{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T17:51:11Z","timestamp":1772301071237,"version":"3.50.1"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2020,4,22]],"date-time":"2020-04-22T00:00:00Z","timestamp":1587513600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,4,22]],"date-time":"2020-04-22T00:00:00Z","timestamp":1587513600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"published-print":{"date-parts":[[2020,6]]},"DOI":"10.1007\/s11128-020-02660-2","type":"journal-article","created":{"date-parts":[[2020,4,22]],"date-time":"2020-04-22T15:04:07Z","timestamp":1587567847000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Hybrid Helmholtz machines: a gate-based quantum circuit implementation"],"prefix":"10.1007","volume":"19","author":[{"given":"Teresa J.","family":"van Dam","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2159-8251","authenticated-orcid":false,"given":"Niels M. P.","family":"Neumann","sequence":"additional","affiliation":[]},{"given":"Frank","family":"Phillipson","sequence":"additional","affiliation":[]},{"given":"Hans","family":"van den Berg","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,4,22]]},"reference":[{"key":"2660_CR1","doi-asserted-by":"publisher","first-page":"74","DOI":"10.1007\/978-3-030-14082-3_7","volume-title":"Quantum Technology and Optimization Problems","author":"E Anschuetz","year":"2019","unstructured":"Anschuetz, E., Olson, J., Aspuru-Guzik, A., Cao, Y.: Variational quantum factoring. In: Feld, S., Linnhoff-Popien, C. (eds.) Quantum Technology and Optimization Problems, pp. 74\u201385. Springer, Cham (2019)"},{"key":"2660_CR2","doi-asserted-by":"publisher","first-page":"238","DOI":"10.1016\/S2212-5671(14)00492-4","volume":"15","author":"LM Badea Stroie","year":"2014","unstructured":"Badea Stroie, L.M.: Predicting consumer behavior with artificial neural networks. Procedia Econ Finance 15, 238\u2013246 (2014). https:\/\/doi.org\/10.1016\/S2212-5671(14)00492-4","journal-title":"Procedia Econ Finance"},{"key":"2660_CR3","doi-asserted-by":"publisher","unstructured":"Benedetti, M., Garcia-Pintos, D., Perdomo, Leyton-Ortega, V., Nam, Y., Perdomo-Ortiz, A.: A generative modeling approach for benchmarking and training shallow quantum circuits. npj Quantum Inf 5, 45 (2019). https:\/\/doi.org\/10.1038\/s41534-019-0157-8","DOI":"10.1038\/s41534-019-0157-8"},{"key":"2660_CR4","doi-asserted-by":"publisher","DOI":"10.1088\/2058-9565\/aabd98","author":"M Benedetti","year":"2018","unstructured":"Benedetti, M., Realpe Gomez, J., Perdomo-Ortiz, A.: Quantum-assisted helmholtz machines: a quantum-classical deep learning framework for industrial datasets in near-term devices. Quantum Sci Technol (2018). https:\/\/doi.org\/10.1088\/2058-9565\/aabd98","journal-title":"Quantum Sci Technol"},{"key":"2660_CR5","volume-title":"Data Mining Techniques: For Marketing, Sales, and Customer Support","author":"MJ Berry","year":"1997","unstructured":"Berry, M.J., Linoff, G.: Data Mining Techniques: For Marketing, Sales, and Customer Support. Wiley, New York (1997)"},{"key":"2660_CR6","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198538493.001.0001","volume-title":"Neural Networks for Pattern Recognition","author":"CM Bishop","year":"1995","unstructured":"Bishop, C.M.: Neural Networks for Pattern Recognition. Oxford University Press Inc, New York (1995)"},{"key":"2660_CR7","doi-asserted-by":"publisher","unstructured":"Clark, J., Koprinska, I., Poon, J.: A neural network based approach to automated e-mail classification. In: Proceedings IEEE\/WIC International Conference on Web Intelligence (WI 2003), pp. 702\u2013705 (2003). https:\/\/doi.org\/10.1109\/WI.2003.1241300","DOI":"10.1109\/WI.2003.1241300"},{"key":"2660_CR8","unstructured":"Coles, P.J., Eidenbenz, S., Pakin, S., Adedoyin, A., Ambrosiano, J., Anisimov, P., Casper, W., Chennupati, G., Coffrin, C., Djidjev, H., et\u00a0al.: Quantum algorithm implementations for beginners. arXiv:1804.03719 [quant-ph] (2018)"},{"issue":"5214","key":"2660_CR9","doi-asserted-by":"publisher","first-page":"1158","DOI":"10.1126\/science.7761831","volume":"268","author":"G Hinton","year":"1995","unstructured":"Hinton, G., Dayan, P., Frey, B., Neal, R.: The \u201cwake-sleep\u201d algorithm for unsupervised neural networks. Science 268(5214), 1158\u20131161 (1995). https:\/\/doi.org\/10.1126\/science.7761831","journal-title":"Science"},{"key":"2660_CR10","doi-asserted-by":"publisher","first-page":"5355","DOI":"10.1103\/PhysRevE.58.5355","volume":"58","author":"T Kadowaki","year":"1998","unstructured":"Kadowaki, T., Nishimori, H.: Quantum annealing in the transverse ising model. Phys. Rev. E 58, 5355\u20135363 (1998). https:\/\/doi.org\/10.1103\/PhysRevE.58.5355","journal-title":"Phys. Rev. E"},{"key":"2660_CR11","unstructured":"Kirby, K.G.: A tutorial on helmholtz machines (2006). https:\/\/www.nku.edu\/~kirby\/docs\/HelmholtzTutorialKoeln.pdf. Accessed 20 Apr 2020"},{"issue":"1","key":"2660_CR12","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1214\/aoms\/1177729694","volume":"22","author":"S Kullback","year":"1951","unstructured":"Kullback, S., Leibler, R.A.: On information and sufficiency. Ann Math Stat 22(1), 79\u201386 (1951). https:\/\/doi.org\/10.1214\/aoms\/1177729694","journal-title":"Ann Math Stat"},{"issue":"1","key":"2660_CR13","doi-asserted-by":"publisher","first-page":"98","DOI":"10.1109\/72.554195","volume":"8","author":"S Lawrence","year":"1997","unstructured":"Lawrence, S., Giles, C.L., Tsoi, A.C., Back, A.D.: Face recognition: a convolutional neural-network approach. IEEE Trans Neural Netw 8(1), 98\u2013113 (1997). https:\/\/doi.org\/10.1109\/72.554195","journal-title":"IEEE Trans Neural Netw"},{"key":"2660_CR14","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.89.062315","author":"GH Low","year":"2014","unstructured":"Low, G.H., Yoder, T.J., Chuang, I.L.: Quantum inference on Bayesian networks. Phys Rev A (2014). https:\/\/doi.org\/10.1103\/PhysRevA.89.062315","journal-title":"Phys Rev A"},{"key":"2660_CR15","volume-title":"Information Theory, Inference, and Learning Algorithms","author":"DJC MacKay","year":"2003","unstructured":"MacKay, D.J.C.: Information Theory, Inference, and Learning Algorithms, vol. 6. Cambridge University Press, Cambridge (2003)"},{"issue":"2","key":"2660_CR16","doi-asserted-by":"publisher","first-page":"023023","DOI":"10.1088\/1367-2630\/18\/2\/023023","volume":"18","author":"JR McClean","year":"2016","unstructured":"McClean, J.R., Romero, J., Babbush, R., Aspuru-Guzik, A.: The theory of variational hybrid quantum-classical algorithms. New J. Phys. 18(2), 023023 (2016). https:\/\/doi.org\/10.1088\/1367-2630\/18\/2\/023023","journal-title":"New J. Phys."},{"issue":"2","key":"2660_CR17","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1007\/s42354-019-0164-0","volume":"3","author":"NMP Neumann","year":"2019","unstructured":"Neumann, N.M.P., Phillipson, F., Versluis, R.: Machine learning in the quantum era. Digitale Welt 3(2), 24\u201329 (2019). https:\/\/doi.org\/10.1007\/s42354-019-0164-0","journal-title":"Digitale Welt"},{"key":"2660_CR18","volume-title":"Quantum computation and quantum information","author":"MA Nielsen","year":"2008","unstructured":"Nielsen, M.A., Chuang, I.L.: Quantum computation and quantum information. Cambridge University Press, Cambridge (2008)"},{"issue":"22","key":"2660_CR19","doi-asserted-by":"publisher","first-page":"277","DOI":"10.4018\/978-1-60566-214-5.ch013","volume":"3","author":"M Nobuyuki","year":"2005","unstructured":"Nobuyuki, M., Haruhiko, N., Isokawa, T.: Qubit neural network: its performance and applications. Neural Process. Lett. 3(22), 277\u2013290 (2005). https:\/\/doi.org\/10.4018\/978-1-60566-214-5.ch013","journal-title":"Neural Process. Lett."},{"key":"2660_CR20","doi-asserted-by":"publisher","first-page":"031007","DOI":"10.1103\/PhysRevX.6.031007","volume":"6","author":"PJJ O\u2019Malley","year":"2016","unstructured":"O\u2019Malley, P.J.J., Babbush, R., Kivlichan, I.D., Romero, J., McClean, J.R., Barends, R., Kelly, J., Roushan, P., Tranter, A., Ding, N., Campbell, B., Chen, Y., Chen, Z., Chiaro, B., Dunsworth, A., Fowler, A.G., Jeffrey, E., Lucero, E., Megrant, A., Mutus, J.Y., Neeley, M., Neill, C., Quintana, C., Sank, D., Vainsencher, A., Wenner, J., White, T.C., Coveney, P.V., Love, P.J., Neven, H., Aspuru-Guzik, A., Martinis, J.M.: Scalable quantum simulation of molecular energies. Phys. Rev. X 6, 031007 (2016). https:\/\/doi.org\/10.1103\/PhysRevX.6.031007","journal-title":"Phys. Rev. X"},{"issue":"3","key":"2660_CR21","doi-asserted-by":"publisher","first-page":"030502","DOI":"10.1088\/2058-9565\/aab859","volume":"3","author":"A Perdomo-Ortiz","year":"2018","unstructured":"Perdomo-Ortiz, A., Benedetti, M., Realpe-G\u00f3mez, J., Biswas, R.: Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers. Quantum Sci Technol 3(3), 030502 (2018). https:\/\/doi.org\/10.1088\/2058-9565\/aab859","journal-title":"Quantum Sci Technol"},{"key":"2660_CR22","doi-asserted-by":"publisher","DOI":"10.1038\/ncomms5213","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 (2014). https:\/\/doi.org\/10.1038\/ncomms5213","journal-title":"Nat Commun"},{"key":"2660_CR23","doi-asserted-by":"publisher","first-page":"79","DOI":"10.22331\/q-2018-08-06-79","volume":"2","author":"J Preskill","year":"2018","unstructured":"Preskill, J.: Quantum computing in the NISQ era and beyond. Quantum 2, 79 (2018). https:\/\/doi.org\/10.22331\/q-2018-08-06-79","journal-title":"Quantum"},{"key":"2660_CR24","unstructured":"QuTech: (2019). https:\/\/www.quantum-inspire.com\/. Accessed 13 May 2019"},{"key":"2660_CR25","doi-asserted-by":"publisher","first-page":"042308","DOI":"10.1103\/PhysRevA.98.042308","volume":"98","author":"P Rebentrost","year":"2018","unstructured":"Rebentrost, P., Bromley, T.R., Weedbrook, C., Lloyd, S.: Quantum hopfield neural network. Phys. Rev. A 98, 042308 (2018). https:\/\/doi.org\/10.1103\/PhysRevA.98.042308","journal-title":"Phys. Rev. A"},{"issue":"1","key":"2660_CR26","doi-asserted-by":"publisher","first-page":"014008","DOI":"10.1088\/2058-9565\/aad3e4","volume":"4","author":"J Romero","year":"2018","unstructured":"Romero, J., Babbush, R., McClean, J.R., Hempel, C., Love, P.J., Aspuru-Guzik, A.: Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz. Quantum Sci. Technol. 4(1), 014008 (2018). https:\/\/doi.org\/10.1088\/2058-9565\/aad3e4","journal-title":"Quantum Sci. Technol."},{"issue":"1\u20132","key":"2660_CR27","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1016\/0004-3702(94)00092-1","volume":"82","author":"D Roth","year":"1996","unstructured":"Roth, D.: On the hardness of approximate reasoning. Artif. Intell. 82(1\u20132), 273\u2013302 (1996)","journal-title":"Artif. Intell."},{"issue":"2","key":"2660_CR28","doi-asserted-by":"publisher","first-page":"172","DOI":"10.1080\/00107514.2014.964942","volume":"56","author":"M Schuld","year":"2015","unstructured":"Schuld, M., Sinayskiy, I., Petruccione, F.: An introduction to quantum machine learning. Contemp. Phys. 56(2), 172\u2013185 (2015). https:\/\/doi.org\/10.1080\/00107514.2014.964942","journal-title":"Contemp. Phys."},{"key":"2660_CR29","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, 022342 (2016). https:\/\/doi.org\/10.1103\/PhysRevA.94.022342","journal-title":"Phys. Rev. A"},{"key":"2660_CR30","unstructured":"Wiebe, N., Kapoor, A., Svore, K.M.: Quantum deep learning. arXiv:1412.3489 [quant-ph] (2014)"},{"issue":"10","key":"2660_CR31","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 a N-bit Boolean function for a classification. New J. Phys. 16(10), 103014 (2014). https:\/\/doi.org\/10.1088\/1367-2630\/16\/10\/103014","journal-title":"New J. Phys."}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-020-02660-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-020-02660-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-020-02660-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,4]],"date-time":"2024-08-04T12:58:58Z","timestamp":1722776338000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-020-02660-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,4,22]]},"references-count":31,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2020,6]]}},"alternative-id":["2660"],"URL":"https:\/\/doi.org\/10.1007\/s11128-020-02660-2","relation":{},"ISSN":["1570-0755","1573-1332"],"issn-type":[{"value":"1570-0755","type":"print"},{"value":"1573-1332","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,4,22]]},"assertion":[{"value":"30 October 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 March 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 April 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"174"}}