{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T17:50:59Z","timestamp":1772301059794,"version":"3.50.1"},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2021,6,1]],"date-time":"2021-06-01T00:00:00Z","timestamp":1622505600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2021,6,1]],"date-time":"2021-06-01T00:00:00Z","timestamp":1622505600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12074107"],"award-info":[{"award-number":["12074107"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003819","name":"Natural Science Foundation of Hubei Province","doi-asserted-by":"publisher","award":["2020CFB263"],"award-info":[{"award-number":["2020CFB263"]}],"id":[{"id":"10.13039\/501100003819","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"published-print":{"date-parts":[[2021,6]]},"DOI":"10.1007\/s11128-021-03148-3","type":"journal-article","created":{"date-parts":[[2021,6,18]],"date-time":"2021-06-18T06:02:39Z","timestamp":1623996159000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Optimal quantum state transformations based on machine learning"],"prefix":"10.1007","volume":"20","author":[{"given":"Tian-Hui","family":"Zhao","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2491-2330","authenticated-orcid":false,"given":"Ming-Hao","family":"Wang","sequence":"additional","affiliation":[]},{"given":"Bin","family":"Zhou","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,6,18]]},"reference":[{"key":"3148_CR1","doi-asserted-by":"crossref","unstructured":"Nielsen, M.A., Chuang I.L.: Quantum Computation and Quantum Information, p. 9781107002173 . Cambridge University Press, I.L. (2011)","DOI":"10.1017\/CBO9780511976667"},{"key":"3148_CR2","doi-asserted-by":"publisher","first-page":"1484","DOI":"10.1137\/S0097539795293172","volume":"26","author":"PW Shor","year":"1997","unstructured":"Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26, 1484 (1997)","journal-title":"SIAM J. Comput."},{"key":"3148_CR3","doi-asserted-by":"crossref","unstructured":"Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of Twenty-eighth ACM Symposium on Theory of Computing, pp. 212\u2013219 (1996)","DOI":"10.1145\/237814.237866"},{"key":"3148_CR4","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, 150502 (2009)","journal-title":"Phys. Rev. Lett."},{"key":"3148_CR5","doi-asserted-by":"publisher","first-page":"103014","DOI":"10.1088\/1367-2630\/16\/10\/103014","volume":"16","author":"S Yoo","year":"2014","unstructured":"Yoo, S., Bang, J., Lee, C., Lee, J.: A quantum speedup in machine learning: finding an N -bit Boolean function for a classification. New J. Phys. 16, 103014 (2014)","journal-title":"New J. Phys."},{"key":"3148_CR6","doi-asserted-by":"publisher","first-page":"432","DOI":"10.1103\/PhysRevLett.83.432","volume":"83","author":"N Gisin","year":"1999","unstructured":"Gisin, N., Popescu, S.: Spin flips and quantum information for antiparallel spins. Phys. Rev. Lett. 83, 432 (1999)","journal-title":"Phys. Rev. Lett."},{"key":"3148_CR7","doi-asserted-by":"publisher","first-page":"022303","DOI":"10.1103\/PhysRevA.62.022303","volume":"62","author":"V Bu\u017eek","year":"2000","unstructured":"Bu\u017eek, V., Hillery, M.: Optimal manipulations with qubits: Universal quantum entanglers. Phys. Rev. A 62, 022303 (2000)","journal-title":"Phys. Rev. A"},{"key":"3148_CR8","doi-asserted-by":"publisher","first-page":"1844","DOI":"10.1103\/PhysRevA.54.1844","volume":"54","author":"V Bu\u017eek","year":"1996","unstructured":"Bu\u017eek, V., Hillery, M.: Quantum copying: beyond the no-cloning theorem. Phys. Rev. A 54, 1844 (1996)","journal-title":"Phys. Rev. A"},{"key":"3148_CR9","doi-asserted-by":"publisher","first-page":"2153","DOI":"10.1103\/PhysRevLett.79.2153","volume":"79","author":"N Gisin","year":"1997","unstructured":"Gisin, N., Massar, S.: Optimal quantum cloning machines. Phys. Rev. Lett. 79, 2153 (1997)","journal-title":"Phys. Rev. Lett."},{"key":"3148_CR10","doi-asserted-by":"publisher","first-page":"436","DOI":"10.1103\/PhysRevLett.83.436","volume":"83","author":"MA Nielsen","year":"1999","unstructured":"Nielsen, M.A.: Conditions for a class of entanglement transformations. Phys. Rev. Lett. 83, 436 (1999)","journal-title":"Phys. Rev. Lett."},{"key":"3148_CR11","doi-asserted-by":"publisher","first-page":"012324","DOI":"10.1103\/PhysRevA.99.012324","volume":"99","author":"M-H Wang","year":"2019","unstructured":"Wang, M.-H., Cai, Q.-Y.: High-fidelity quantum cloning of two nonorthogonal quantum states via weak measurements. Phys. Rev. A 99, 012324 (2019)","journal-title":"Phys. Rev. A"},{"key":"3148_CR12","doi-asserted-by":"publisher","first-page":"062306","DOI":"10.1103\/PhysRevA.98.062306","volume":"98","author":"M-S Li","year":"2018","unstructured":"Li, M.-S., Wang, Y.-L.: Masking quantum information in multipartite scenario. Phys. Rev. A 98, 062306 (2018)","journal-title":"Phys. Rev. A"},{"key":"3148_CR13","doi-asserted-by":"publisher","first-page":"802","DOI":"10.1038\/299802a0","volume":"299","author":"WK Wootters","year":"1982","unstructured":"Wootters, W.K., Zurek, W.H.: A single quantum cannot be cloned. Nature 299, 802 (1982)","journal-title":"Nature"},{"key":"3148_CR14","doi-asserted-by":"publisher","first-page":"2818","DOI":"10.1103\/PhysRevLett.76.2818","volume":"76","author":"H Barnum","year":"1996","unstructured":"Barnum, H., Caves, C.M., Fuchs, C.A., Jozsa, R., Schumacher, B.: Noncommuting mixed states cannot be broadcast. Phys. Rev. Lett. 76, 2818 (1996)","journal-title":"Phys. Rev. Lett."},{"key":"3148_CR15","doi-asserted-by":"publisher","first-page":"240501","DOI":"10.1103\/PhysRevLett.99.240501","volume":"99","author":"H Barnum","year":"2007","unstructured":"Barnum, H., Barrett, J., Leifer, M., Wilce, A.: Generalized no-broadcasting theorem. Phys. Rev. Lett. 99, 240501 (2007)","journal-title":"Phys. Rev. Lett."},{"key":"3148_CR16","doi-asserted-by":"publisher","first-page":"110403","DOI":"10.1103\/PhysRevLett.116.110403","volume":"116","author":"M Oszmaniec","year":"2016","unstructured":"Oszmaniec, M., Grudka, A., Horodecki, M., W\u00f3jcik, A.: Creating a superposition of unknown quantum states. Phys. Rev. Lett. 116, 110403 (2016)","journal-title":"Phys. Rev. Lett."},{"key":"3148_CR17","doi-asserted-by":"publisher","first-page":"230501","DOI":"10.1103\/PhysRevLett.120.230501","volume":"120","author":"K Modi","year":"2018","unstructured":"Modi, K., Pati, A.K., de Sen, A., Sen, U.: Masking quantum information is impossible. Phys. Rev. Lett. 120, 230501 (2018)","journal-title":"Phys. Rev. Lett."},{"key":"3148_CR18","doi-asserted-by":"publisher","first-page":"431","DOI":"10.1038\/nphys4035","volume":"13","author":"J Carrasquilla","year":"2017","unstructured":"Carrasquilla, J., Melko, R.G.: Machine learning phases of matter. Nat. Phys. 13, 431 (2017)","journal-title":"Nat. Phys."},{"key":"3148_CR19","doi-asserted-by":"publisher","first-page":"200401","DOI":"10.1103\/PhysRevLett.122.200401","volume":"122","author":"A Canabarro","year":"2019","unstructured":"Canabarro, A., Brito, S., Chaves, R.: Machine learning nonlocal correlations. Phys. Rev. Lett. 122, 200401 (2019)","journal-title":"Phys. Rev. Lett."},{"key":"3148_CR20","doi-asserted-by":"publisher","first-page":"045002","DOI":"10.1103\/RevModPhys.91.045002","volume":"91","author":"G Carleo","year":"2019","unstructured":"Carleo, G., Cirac, I., Cranmer, K., Daudet, L., Schuld, M., Tishby, N., Vogt-Maranto, L., Zdeborov\u00e1, L.: Machine learning and the physical sciences. Rev. Mod. Phys. 91, 045002 (2019)","journal-title":"Rev. Mod. Phys."},{"key":"3148_CR21","doi-asserted-by":"publisher","first-page":"033017","DOI":"10.1088\/1367-2630\/11\/3\/033017","volume":"11","author":"S Gammelmark","year":"2009","unstructured":"Gammelmark, S., M\u00f8lmer, K.: Quantum learning by measurement and feedback. New J. Phys. 11, 033017 (2009)","journal-title":"New J. Phys."},{"key":"3148_CR22","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, 050505 (2012)","journal-title":"Phys. Rev. Lett."},{"key":"3148_CR23","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, 130503 (2014)","journal-title":"Phys. Rev. Lett."},{"key":"3148_CR24","doi-asserted-by":"publisher","first-page":"130501","DOI":"10.1103\/PhysRevLett.117.130501","volume":"117","author":"V Dunjko","year":"2016","unstructured":"Dunjko, V., Taylor, J.M., Briegel, H.J.: Quantum-enhanced machine learning. Phys. Rev. Lett. 117, 130501 (2016)","journal-title":"Phys. Rev. Lett."},{"key":"3148_CR25","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1038\/nature23474","volume":"549","author":"J Biamonte","year":"2017","unstructured":"Biamonte, J., Wittek, P., Pancotti, N., Rebentrost, P., Wiebe, N., Lloyd, S.: Quantum machine learning. Nature 549, 195 (2017)","journal-title":"Nature"},{"key":"3148_CR26","doi-asserted-by":"publisher","first-page":"032309","DOI":"10.1103\/PhysRevA.98.032309","volume":"98","author":"K Mitarai","year":"2018","unstructured":"Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Phys. Rev. A 98, 032309 (2018)","journal-title":"Phys. Rev. A"},{"key":"3148_CR27","first-page":"031086","volume":"8","author":"M Bukov","year":"2018","unstructured":"Bukov, M., Day, A.G.R., Sels, D., Weinberg, P., Polkovnikov, A., Mehta, P.: Reinforcement learning in different phases of quantum control. Phys. Rev. X 8, 031086 (2018)","journal-title":"Phys. Rev. X"},{"key":"3148_CR28","doi-asserted-by":"publisher","first-page":"040504","DOI":"10.1103\/PhysRevLett.122.040504","volume":"122","author":"M Schuld","year":"2019","unstructured":"Schuld, M., Killoran, N.: Quantum machine learning in feature hilbert spaces. Phys. Rev. Lett. 122, 040504 (2019)","journal-title":"Phys. Rev. Lett."},{"key":"3148_CR29","doi-asserted-by":"publisher","first-page":"052309","DOI":"10.1103\/PhysRevA.101.052309","volume":"101","author":"S-X Cao","year":"2020","unstructured":"Cao, S.-X., Wossnig, L., Vlastakis, B., Leek, P., Grant, E.: Cost-function embedding and dataset encoding for machine learning with parametrized quantum circuits. Phys. Rev. A 101, 052309 (2020)","journal-title":"Phys. Rev. A"},{"key":"3148_CR30","doi-asserted-by":"publisher","first-page":"113022","DOI":"10.1088\/1367-2630\/aae94a","volume":"20","author":"L Cincio","year":"2018","unstructured":"Cincio, L., Suba\u015fi, Y., Sornborger, A.T., Coles, P.J.: Learning the quantum algorithm for state overlap. New J. Phys. 20, 113022 (2018)","journal-title":"New J. Phys."},{"key":"3148_CR31","doi-asserted-by":"publisher","first-page":"052327","DOI":"10.1103\/PhysRevA.101.052327","volume":"101","author":"J Lin","year":"2020","unstructured":"Lin, J., Lai, Z.-Y., Li, X.-P.: Quantum adiabatic algorithm design using reinforcement learning. Phys. Rev. A 101, 052327 (2020)","journal-title":"Phys. Rev. A"},{"key":"3148_CR32","doi-asserted-by":"publisher","first-page":"043001","DOI":"10.1088\/2058-9565\/ab4eb5","volume":"4","author":"M Benedetti","year":"2019","unstructured":"Benedetti, M., Lloyd, E., Sack, S., Fiorentini, M.: Parameterized quantum circuits as machine learning models. Quantum Sci. Technol. 4, 043001 (2019)","journal-title":"Quantum Sci. Technol."},{"key":"3148_CR33","doi-asserted-by":"publisher","first-page":"242","DOI":"10.1038\/nature23879","volume":"549","author":"A Kandala","year":"2017","unstructured":"Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549, 242 (2017)","journal-title":"Nature"},{"key":"3148_CR34","doi-asserted-by":"publisher","first-page":"4812","DOI":"10.1038\/s41467-018-07090-4","volume":"9","author":"JR McClean","year":"2018","unstructured":"McClean, J.R., Boixo, S., Smelyanskiy, V.N., Babbush, R., Neven, H.: Barren plateaus in quantum neural network training landscapes. Nat. Commun. 9, 4812 (2018)","journal-title":"Nat. Commun."},{"key":"3148_CR35","doi-asserted-by":"publisher","first-page":"032331","DOI":"10.1103\/PhysRevA.99.032331","volume":"99","author":"M Schuld","year":"2019","unstructured":"Schuld, M., Bergholm, V., Gogolin, C., Izaac, J., Killoran, N.: Evaluating analytic gradients on quantum hardware. Phys. Rev. A 99, 032331 (2019)","journal-title":"Phys. Rev. A"},{"key":"3148_CR36","doi-asserted-by":"publisher","first-page":"045005","DOI":"10.1088\/2058-9565\/ab3951","volume":"4","author":"P-L Dallaire-Demers","year":"2019","unstructured":"Dallaire-Demers, P.-L., Romero, J., Veis, L., Sim, S., Aspuru-Guzik, A.: Low-depth circuit ansatz for preparing correlated fermionic states on a quantum computer. Quantum Sci. Technol. 4, 045005 (2019)","journal-title":"Quantum Sci. Technol."},{"key":"3148_CR37","doi-asserted-by":"publisher","first-page":"043158","DOI":"10.1103\/PhysRevResearch.2.043158","volume":"2","author":"KM Nakanishi","year":"2020","unstructured":"Nakanishi, K.M., Fujii, K., Todo, S.: Sequential minimal optimization for quantum-classical hybrid algorithms. Phys. Rev. Res. 2, 043158 (2020)","journal-title":"Phys. Rev. Res."},{"key":"3148_CR38","doi-asserted-by":"publisher","first-page":"150503","DOI":"10.1103\/PhysRevLett.118.150503","volume":"118","author":"J Li","year":"2017","unstructured":"Li, J., Yang, X.-D., Peng, X.-H., Sun, C.-P.: Hybrid quantum-classical approach to quantum optimal control. Phys. Rev. Lett. 118, 150503 (2017)","journal-title":"Phys. Rev. Lett."},{"key":"3148_CR39","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, 167902 (2001)","journal-title":"Phys. Rev. Lett."},{"key":"3148_CR40","unstructured":"Bennett, C.H., Brassard, G.: Quantum cryptography: Public key distribution and coin tossing. In: Proceedings of IEEE International Conference on Computers, Systems, and Signal Processing, Bangalore, pp. 175\u2013179. (1984)"},{"key":"3148_CR41","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1103\/RevModPhys.74.145","volume":"74","author":"N Gisin","year":"2002","unstructured":"Gisin, N., Ribordy, G., Tittel, W., Zbinden, H.: Quantum cryptography. Rev. Modern Phys. 74, 145 (2002)","journal-title":"Rev. Modern Phys."},{"key":"3148_CR42","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1016\/j.physrep.2014.06.004","volume":"544","author":"H Fan","year":"2014","unstructured":"Fan, H., Wang, Y.N., Jing, L., Yue, J.D., Shi, H.D., Zhang, Y.L., Mu, L.Z.: Quantum cloning machines and the applications. Phys. Rep. 544, 241 (2014)","journal-title":"Phys. Rep."},{"key":"3148_CR43","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1016\/S0375-9601(97)00083-2","volume":"228","author":"NG Huttner","year":"1997","unstructured":"Huttner, N.G.: Quantum cloning, eavesdropping and bell\u2019s inequality. Phys. Lett. A 228, 13 (1997)","journal-title":"Phys. Lett. A"},{"key":"3148_CR44","doi-asserted-by":"publisher","first-page":"173601","DOI":"10.1103\/PhysRevLett.110.173601","volume":"110","author":"K Bartkiewicz","year":"2013","unstructured":"Bartkiewicz, K., Lemr, K., Cernoch, A., Soubusta, J., Miranowicz, A.: Experimental eavesdropping based on optimal quantum cloning. Phys. Rev. Lett. 110, 173601 (2013)","journal-title":"Phys. Rev. Lett."},{"key":"3148_CR45","doi-asserted-by":"publisher","first-page":"4377","DOI":"10.1103\/PhysRevA.58.4377","volume":"58","author":"CS Niu","year":"1998","unstructured":"Niu, C.S., Griffiths, R.B.: Optimal copying of one quantum bit. Phys. Rev. A 58, 4377 (1998)","journal-title":"Phys. Rev. A"},{"key":"3148_CR46","doi-asserted-by":"publisher","first-page":"4497","DOI":"10.1103\/PhysRevLett.84.4497","volume":"84","author":"NJ Cerf","year":"2000","unstructured":"Cerf, N.J.: Pauli cloning of a quantum bit. Phys. Rev. Lett. 84, 4497 (2000)","journal-title":"Phys. Rev. Lett."},{"key":"3148_CR47","unstructured":"Kingma, D., Ba, J.: Adam: a method for stochastic optimization. arXiv:1412.6980v5. (2014)"}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-021-03148-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-021-03148-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-021-03148-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,4]],"date-time":"2023-02-04T03:41:38Z","timestamp":1675482098000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-021-03148-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6]]},"references-count":47,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2021,6]]}},"alternative-id":["3148"],"URL":"https:\/\/doi.org\/10.1007\/s11128-021-03148-3","relation":{},"ISSN":["1570-0755","1573-1332"],"issn-type":[{"value":"1570-0755","type":"print"},{"value":"1573-1332","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6]]},"assertion":[{"value":"24 February 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 June 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 June 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"212"}}