{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T23:18:50Z","timestamp":1781306330958,"version":"3.54.1"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"9","license":[{"start":{"date-parts":[[2020,8,24]],"date-time":"2020-08-24T00:00:00Z","timestamp":1598227200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,8,24]],"date-time":"2020-08-24T00:00:00Z","timestamp":1598227200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"name":"National Key R&D Program of China","award":["2018YFA0306703"],"award-info":[{"award-number":["2018YFA0306703"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"published-print":{"date-parts":[[2020,9]]},"DOI":"10.1007\/s11128-020-02818-y","type":"journal-article","created":{"date-parts":[[2020,8,24]],"date-time":"2020-08-24T08:03:54Z","timestamp":1598256234000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["Quantum locally linear embedding for nonlinear dimensionality reduction"],"prefix":"10.1007","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2676-9742","authenticated-orcid":false,"given":"Xi","family":"He","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Li","family":"Sun","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chufan","family":"Lyu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaoting","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2020,8,24]]},"reference":[{"issue":"11","key":"2818_CR1","doi-asserted-by":"publisher","first-page":"559","DOI":"10.1080\/14786440109462720","volume":"2","author":"K Pearson","year":"1901","unstructured":"Pearson, K.: LIII. On lines and planes of closest fit to systems of points in space. Lond. Edinb. Dublin Philos. Mag. J. Sci. 2(11), 559\u2013572 (1901)","journal-title":"Lond. Edinb. Dublin Philos. Mag. J. Sci."},{"issue":"6","key":"2818_CR2","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1037\/h0071325","volume":"24","author":"H Hotelling","year":"1933","unstructured":"Hotelling, H.: Analysis of a complex of statistical variables into principal components. J. Educ. Psychol. 24(6), 417 (1933)","journal-title":"J. Educ. Psychol."},{"issue":"2","key":"2818_CR3","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1111\/j.1469-1809.1936.tb02137.x","volume":"7","author":"RA Fisher","year":"1936","unstructured":"Fisher, R.A.: The use of multiple measurements in taxonomic problems. Ann. Eugen. 7(2), 179\u2013188 (1936)","journal-title":"Ann. Eugen."},{"issue":"5","key":"2818_CR4","doi-asserted-by":"publisher","first-page":"1009","DOI":"10.1109\/TPAMI.2015.2439252","volume":"38","author":"X He","year":"2015","unstructured":"He, X., Zhang, C., Zhang, L., Li, X.: A-optimal projection for image representation. IEEE Trans. Pattern Anal. Mach. Intell. 38(5), 1009\u20131015 (2015)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"issue":"5500","key":"2818_CR5","doi-asserted-by":"publisher","first-page":"2323","DOI":"10.1126\/science.290.5500.2323","volume":"290","author":"ST Roweis","year":"2000","unstructured":"Roweis, S.T., Saul, L.K.: Nonlinear dimensionality reduction by locally linear embedding. Science 290(5500), 2323\u20132326 (2000)","journal-title":"Science"},{"key":"2818_CR6","unstructured":"Nielsen, M.A., Chuang, I.: Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England) (2002)."},{"issue":"15","key":"2818_CR7","doi-asserted-by":"publisher","first-page":"150502","DOI":"10.1103\/PhysRevLett.103.150502","volume":"103","author":"AW Harrow","year":"2009","unstructured":"Harrow, A.W., Hassidim, A., Lloyd, S.: Quantum algorithm for linear systems of equations. Phys. Rev. Lett. 103(15), 150502 (2009)","journal-title":"Phys. Rev. Lett."},{"key":"2818_CR8","doi-asserted-by":"crossref","unstructured":"Grover, L.K.: A fast quantum mechanical algorithm for database search. arXiv:quant-ph\/9605043 (1996)","DOI":"10.1145\/237814.237866"},{"issue":"13","key":"2818_CR9","doi-asserted-by":"publisher","first-page":"130503","DOI":"10.1103\/PhysRevLett.113.130503","volume":"113","author":"P Rebentrost","year":"2014","unstructured":"Rebentrost, P., Mohseni, M., Lloyd, S.: Quantum support vector machine for big data classification. Phys. Rev. Lett. 113(13), 130503 (2014)","journal-title":"Phys. Rev. Lett."},{"issue":"5","key":"2818_CR10","doi-asserted-by":"publisher","first-page":"050505","DOI":"10.1103\/PhysRevLett.109.050505","volume":"109","author":"N Wiebe","year":"2012","unstructured":"Wiebe, N., Braun, D., Lloyd, S.: Quantum algorithm for data fitting. Phys. Rev. Lett. 109(5), 050505 (2012)","journal-title":"Phys. Rev. Lett."},{"issue":"2","key":"2818_CR11","doi-asserted-by":"publisher","first-page":"022342","DOI":"10.1103\/PhysRevA.94.022342","volume":"94","author":"M Schuld","year":"2016","unstructured":"Schuld, M., Sinayskiy, I., Petruccione, F.: Prediction by linear regression on a quantum computer. Phys. Rev. A 94(2), 022342 (2016)","journal-title":"Phys. Rev. A"},{"issue":"2","key":"2818_CR12","first-page":"021050","volume":"8","author":"MH Amin","year":"2018","unstructured":"Amin, M.H., Andriyash, E., Rolfe, J., Kulchytskyy, B., Melko, R.: Quantum boltzmann machine. Phys. Rev. X 8(2), 021050 (2018)","journal-title":"Phys. Rev. X"},{"issue":"4","key":"2818_CR13","doi-asserted-by":"publisher","first-page":"040502","DOI":"10.1103\/PhysRevLett.121.040502","volume":"121","author":"S Lloyd","year":"2018","unstructured":"Lloyd, S., Weedbrook, C.: Quantum generative adversarial learning. Phys. Rev. Lett. 121(4), 040502 (2018)","journal-title":"Phys. Rev. Lett."},{"issue":"1","key":"2818_CR14","doi-asserted-by":"publisher","first-page":"012324","DOI":"10.1103\/PhysRevA.98.012324","volume":"98","author":"P-L Dallaire-Demers","year":"2018","unstructured":"Dallaire-Demers, P.-L., Killoran, N.: Quantum generative adversarial networks. Phys. Rev. A 98(1), 012324 (2018)","journal-title":"Phys. Rev. A"},{"key":"2818_CR15","doi-asserted-by":"publisher","first-page":"4213","DOI":"10.1038\/ncomms5213","volume":"5","author":"A Peruzzo","year":"2014","unstructured":"Peruzzo, A., McClean, J., Shadbolt, P., Yung, M.H., Zhou, X.Q., Love, P.J., Aspuru-Guzik, A., O\u2019brien, J.L.: A variational eigenvalue solver on a photonic quantum processor. Nat. Commun. 5, 4213 (2014)","journal-title":"Nat. Commun."},{"key":"2818_CR16","doi-asserted-by":"publisher","first-page":"156","DOI":"10.22331\/q-2019-07-01-156","volume":"3","author":"O Higgott","year":"2019","unstructured":"Higgott, O., Wang, D., Brierley, S.: Variational quantum computation of excited states. Quantum 3, 156 (2019)","journal-title":"Quantum"},{"issue":"1","key":"2818_CR17","doi-asserted-by":"publisher","first-page":"8","DOI":"10.1038\/s41534-019-0167-6","volume":"5","author":"R LaRose","year":"2019","unstructured":"LaRose, R., Tikku, A., O\u2019Neel-Judy, \u00c9., Cincio, L., Coles, P.J.: Variational quantum state diagonalization. npj Quantum Inf. 5(1), 8 (2019)","journal-title":"npj Quantum Inf."},{"issue":"9","key":"2818_CR18","doi-asserted-by":"publisher","first-page":"631","DOI":"10.1038\/nphys3029","volume":"10","author":"S Lloyd","year":"2014","unstructured":"Lloyd, S., Mohseni, M., Rebentrost, P.: Quantum principal component analysis. Nat. Phys. 10(9), 631 (2014)","journal-title":"Nat. Phys."},{"issue":"7","key":"2818_CR19","doi-asserted-by":"publisher","first-page":"073011","DOI":"10.1088\/1367-2630\/18\/7\/073011","volume":"18","author":"I Cong","year":"2016","unstructured":"Cong, I., Duan, L.: Quantum discriminant analysis for dimensionality reduction and classification. New J. Phys. 18(7), 073011 (2016)","journal-title":"New J. Phys."},{"issue":"3","key":"2818_CR20","doi-asserted-by":"publisher","first-page":"032311","DOI":"10.1103\/PhysRevA.99.032311","volume":"99","author":"B Duan","year":"2019","unstructured":"Duan, B., Yuan, J., Xu, J., Li, D.: Quantum algorithm and quantum circuit for a-optimal projection: Dimensionality reduction. Phys. Rev. A 99(3), 032311 (2019)","journal-title":"Phys. Rev. A"},{"issue":"9","key":"2818_CR21","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1007\/s11128-018-2004-9","volume":"17","author":"Y Dang","year":"2018","unstructured":"Dang, Y., Jiang, N., Hu, H., Ji, Z., Zhang, W.: Image classification based on quantum K-Nearest-Neighbor algorithm. Quantum Inf. Process. 17(9), 239 (2018)","journal-title":"Quantum Inf. Process."},{"key":"2818_CR22","unstructured":"Coppersmith, D.: An approximate fourier transform useful in quantum factoring (2002) arXiv:quant-ph\/0201067"},{"issue":"1","key":"2818_CR23","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1103\/PhysRevA.54.139","volume":"54","author":"A Barenco","year":"1996","unstructured":"Barenco, A., Ekert, A., Suominen, K.A., T\u00f6rm\u00e4, P.: Approximate quantum fourier transform and decoherence. Phys. Rev. A 54(1), 139 (1996)","journal-title":"Phys. Rev. A"},{"key":"2818_CR24","unstructured":"Zalka, C.: Fast versions of Shor\u2019s quantum factoring algorithm (1998) arXiv:quant-ph\/9806084"},{"key":"2818_CR25","unstructured":"Draper, T. G.: Addition on a quantum computer (2000) arXiv:quant-ph\/0008033"},{"issue":"16","key":"2818_CR26","doi-asserted-by":"publisher","first-page":"167902","DOI":"10.1103\/PhysRevLett.87.167902","volume":"87","author":"H Buhrman","year":"2001","unstructured":"Buhrman, H., Cleve, R., Watrous, J., De Wolf, R.: Quantum fingerprinting. Phys. Rev. Lett. 87(16), 167902 (2001)","journal-title":"Phys. Rev. Lett."},{"key":"2818_CR27","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-96424-9","volume-title":"Supervised Learning with Quantum Computers","author":"M Schuld","year":"2018","unstructured":"Schuld, M., Petruccione, F.: Supervised Learning with Quantum Computers, vol. 17. Springer, Berlin (2018)"},{"key":"2818_CR28","unstructured":"Dervovic, D., Herbster, M., Mountney, P., Severini, S., Usher, N., Wossnig, L.: Quantum linear systems algorithms: a primer (2018) arXiv:1802.08227"},{"issue":"3","key":"2818_CR29","doi-asserted-by":"publisher","first-page":"032301","DOI":"10.1103\/PhysRevA.96.032301","volume":"96","author":"B Duan","year":"2017","unstructured":"Duan, B., Yuan, J., Liu, Y., Li, D.: Quantum algorithm for support matrix machines. Phys. Rev. A 96(3), 032301 (2017)","journal-title":"Phys. Rev. A"},{"issue":"6","key":"2818_CR30","doi-asserted-by":"publisher","first-page":"891","DOI":"10.1145\/293347.293348","volume":"45","author":"S Arya","year":"1998","unstructured":"Arya, S., Mount, D.M., Netanyahu, N.S., Silverman, R., Wu, A.Y.: An optimal algorithm for approximate nearest neighbor searching fixed dimensions. J. ACM (JACM) 45(6), 891\u2013923 (1998)","journal-title":"J. ACM (JACM)"},{"key":"2818_CR31","unstructured":"Saul, L.K., Roweis, S.T.: An introduction to locally linear embedding. unpublished (2000) Available at: https:\/\/www.cs.toronto.edu\/~roweis\/lle\/publications.html"},{"key":"2818_CR32","unstructured":"Bravo-Prieto, C., LaRose, R., Cerezo, M., Subasi, Y., Cincio, L., Coles, P.J.: Variational quantum linear solver: A hybrid algorithm for linear systems (2019) arXiv:1909.05820"},{"key":"2818_CR33","doi-asserted-by":"crossref","unstructured":"He, X.: Quantum correlation alignment for unsupervised domain adaptation (2020) arXiv:2005.03355","DOI":"10.1103\/PhysRevA.102.032410"},{"key":"2818_CR34","doi-asserted-by":"crossref","unstructured":"Roggero, A., Baroni, A.: Short-depth circuits for efficient expectation value estimation (2019) arXiv:1905.08383","DOI":"10.1103\/PhysRevA.101.022328"},{"issue":"7747","key":"2818_CR35","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1038\/s41586-019-0980-2","volume":"567","author":"V Havl\u00ed\u010dek","year":"2019","unstructured":"Havl\u00ed\u010dek, V., C\u00f3rcoles, A.D., Temme, K., Harrow, A.W., Kandala, A., Chow, J.M., Gambetta, J.M.: Supervised learning with quantum-enhanced feature spaces. Nature 567(7747), 209 (2019)","journal-title":"Nature"},{"key":"2818_CR36","first-page":"2825","volume":"12","author":"F Pedregosa","year":"2011","unstructured":"Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R., Dubourg, V., Vanderplas, J., Passos, A., Cournapeau, D., Brucher, M., Perrot, M., Duchesnay, E.: Scikit-learn: Machine Learning in Python. J. Mach. Learn. Res. 12, 2825 (2011)","journal-title":"J. Mach. Learn. Res."},{"key":"2818_CR37","unstructured":"Aleksandrowicz, G., Alexander, T., Barkoutsos, P., Bello, Luciano., Ben-Haim, Y., Bucher, D., Cabrera-Hern\u00e1ndez, FJ., Carballo-Franquis, J., Chen, A., Chen, CF., et al.: Qiskit: An open-source framework for quantum computing. Accessed on: Mar 16 (2019)"},{"key":"2818_CR38","unstructured":"Duchi, J., Hazan, E., Singer, Y.: Adaptive subgradient methods for online learning and stochastic optimization. J. Mach. Learn. Res. 12, 2121 (2011)"}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-020-02818-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-020-02818-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-020-02818-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,8,23]],"date-time":"2021-08-23T23:11:40Z","timestamp":1629760300000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-020-02818-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,24]]},"references-count":38,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2020,9]]}},"alternative-id":["2818"],"URL":"https:\/\/doi.org\/10.1007\/s11128-020-02818-y","relation":{},"ISSN":["1570-0755","1573-1332"],"issn-type":[{"value":"1570-0755","type":"print"},{"value":"1573-1332","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,8,24]]},"assertion":[{"value":"5 November 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 August 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 August 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"309"}}