemistry simulations. Research 2020, 1486935 (2020)","journal-title":"Research"},{"key":"3801_CR17","volume":"3","author":"H Tang","year":"2021","unstructured":"Tang, H., Pal, A., Wang, T.Y., Qiao, L.F., Gao, J., Jin, X.M.: Quantum computation for pricing the collateralized debt obligationslearning. Quantum Eng. 3, e84 (2021)","journal-title":"Quantum Eng."},{"key":"3801_CR18","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1007\/s43673-022-00058-z","volume":"32","author":"JWZ Lau","year":"2022","unstructured":"Lau, J.W.Z., Lim, K.H., Shrotriya, H., Kwek, L.C.: NISQ computing: where are we and where do we go? AAPPS Bull. 32, 27 (2022)","journal-title":"AAPPS Bull."},{"key":"3801_CR19","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1007\/s11128-022-03693-5","volume":"21","author":"Y Zhang","year":"2022","unstructured":"Zhang, Y., Wu, K.I.: Quantum computation using action variables. Quantum Inf. Process. 21, 355 (2022)","journal-title":"Quantum Inf. Process."},{"key":"3801_CR20","first-page":"125","volume":"8","author":"Y Zhang","year":"2022","unstructured":"Zhang, Y., Wu, Q.L., Wu, H., Yang, X., Su, S.L., Shan, C.X., M\u00f8lmer, K.: Microwave mode cooling and cavity quantum electrodynamics effects at room temperature with optically cooled nitrogen-vacancy center spins. Sci. Bull. 8, 125 (2022)","journal-title":"Sci. Bull."},{"key":"3801_CR21","doi-asserted-by":"crossref","first-page":"9638108","DOI":"10.1155\/2022\/9638108","volume":"2022","author":"L Ding","year":"2022","unstructured":"Ding, L., Wang, H.W., Wang, Y.N., Wang, S.M.: Based on quantum topological stabilizer color code morphism neural network decoder. Quantum Eng. 2022, 9638108 (2022)","journal-title":"Quantum Eng."},{"key":"3801_CR22","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1038\/nature18592","volume":"536","author":"B Hacker","year":"2016","unstructured":"Hacker, B., Welte, S., Rempe, G., Ritter, S.: A photon-photon quantum gate based on a single atom in an optical resonator. Nature 536, 193 (2016)","journal-title":"Nature"},{"key":"3801_CR23","doi-asserted-by":"crossref","first-page":"534","DOI":"10.1038\/s41566-018-0236-y","volume":"12","author":"X Qiang","year":"2018","unstructured":"Qiang, X., Zhou, X., Wang, J., Wilkes, C.M., Loke, T., O\u2019Gara, S., Kling, L.G., Marshall, D., Santagati, R., Ralph, T.C., Wang, J.B., O\u2019Brien, J.L., Thompson, M.G., Matthews, J.C.F.: Large-scale silicon quantum photonics implementing arbitrary two-qubit processing. Nat. Photon. 12, 534 (2018)","journal-title":"Nat. Photon."},{"key":"3801_CR24","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1038\/s41567-018-0313-7","volume":"15","author":"D Tiarks","year":"2019","unstructured":"Tiarks, D., Schmidt-Eberle, S., Stolz, T., Rempe, G., D\u00fcrr, S.: A photon-photon quantum gate based on Rydberg interactions. Nat. Phys. 15, 124 (2019)","journal-title":"Nat. Phys."},{"key":"3801_CR25","doi-asserted-by":"crossref","first-page":"256","DOI":"10.1007\/s11128-019-2369-4","volume":"18","author":"JH Lopes","year":"2019","unstructured":"Lopes, J.H., Soares, W.C., de Lima Bernardo, B., Caetano, D.P., Canabarro, A.: Linear optical CNOT gate with orbital angular momentum and polarization. Quantum Inf. Process. 18, 256 (2019)","journal-title":"Quantum Inf. Process."},{"key":"3801_CR26","doi-asserted-by":"crossref","first-page":"3457","DOI":"10.1103\/PhysRevA.52.3457","volume":"52","author":"A Barenco","year":"1995","unstructured":"Barenco, A., Bennett, C.H., Cleve, R., DiVincenzo, D.P., Margolus, N., Shor, P., Sleator, T., Smolin, J.A., Weinfurter, H.: Elementary gates for quantum computation. Phys. Rev. A 52, 3457 (1995)","journal-title":"Phys. Rev. A"},{"key":"3801_CR27","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevA.69.062321","volume":"69","author":"VV Shende","year":"2004","unstructured":"Shende, V.V., Markov, I.L., Bullock, S.S.: Minimal universal two-qubit controlled-NOT-based circuits. Phys. Rev. A 69, 062321 (2004)","journal-title":"Phys. Rev. A"},{"key":"3801_CR28","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1103\/PhysRevLett.79.325","volume":"79","author":"LK Grover","year":"1997","unstructured":"Grover, L.K.: Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79, 325 (1997)","journal-title":"Phys. Rev. Lett."},{"key":"3801_CR29","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1137\/S0036144598347011","volume":"41","author":"PW Shor","year":"1999","unstructured":"Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev. 41, 303 (1999)","journal-title":"SIAM Rev."},{"key":"3801_CR30","doi-asserted-by":"crossref","first-page":"2041","DOI":"10.1038\/s41467-017-01904-7","volume":"8","author":"C Figgatt","year":"2017","unstructured":"Figgatt, C., Maslov, D., Landsman, K., Linke, N.M., Debnath, S., Monroe, C.: Complete 3-qubit Grover search on a programmable quantum computer. Nat. Commun. 8, 2041 (2017)","journal-title":"Nat. Commun."},{"key":"3801_CR31","first-page":"2056","volume":"6","author":"Y Nam","year":"2020","unstructured":"Nam, Y., Su, Y., Maslov, D.: Approximate quantum Fourier transform with o(n log(n)) T gates. npj Quantum Inf. 6, 2056 (2020)","journal-title":"npj Quantum Inf."},{"key":"3801_CR32","doi-asserted-by":"crossref","first-page":"2152","DOI":"10.1103\/PhysRevLett.81.2152","volume":"81","author":"DG Cory","year":"1998","unstructured":"Cory, D.G., Price, M., Maas, W., Knill, E., Laflamme, R., Zurek, W.H., Havel, T.F., Somaroo, S.S.: Experimental quantum error correction. Phys. Rev. Lett. 81, 2152 (1998)","journal-title":"Phys. Rev. Lett."},{"key":"3801_CR33","first-page":"1476","volume":"482","author":"MD Reed","year":"2012","unstructured":"Reed, M.D., DiCarlo, L., Nigg, S.E., Sun, L., Frunzio, L., Girvin, S.M., Schoelkopf, R.J.: Realization of three-qubit quantum error correction with superconducting circuits. Nature 482, 1476 (2012)","journal-title":"Nature"},{"key":"3801_CR34","doi-asserted-by":"crossref","first-page":"1025","DOI":"10.1016\/j.scib.2017.06.007","volume":"62","author":"YB Sheng","year":"2017","unstructured":"Sheng, Y.B., Zhou, L.: Distributed secure quantum machine learning. Sci. Bull. 62, 1025 (2017)","journal-title":"Sci. Bull."},{"key":"3801_CR35","first-page":"2","volume":"32","author":"SJ Wei","year":"2022","unstructured":"Wei, S.J., Chen, Y.H., Zhou, Z.R., Long, G.L.: A quantum convolutional neural network on NISQ devices. Quantum Eng. 32, 2 (2022)","journal-title":"Quantum Eng."},{"key":"3801_CR36","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevLett.111.090505","volume":"111","author":"A Paetznick","year":"2013","unstructured":"Paetznick, A., Reichardt, B.W.: Universal fault-tolerant quantum computation with only transversal gates and error correction. Phys. Rev. Let. 111, 090505 (2013)","journal-title":"Phys. Rev. Let."},{"key":"3801_CR37","volume":"9","author":"J Guillaud","year":"2019","unstructured":"Guillaud, J., Mirrahimi, M.: Repetition cat qubits for fault-tolerant quantum computation. Phys. Rev. X 9, 041053 (2019)","journal-title":"Phys. Rev. X"},{"key":"3801_CR38","volume":"88","author":"HR Wei","year":"2013","unstructured":"Wei, H.R., Deng, F.G.: Compact quantum gates on electron-spin qubits assisted by diamond nitrogenvacancy centers inside cavities. Phys. Rev. A 88, 042323 (2013)","journal-title":"Phys. Rev. A"},{"key":"3801_CR39","doi-asserted-by":"crossref","first-page":"7551","DOI":"10.1038\/srep07551","volume":"4","author":"HR Wei","year":"2014","unstructured":"Wei, H.R., Deng, F.G.: Scalable quantum computing based on stationary spin qubits in coupled quantum dots inside double-sided optical microcavities. Sci. Rep. 4, 7551 (2014)","journal-title":"Sci. Rep."},{"key":"3801_CR40","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1364\/OE.22.000593","volume":"22","author":"HR Wei","year":"2014","unstructured":"Wei, H.R., Deng, F.G.: Universal quantum gates on electron-spin qubits with quantum dots inside single-side optical microcavities. Opt. Express 22, 593 (2014)","journal-title":"Opt. Express"},{"key":"3801_CR41","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1007\/s11128-018-1908-8","volume":"17","author":"XY Cheng","year":"2018","unstructured":"Cheng, X.Y., Guan, Z.J., Ding, W.P.: Mapping from multiple-control Toffoli circuits to linear nearest neighbor quantum circuits. Quantum Inf. Process. 17, 169 (2018)","journal-title":"Quantum Inf. Process."},{"key":"3801_CR42","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevA.101.022308","volume":"101","author":"SE Rasmussen","year":"2020","unstructured":"Rasmussen, S.E., Groenland, K., Gerritsma, R., Schoutens, K., Zinner, N.T.: Single-step implementation of high-fidelity $$n$$-bit Toffoli gates. Phys. Rev. A 101, 022308 (2020)","journal-title":"Phys. Rev. A"},{"key":"3801_CR43","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevA.102.012601","volume":"102","author":"S Daraeizadeh","year":"2020","unstructured":"Daraeizadeh, S., Premaratne, S.P., Khammassi, N., Song, X., Perkowski, M., Matsuura, A.Y.: Machine-learning-based three-qubit gate design for the Toffoli gate and parity check in transmon systems. Phys. Rev. A 102, 012601 (2020)","journal-title":"Phys. Rev. A"},{"key":"3801_CR44","volume":"22","author":"WQ Liu","year":"2020","unstructured":"Liu, W.Q., Wei, H.R.: Optimal synthesis of the Fredkin gate in a multilevel system. New J. Phys. 22, 063026 (2020)","journal-title":"New J. Phys."},{"key":"3801_CR45","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1007\/s11128-021-03279-7","volume":"20","author":"J Heo","year":"2021","unstructured":"Heo, J., Choi, S.G.: Toffoli gate with photonic qubits based on weak cross-Kerr nonlinearities. Quantum Inf. Process. 20, 345 (2021)","journal-title":"Quantum Inf. Process."},{"key":"3801_CR46","doi-asserted-by":"crossref","first-page":"1006255","DOI":"10.3389\/fphy.2022.1006255","volume":"10","author":"YH Han","year":"2022","unstructured":"Han, Y.H., Cao, C., Fan, L., Zhang, R.: Scheme for implementing nonlocal high-fidelity quantum controlled-not gates on quantum-dot-confined electron spins using optical microcavities and photonic hyperentanglement. Front. Phys. 10, 1006255 (2022)","journal-title":"Front. Phys."},{"key":"3801_CR47","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1007\/s11128-020-02682-w","volume":"19","author":"M Hua","year":"2020","unstructured":"Hua, M., Tao, M.J., Zhou, Z.R., Wei, H.R.: Controlled phase gate and Grover\u2019s search algorithm on two distant NV-centers assisted by an NAMR. Quantum Inf. Process. 19, 187 (2020)","journal-title":"Quantum Inf. Process."},{"key":"3801_CR48","volume":"14","author":"WQ Liu","year":"2020","unstructured":"Liu, W.Q., Wei, H.R., Kwek, L.C.: Low-cost Fredkin gate with auxiliary space. Phys. Rev. Appl. 14, 054057 (2020)","journal-title":"Phys. Rev. Appl."},{"key":"3801_CR49","doi-asserted-by":"crossref","first-page":"2100136","DOI":"10.1002\/qute.202100136","volume":"5","author":"WQ Liu","year":"2022","unstructured":"Liu, W.Q., Wei, H.R., Kwek, L.C.: Universal quantum multi-qubit entangling gates with auxiliary spaces. Adv. Quantum Technol. 5, 2100136 (2022)","journal-title":"Adv. Quantum Technol."},{"key":"3801_CR50","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1038\/s41534-018-0102-2","volume":"4","author":"BX Wang","year":"2018","unstructured":"Wang, B.X., Tao, M.J., Ai, Q., Xin, T., Lambert, N., Ruan, D., Cheng, Y.C., Nori, F., Deng, F.G., Long, G.L.: Efficient quantum simulation of photosynthetic light harvesting. npj Quantum Inf. 4, 52 (2018)","journal-title":"npj Quantum Inf."},{"key":"3801_CR51","volume":"104","author":"GZ Song","year":"2021","unstructured":"Song, G.Z., Guo, J.L., Liu, Q., Wei, H.R., Long, G.L.: Heralded quantum gates for hybrid systems via waveguide-mediated photon scattering. Phys. Rev. A 104, 012608 (2021)","journal-title":"Phys. Rev. A"},{"key":"3801_CR52","volume":"90","author":"L Zhou","year":"2014","unstructured":"Zhou, L., Sheng, Y.B.: Detection of nonlocal atomic entanglement assisted by single photons. Phys. Rev. A 90, 024301 (2014)","journal-title":"Phys. Rev. A"},{"key":"3801_CR53","volume":"92","author":"L Zhou","year":"2015","unstructured":"Zhou, L., Sheng, Y.B.: Complete logic Bell-state analysis assisted with photonic Faraday rotation. Phys. Rev. A 92, 042314 (2015)","journal-title":"Phys. Rev. A"},{"key":"3801_CR54","volume":"65","author":"TT Chen","year":"2022","unstructured":"Chen, T.T., Shi, Y.H., Xiang, Z.C., Wang, Z.A., Li, T.M., Sun, H.Y., He, T.S., Song, X.H., Zhao, S., Zheng, D.N., Xu, K., Fan, H.: ScQ cloud quantum computation for generating Greenberger\u2013Horne\u2013Zeilinger states of up to 10 qubits. Sci. China Phys. Mech. 65, 110362 (2022)","journal-title":"Sci. China Phys. Mech."},{"key":"3801_CR55","volume":"90","author":"TJ Wang","year":"2014","unstructured":"Wang, T.J., Wang, C.: Universal hybrid three-qubit quantum gates assisted by a nitrogen-vacancy center coupled with a whispering-gallery-mode microresonator. Phys. Rev. A 90, 052310 (2014)","journal-title":"Phys. Rev. A"},{"key":"3801_CR56","volume":"91","author":"BC Ren","year":"2015","unstructured":"Ren, B.C., Wang, G.Y., Deng, F.G.: Universal hyperparallel hybrid photonic quantum gates with dipole-induced transparency in the weak-coupling regime. Phys. Rev. A 91, 032328 (2015)","journal-title":"Phys. Rev. A"},{"key":"3801_CR57","volume":"94","author":"T Li","year":"2016","unstructured":"Li, T., Long, G.L.: Hyperparallel optical quantum computation assisted by atomic ensembles embedded in double-sided optical cavities. Phys. Rev. A 94, 022343 (2016)","journal-title":"Phys. Rev. A"},{"key":"3801_CR58","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1007\/s11128-022-03577-8","volume":"21","author":"M Bataille","year":"2022","unstructured":"Bataille, M.: Quantum circuits of CNOT gates: optimization and entanglement. Quantum Inf. Process. 21, 269 (2022)","journal-title":"Quantum Inf. Process."},{"key":"3801_CR59","volume":"11","author":"TJ Wang","year":"2014","unstructured":"Wang, T.J., Zhang, Y., Wang, C.: Universal hybrid hyper-controlled quantum gates assisted by quantum dots in optical double-sided microcavities. Laser Phys. Lett. 11, 025203 (2014)","journal-title":"Laser Phys. Lett."},{"key":"3801_CR60","doi-asserted-by":"crossref","first-page":"10863","DOI":"10.1364\/OE.25.010863","volume":"25","author":"BC Ren","year":"2017","unstructured":"Ren, B.C., Deng, F.G.: Robust hyperparallel photonic quantum entangling gate with cavity QED. Opt. Express 25, 10863 (2017)","journal-title":"Opt. Express"},{"key":"3801_CR61","volume":"13","author":"HR Wei","year":"2020","unstructured":"Wei, H.R., Zheng, Y.B., Hua, M., Xu, G.F.: Robust-fidelity hyperparallel controlled-phase-flip gate through microcavities. Appl. Phys. Express 13, 082007 (2020)","journal-title":"Appl. Phys. Express"},{"key":"3801_CR62","doi-asserted-by":"crossref","first-page":"1900578","DOI":"10.1002\/andp.201900578","volume":"532","author":"HR Wei","year":"2020","unstructured":"Wei, H.R., Liu, W.Q., Chen, N.Y.: Implementing a two-photon three-degrees-of-freedom hyper-parallel controlled phase flip gate through cavity-assisted interactions. Ann. Phys. 532, 1900578 (2020)","journal-title":"Ann. Phys."},{"key":"3801_CR63","doi-asserted-by":"crossref","first-page":"18619","DOI":"10.1364\/OE.24.018619","volume":"24","author":"HR Wei","year":"2016","unstructured":"Wei, H.R., Deng, F.G., Long, G.L.: Hyper-parallel Toffoli gate on three-photon system with two degrees of freedom assisted by single-sided optical microcavities. Opt. Express 24, 18619 (2016)","journal-title":"Opt. Express"},{"key":"3801_CR64","doi-asserted-by":"crossref","first-page":"1885","DOI":"10.1038\/s41598-018-20148-z","volume":"8","author":"JZ Liu","year":"2018","unstructured":"Liu, J.Z., Wei, H.R., Chen, N.Y.: A heralded and error-rejecting three-photon hyper-parallel quantum gate through cavityassisted interactions. Sci. Rep. 8, 1885 (2018)","journal-title":"Sci. Rep."},{"key":"3801_CR65","doi-asserted-by":"crossref","first-page":"51502","DOI":"10.1007\/s11467-022-1172-3","volume":"17","author":"YM Wu","year":"2022","unstructured":"Wu, Y.M., Fan, G., Du, F.F.: Error-detected three-photon hyperparallel Toffoli gate with state-selective reflection. Front. Phys. 17, 51502 (2022)","journal-title":"Front. Phys."},{"key":"3801_CR66","doi-asserted-by":"publisher","DOI":"10.1002\/andp.202200507","author":"FF Du","year":"2022","unstructured":"Du, F.F., Wu, Y.M., Fan, G., Ma, Z.M.: High-fidelity and low-cost hyperparallel quantum gates for photon systems via $$\\rm \\Lambda $$-type systems. Ann. Phys. (2022). https:\/\/doi.org\/10.1002\/andp.202200507","journal-title":"Ann. Phys."},{"key":"3801_CR67","doi-asserted-by":"crossref","first-page":"1800043","DOI":"10.1002\/andp.201800043","volume":"530","author":"BC Ren","year":"2018","unstructured":"Ren, B.C., Wang, A.H., Ahmed, A., Tasawar, H., Deng, F.G.: Three-photon polarization-spatial hyperparallel quantum Fredkin gate assisted by diamond nitrogen vacancy center in optical cavity. Ann. Phys. 530, 1800043 (2018)","journal-title":"Ann. Phys."},{"key":"3801_CR68","doi-asserted-by":"crossref","first-page":"35529","DOI":"10.1038\/srep35529","volume":"6","author":"HR Wei","year":"2016","unstructured":"Wei, H.R., Zhu, P.J.: Implementations of two-photon four-qubit Toffoli and Fredkin gates assisted by nitrogen-vacancy centers. Sci. Rep. 6, 35529 (2016)","journal-title":"Sci. Rep."},{"key":"3801_CR69","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1038\/35051009","volume":"409","author":"E Knill","year":"2001","unstructured":"Knill, E., Laflamme, R., Milburn, G.J.: A scheme for efficient quantum computation with linear optics. Nature 409, 46 (2001)","journal-title":"Nature"},{"key":"3801_CR70","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevLett.93.250502","volume":"93","author":"K Nemoto","year":"2004","unstructured":"Nemoto, K., Munro, W.J.: Nearly deterministic linear optical controlled-NOT gate. Phys. Rev. Lett. 93, 250502 (2004)","journal-title":"Phys. Rev. Lett."},{"key":"3801_CR71","volume":"92","author":"LM Duan","year":"2004","unstructured":"Duan, L.M., Kimble, H.J.: Scalable photonic quantum computation through cavity-assisted interactions. Phys. Rev. Lett. 92, 127902 (2004)","journal-title":"Phys. Rev. Lett."},{"key":"3801_CR72","volume":"80","author":"CY Hu","year":"2009","unstructured":"Hu, C.Y., Munro, W.J., O\u2019Brien, J.L., Rarity, J.G.: Proposed entanglement beam splitter using a quantum-dot spin in a double-sided optical microcavity. Phys. Rev. B 80, 205326 (2009)","journal-title":"Phys. Rev. B"},{"key":"3801_CR73","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1038\/nphoton.2015.57","volume":"9","author":"JS Douglas","year":"2015","unstructured":"Douglas, J.S., Habibian, H., Hung, C.L., Gorshkov, A.V., Kimble, H.J., Chang, D.E.: Quantum many-body models with cold atoms coupled to photonic crystals. Nat. Photon. 9, 326 (2015)","journal-title":"Nat. Photon."},{"key":"3801_CR74","volume":"98","author":"GZ Song","year":"2018","unstructured":"Song, G.Z., Munro, E., Nie, W., Kwek, L.C., Deng, F.G., Long, G.L.: Photon transport mediated by an atomic chain trapped along a photonic crystal waveguide. Phys. Rev. A 98, 023814 (2018)","journal-title":"Phys. Rev. A"},{"key":"3801_CR75","doi-asserted-by":"crossref","first-page":"847","DOI":"10.1126\/science.aah6875","volume":"354","author":"A Sipahigil","year":"2016","unstructured":"Sipahigil, A., Evans, R.E., Sukachev, D.D., Burek, M.J., Borregaard, J., Bhaskar, M.K., Nguyen, C.T., Pacheco, J.L., Atikian, H.A., Meuwly, C., Camacho, R.M., Jelezko, F., Bielejec, E., Park, H., Lon\u010dar, M., Lukin, M.D.: An integrated diamond nanophotonics platform for quantum-optical networks. Science 354, 847 (2016)","journal-title":"Science"},{"key":"3801_CR76","volume":"9","author":"NM Sundaresan","year":"2019","unstructured":"Sundaresan, N.M., Lundgren, R., Zhu, G., Gorshkov, A.V., Houck, A.A.: Interacting qubit-photon bound states with superconducting circuits. Phys. Rev. X 9, 011021 (2019)","journal-title":"Phys. Rev. X"},{"key":"3801_CR77","volume":"99","author":"GZ Song","year":"2019","unstructured":"Song, G.Z., Kwek, L.C., Deng, F.G., Long, G.L.: Microwave transmission through an artificial atomic chain coupled to a superconducting photonic crystal. Phys. Rev. A 99, 043830 (2019)","journal-title":"Phys. Rev. A"},{"key":"3801_CR78","doi-asserted-by":"crossref","first-page":"807","DOI":"10.1038\/nphys708","volume":"3","author":"DE Chang","year":"2007","unstructured":"Chang, D.E., S\u00f8rensen, A.S., Demler, E.A., Lukin, M.D.: A single-photon transistor using nanoscale surface plasmons. Nat. Phys. 3, 807 (2007)","journal-title":"Nat. Phys."},{"key":"3801_CR79","volume":"96","author":"GZ Song","year":"2017","unstructured":"Song, G.Z., Munro, E., Nie, W., Deng, F.G., Yang, G.J., Kwek, L.C.: Photon scattering by an atomic ensemble coupled to a one-dimensional nanophotonic waveguide. Phys. Rev. A 96, 043872 (2017)","journal-title":"Phys. Rev. A"},{"key":"3801_CR80","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.aop.2017.01.007","volume":"378","author":"GZ Song","year":"2017","unstructured":"Song, G.Z., Zhang, M., Ai, Q., Yang, G.J., Alsaedi, A., Hobiny, A., Deng, F.G.: Heralded quantum repeater based on the scattering of photons off single emitters in one-dimensional waveguides. Ann. Phys. 378, 33 (2017)","journal-title":"Ann. Phys."},{"key":"3801_CR81","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1016\/j.aop.2017.10.005","volume":"387","author":"GZ Song","year":"2017","unstructured":"Song, G.Z., Liu, Q., Qiu, J., Yang, G.J., Alzahrani, F., Hobiny, A., Deng, F.G., Zhang, M.: Heralded quantum gates for atomic systems assisted by the scattering of photons off single emitters. Ann. Phys. 387, 152 (2017)","journal-title":"Ann. Phys."},{"key":"3801_CR82","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1038\/nature06472","volume":"451","author":"BD Gerardot","year":"2008","unstructured":"Gerardot, B.D., Brunner, D., Dalgarno, P.A., \u00d6hberg, P., Seidl, S., Kroner, M., Karrai, K., Stoltz, N.G., Petroff, P.M., Warburton, R.J.: Optical pumping of a single hole spin in a quantum dot. Nature 451, 441 (2008)","journal-title":"Nature"},{"key":"3801_CR83","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1038\/nmat3585","volume":"12","author":"RJ Warburton","year":"2013","unstructured":"Warburton, R.J.: Single spins in self-assembled quantum dots. Nat. Mater. 12, 483 (2013)","journal-title":"Nat. Mater."},{"key":"3801_CR84","doi-asserted-by":"crossref","first-page":"2001","DOI":"10.1364\/OL.30.002001","volume":"30","author":"JT Shen","year":"2005","unstructured":"Shen, J.T., Fan, S.: Coherent photon transport from spontaneous emission in one-dimensional waveguides. Opt. Lett. 30, 2001 (2005)","journal-title":"Opt. Lett."},{"key":"3801_CR85","volume":"97","author":"T Li","year":"2018","unstructured":"Li, T., Miranowicz, A., Hu, X., Xia, K., Nori, F.: Quantum memory and gates using a $$\\Lambda $$-type quantum emitter coupled to a chiral waveguide. Phys. Rev. A 97, 062318 (2018)","journal-title":"Phys. Rev. A"},{"key":"3801_CR86","doi-asserted-by":"crossref","first-page":"1903","DOI":"10.1364\/OE.409471","volume":"29","author":"GZ Song","year":"2021","unstructured":"Song, G.Z., Guo, J.L., Nie, W., Kwek, L.C., Long, G.L.: Optical properties of a waveguide-mediated chain of randomly positioned atoms. Opt. Express 29, 1903 (2021)","journal-title":"Opt. Express"},{"key":"3801_CR87","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1103\/RevModPhys.87.347","volume":"87","author":"P Lodahl","year":"2015","unstructured":"Lodahl, P., Mahmoodian, S., Stobbe, S.: Interfacing single photons and single quantum dots with photonic nanostructures. Rev. Mod. Phys. 87, 347 (2015)","journal-title":"Rev. Mod. Phys."},{"key":"3801_CR88","volume":"109","author":"Y Li","year":"2012","unstructured":"Li, Y., Aolita, L., Chang, D.E., Kwek, L.C.: Robust-fidelity atom-photon entangling gates in the weak-coupling regime. Phys. Rev. Lett. 109, 160504 (2012)","journal-title":"Phys. Rev. Lett."},{"key":"3801_CR89","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1038\/nature07530","volume":"456","author":"D Press","year":"2008","unstructured":"Press, D., Ladd, T.D., Zhang, B.Y., Yamamoto, Y.: Complete quantum control of a single quantum dot spin using ultrafast optical pulses. Nature 456, 218 (2008)","journal-title":"Nature"},{"key":"3801_CR90","doi-asserted-by":"crossref","first-page":"1919","DOI":"10.1007\/s11128-015-0960-x","volume":"14","author":"X Han","year":"2015","unstructured":"Han, X., Hu, S., Guo, Q., Wang, H.F., Zhang, S.: Effective scheme for W-state fusion with weak cross-Kerr nonlinearities. Quantum Inf. Process. 14, 1919 (2015)","journal-title":"Quantum Inf. Process."},{"key":"3801_CR91","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevLett.101.113903","volume":"101","author":"T Lund-Hansen","year":"2008","unstructured":"Lund-Hansen, T., Stobbe, S., Julsgaard, B., Thyrrestrup, H., S\u00fcnner, T., Kamp, M., Forchel, A., Lodahl, P.: Experimental realization of highly efficient broadband coupling of single quantum dots to a photonic crystal waveguide. Phys. Rev. Lett. 101, 113903 (2008)","journal-title":"Phys. Rev. Lett."},{"key":"3801_CR92","volume":"93","author":"J Gao","year":"2008","unstructured":"Gao, J., Sun, F.W., Wong, C.W.: Implementation scheme for quantum controlled phase-flip gate through quantum dot in slow-light photonic crystal waveguide. Appl. Phys. Lett. 93, 151108 (2008)","journal-title":"Appl. Phys. Lett."},{"key":"3801_CR93","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1038\/nphoton.2010.83","volume":"4","author":"D Press","year":"2010","unstructured":"Press, D., Greve, K.D., McMahon, P.L., Ladd, T.D., Friess, B., Schneider, C., Kamp, M., H\u00f6fling, S., Forchel, A., Yamamoto, Y.: Ultrafast optical spin echo in a single quantum dot. Nat. Photon. 4, 367 (2010)","journal-title":"Nat. Photon."},{"key":"3801_CR94","doi-asserted-by":"crossref","first-page":"817","DOI":"10.1126\/science.1159221","volume":"321","author":"DJ Reilly","year":"2008","unstructured":"Reilly, D.J., Taylor, J.M., Petta, J.R., Marcus, C.M., Hanson, M.P., Gossard, A.C.: Suppressing spin qubit dephasing by nuclear state preparation. Science 321, 817 (2008)","journal-title":"Science"},{"key":"3801_CR95","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevLett.93.093601","volume":"93","author":"AB U\u2019Ren","year":"2004","unstructured":"U\u2019Ren, A.B., Silberhorn, C., Banaszek, K., Walmsley, I.A.: Efficient conditional preparation of high-fidelity single photon states for fiber-optic quantum networks. Phys. Rev. Lett. 93, 093601 (2004)","journal-title":"Phys. Rev. Lett."},{"key":"3801_CR96","doi-asserted-by":"crossref","first-page":"464","DOI":"10.1021\/nl5037808","volume":"15","author":"P Kolchin","year":"2015","unstructured":"Kolchin, P., Pholchai, N., Mikkelsen, M.H., Oh, J., Ota, S., Islam, M.S., Yin, X.B., Zhang, X.: High purcell factor due to coupling of a single emitter to a dielectric slot waveguide. Nano Lett. 15, 464 (2015)","journal-title":"Nano Lett."}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-022-03801-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-022-03801-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-022-03801-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,15]],"date-time":"2023-02-15T21:57:03Z","timestamp":1676498223000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-022-03801-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,18]]},"references-count":96,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,1]]}},"alternative-id":["3801"],"URL":"https:\/\/doi.org\/10.1007\/s11128-022-03801-5","relation":{},"ISSN":["1573-1332"],"issn-type":[{"type":"electronic","value":"1573-1332"}],"subject":[],"published":{"date-parts":[[2023,1,18]]},"assertion":[{"value":"26 April 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 December 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 January 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"55"}}