{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,30]],"date-time":"2026-05-30T11:51:00Z","timestamp":1780141860552,"version":"3.54.0"},"reference-count":109,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2023,2,25]],"date-time":"2023-02-25T00:00:00Z","timestamp":1677283200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,2,25]],"date-time":"2023-02-25T00:00:00Z","timestamp":1677283200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Mach. Intell."],"published-print":{"date-parts":[[2023,6]]},"DOI":"10.1007\/s42484-023-00096-2","type":"journal-article","created":{"date-parts":[[2023,2,25]],"date-time":"2023-02-25T17:02:26Z","timestamp":1677344546000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Stationary states of a dissipative two-qubit quantum channel and their applications for quantum machine learning"],"prefix":"10.1007","volume":"5","author":[{"given":"E.","family":"Ghasemian","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,2,25]]},"reference":[{"key":"96_CR1","doi-asserted-by":"publisher","first-page":"505","DOI":"10.1038\/s41586-019-1666-5","volume":"574.7779","author":"F Arute","year":"2019","unstructured":"Arute F, et al. (2019) Quantum supremacy using a programmable superconducting processor. Nature 574.7779:505\u2013510","journal-title":"Nature"},{"key":"96_CR2","doi-asserted-by":"publisher","first-page":"083602","DOI":"10.1103\/PhysRevLett.127.083602","volume":"127.8","author":"S-Y Bai","year":"2021","unstructured":"Bai S-Y, An J-H (2021) Generating stable spin squeezing by squeezed-reservoir engineering. Phys Rev Lett 127.8:083602","journal-title":"Phys Rev Lett"},{"key":"96_CR3","doi-asserted-by":"publisher","first-page":"140401","DOI":"10.1103\/PhysRevLett.113.140401","volume":"113.14","author":"T Baumgratz","year":"2014","unstructured":"Baumgratz T, Cramer M, Plenio MB (2014) Quantifying coherence. Physical review letters 113.14:140401","journal-title":"Physical review letters"},{"key":"96_CR4","first-page":"1368","volume":"33","author":"J Bausch","year":"2020","unstructured":"Bausch J (2020) Recurrent quantum neural networks. Adv Neural Inf Process Syst 33:1368\u20131379","journal-title":"Adv Neural Inf Process Syst"},{"key":"96_CR5","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 (2019) Parameterized quantum circuits as machine learning models. Quantum Science and Technology 4:043001","journal-title":"Quantum Science and Technology"},{"key":"96_CR6","doi-asserted-by":"crossref","unstructured":"Bottou L (2010) Large-scale machine learning with stochastic gradient descent.. In: Proceedings of COMPSTAT\u20192010: 19th international conference on computational statistics, Paris France, August 22-27, 2010 keynote, invited and contributed papers. Physica-Verlag HD, pp 177\u2013186","DOI":"10.1007\/978-3-7908-2604-3_16"},{"key":"96_CR7","doi-asserted-by":"crossref","unstructured":"Breuer H-P, Petruccione F (2002) The theory of open quantum systems. Oxford University Press on Demand","DOI":"10.1007\/3-540-44874-8_4"},{"key":"96_CR8","unstructured":"Bub J. (2001) Quantum entanglement and information"},{"key":"96_CR9","first-page":"031086","volume":"8.3","author":"M Bukov","year":"2018","unstructured":"Bukov M, et al. (2018) Reinforcement learning in different phases of quantum control. Phys Rev X 8.3:031086","journal-title":"Phys Rev X"},{"key":"96_CR10","doi-asserted-by":"publisher","first-page":"110504","DOI":"10.1103\/PhysRevLett.114.110504","volume":"114","author":"X-D Cai","year":"2015","unstructured":"Cai X-D, Wu D, Su Z-E, Chen M-C, Wang X-L, Li L, Liu N-L, Lu C-Y, Pan J-W (2015) Entanglement-based machine learning on a quantum computer. Phys Rev Lett 114:110504","journal-title":"Phys Rev Lett"},{"key":"96_CR11","unstructured":"Campagne-Ibarcq P, Eickbusch A, Touzard S, Zalys-Geller E, Frattini N, Sivak V, Reinhold P, Puri S, Shankar S, Schoelkopf R et al (2019) arXiv:1907.12487"},{"key":"96_CR12","unstructured":"Cao Y, Guerreschi GG, Aspuru-Guzik A (2017) Quantum neuron: an elementary building block for machine learning on quantum computers. arXiv:1711.11240"},{"key":"96_CR13","doi-asserted-by":"crossref","unstructured":"Cappelletti W, Erbanni R, Keller J (2020) Polyadic quantum classifier. In: 2020 IEEE International Conference on Quantum Computing and Engineering (QCE). IEEE, pp 22\u201329","DOI":"10.1109\/QCE49297.2020.00013"},{"key":"96_CR14","doi-asserted-by":"publisher","first-page":"602","DOI":"10.1126\/science.aag2302","volume":"355","author":"G Carleo","year":"2017","unstructured":"Carleo G, Troyer M (2017) Solving the quantum many-body problem with artificial neural networks. Science 355:602","journal-title":"Science"},{"key":"96_CR15","doi-asserted-by":"publisher","first-page":"040402","DOI":"10.1103\/PhysRevLett.117.040402","volume":"117","author":"RJ Chapman","year":"2016","unstructured":"Chapman RJ, Ferrie C, Peruzzo A (2016) Experimental demonstration of selfguided quantum tomography. Phys Rev Lett 117:040402","journal-title":"Phys Rev Lett"},{"key":"96_CR16","first-page":"015005","volume":"7.1","author":"Y Chen","year":"2021","unstructured":"Chen Y, et al. (2021) Detecting quantum entanglement with unsupervised learning. Quantum Science and Technology 7.1:015005","journal-title":"Quantum Science and Technology"},{"key":"96_CR17","doi-asserted-by":"publisher","first-page":"460","DOI":"10.3390\/e23040460","volume":"23.4","author":"SY-C Chen","year":"2021","unstructured":"Chen SY-C, Yoo S (2021) Federated quantum machine learning. Entropy 23.4:460","journal-title":"Entropy"},{"key":"96_CR18","doi-asserted-by":"publisher","first-page":"025001","DOI":"10.1103\/RevModPhys.91.025001","volume":"91","author":"E Chitambar","year":"2019","unstructured":"Chitambar E, Gour G (2019) Quantum resource theories. Rev Mod Phys 91:025001","journal-title":"Rev Mod Phys"},{"key":"96_CR19","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1016\/0024-3795(75)90075-0","volume":"10","author":"M-D Choi","year":"1975","unstructured":"Choi M-D (1975) Completely positive linear maps on complex matrices. Linear Algebra and Its Applications 10:285","journal-title":"Linear Algebra and Its Applications"},{"key":"96_CR20","doi-asserted-by":"publisher","first-page":"177901","DOI":"10.1103\/PhysRevLett.91.177901","volume":"91","author":"S Clark","year":"2003","unstructured":"Clark S, Peng A, Gu M, Parkins S (2003) Unconditional preparation of entanglement between atoms in cascaded optical cavities. Phys Rev Lett 91:177901","journal-title":"Phys Rev Lett"},{"key":"96_CR21","doi-asserted-by":"publisher","first-page":"1155","DOI":"10.1103\/RevModPhys.82.1155","volume":"82.2","author":"AA Clerk","year":"2010","unstructured":"Clerk AA et al (2010) Introduction to quantum noise, measurement, and amplification. Rev Mod Phys 82.2:1155","journal-title":"Rev Mod Phys"},{"key":"96_CR22","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1098\/rspa.1985.0070","volume":"400","author":"D Deutsch","year":"1985","unstructured":"Deutsch D (1985) Quantum theory, the Church\u2013Turing principle and the universal quantum computer. Proceedings of the Royal Society of London. A Mathematical and Physical Sciences 400:97","journal-title":"Proceedings of the Royal Society of London. A Mathematical and Physical Sciences"},{"key":"96_CR23","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1098\/rspa.1989.0099","volume":"425","author":"DE Deutsch","year":"1989","unstructured":"Deutsch DE (1989) Quantum computational networks. Proceedings of the Royal Society of London. A Mathematical and Physical Sciences 425:73","journal-title":"Proceedings of the Royal Society of London. A Mathematical and Physical Sciences"},{"key":"96_CR24","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-09645-1","volume-title":"Quantum squeezing, vol 27","author":"PD Drummond","year":"2004","unstructured":"Drummond PD, Ficek Z, Spicek Z (2004) Quantum squeezing, vol 27. Springer Science & Business Media, Berlin"},{"key":"96_CR25","unstructured":"Dua D, Graff C (2017) UCI machine learning repository. http:\/\/archive.ics.uci.edu\/ml"},{"key":"96_CR26","doi-asserted-by":"publisher","first-page":"2722","DOI":"10.1103\/PhysRevLett.84.2722","volume":"84.12","author":"L-M Duan","year":"2000","unstructured":"Duan L. -M., et al. (2000) Inseparability criterion for continuous variable systems. Phys Rev Lett 84.12:2722","journal-title":"Phys Rev Lett"},{"key":"96_CR27","doi-asserted-by":"publisher","first-page":"253601","DOI":"10.1103\/PhysRevLett.90.253601","volume":"90","author":"L-M Duan","year":"2003","unstructured":"Duan L-M, Kimble H (2003) Efficient engineering of multiatom entanglement through single-photon detections. Phys Rev Lett 90:253601","journal-title":"Phys Rev Lett"},{"key":"96_CR28","doi-asserted-by":"publisher","first-page":"1769","DOI":"10.1098\/rsta.1998.0248","volume":"356","author":"A Ekert","year":"1998","unstructured":"Ekert A, Jozsa R (1998) Quantum algorithms: entanglementenhanced information processing. Philosophical Transactions of the Royal Society of London. Series A Mathematical, Physical and Engineering Sciences 356:1769","journal-title":"Philosophical Transactions of the Royal Society of London. Series A Mathematical, Physical and Engineering Sciences"},{"key":"96_CR29","doi-asserted-by":"publisher","first-page":"991","DOI":"10.1088\/0256-307X\/21\/6\/003","volume":"21","author":"L Fu-Li","year":"2004","unstructured":"Fu-Li L, Hong-Rong L (2004) An intuitive expression for inseparability condition of a two-mode squeezed vacuum state in a thermal environment. Chin Phys Lett 21:991","journal-title":"Chin Phys Lett"},{"key":"96_CR30","doi-asserted-by":"publisher","first-page":"43","DOI":"10.3390\/batteries8050043","volume":"8","author":"G Gemme","year":"2022","unstructured":"Gemme G, Grossi M, Ferraro D, Vallecorsa S, Sassetti M (2022) IBM quantum platforms: a quantum battery perspective. Batteries 8:43","journal-title":"Batteries"},{"key":"96_CR31","doi-asserted-by":"publisher","first-page":"095202","DOI":"10.1088\/1555-6611\/aa7dcf","volume":"27","author":"E Ghasemian","year":"2017","unstructured":"Ghasemian E, Tavassoly M (2017) Quantum dynamics of a BEC interacting with a single-mode quantized eld under the inuence of a dissipation process: thermal and squeezed vacuum reservoirs. Laser Phys 27:095202","journal-title":"Laser Phys"},{"key":"96_CR32","first-page":"1","volume":"11.1","author":"E Ghasemian","year":"2021","unstructured":"Ghasemian E, Tavassoly M (2021) Generation of Werner-like states via a two-qubit system plunged in a thermal reservoir and their application in solving binary classification problems. Sci Rep 11.1:1","journal-title":"Sci Rep"},{"key":"96_CR33","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1006\/jcss.2001.1769","volume":"63","author":"S Gupta","year":"2001","unstructured":"Gupta S, Zia R (2001) Quantum neural networks. J Comput Syst Sci 63:355","journal-title":"J Comput Syst Sci"},{"key":"96_CR34","doi-asserted-by":"crossref","unstructured":"Gurvits L (2003) Classical deterministic complexity of Edmonds\u2019 problem and quantum entanglement. In: Proceedings of the thirty-fifth annual ACM symposium on Theory of computing, pp 10\u201319","DOI":"10.1145\/780542.780545"},{"key":"96_CR35","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1038\/nphys1453","volume":"6.1","author":"D Hanneke","year":"2010","unstructured":"Hanneke D, et al. (2010) Realization of a programmable two-qubit quantum processor. Nat Phys 6.1:13\u201316","journal-title":"Nat Phys"},{"key":"96_CR36","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 AD, Temme K, Harrow AW, Kandala A, Chow JM, Gambetta JM (2019) Supervised learning with quantum-enhanced feature spaces. Nature 567:209","journal-title":"Nature"},{"key":"96_CR37","doi-asserted-by":"publisher","first-page":"063603","DOI":"10.1103\/PhysRevLett.104.063603","volume":"104","author":"A Hentschel","year":"2010","unstructured":"Hentschel A, Sanders BC (2010) Machine learning for precise quantum measurement. Phys Rev Lett 104:063603","journal-title":"Phys Rev Lett"},{"key":"96_CR38","unstructured":"Herbert N (2011) Quantum reality: Beyond the new physics. Anchor"},{"key":"96_CR39","doi-asserted-by":"publisher","first-page":"042114","DOI":"10.1103\/PhysRevA.78.042114","volume":"78","author":"M Hernandez","year":"2008","unstructured":"Hernandez M, Orszag M (2008) Decoherence and disentanglement for two qubits in a common squeezed reservoir. Phys Rev A 78:042114","journal-title":"Phys Rev A"},{"key":"96_CR40","doi-asserted-by":"publisher","first-page":"19739","DOI":"10.1038\/s41598-021-98523-6","volume":"11.1","author":"BC Hiesmayr","year":"2021","unstructured":"Hiesmayr BC (2021) Free versus bound entanglement, a NP-hard problem tackled by machine learning. Sci Rep 11.1:19739","journal-title":"Sci Rep"},{"key":"96_CR41","doi-asserted-by":"publisher","first-page":"4206","DOI":"10.1103\/PhysRevA.59.4206","volume":"59.6","author":"M Horodecki","year":"1999","unstructured":"Horodecki M, Horodecki P (1999) Reduction criterion of separability and limits for a class of distillation protocols. Phys Rev A 59.6:4206","journal-title":"Phys Rev A"},{"key":"96_CR42","doi-asserted-by":"publisher","first-page":"1838","DOI":"10.1103\/PhysRevA.54.1838","volume":"54.3","author":"R Horodecki","year":"1996","unstructured":"Horodecki R (1996) Information-theoretic aspects of inseparability of mixed states. Phys Rev A 54.3:1838","journal-title":"Phys Rev A"},{"key":"96_CR43","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/s42484-021-00061-x","volume":"4.1","author":"T Hur","year":"2022","unstructured":"Hur T, Kim L, Park DK (2022) Quantum convolutional neural network for classical data classification. Quantum Machine Intelligence 4.1:3","journal-title":"Quantum Machine Intelligence"},{"key":"96_CR44","doi-asserted-by":"publisher","first-page":"062336","DOI":"10.1103\/PhysRevA.75.062336","volume":"75","author":"M Ikram","year":"2007","unstructured":"Ikram M, Li F. -l., Zubairy MS (2007) Disentanglement in a two-qubit system subjected to dissipation environments. Phys Rev A 75:062336","journal-title":"Phys Rev A"},{"key":"96_CR45","doi-asserted-by":"publisher","first-page":"022310","DOI":"10.1103\/PhysRevA.62.022310","volume":"62","author":"S Ishizaka","year":"2000","unstructured":"Ishizaka S, Hiroshima T (2000) Maximally entangled mixed states under nonlocal unitary operations in two qubits. Phys Rev A 62:022310","journal-title":"Phys Rev A"},{"key":"96_CR46","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1016\/0034-4877(72)90011-0","volume":"3","author":"A Jamio\u0142kowski","year":"1972","unstructured":"Jamio\u0142kowski A (1972) Linear transformations which preserve trace and positive semideniteness of operators. Rep Math Phys 3:275","journal-title":"Rep Math Phys"},{"key":"96_CR47","doi-asserted-by":"publisher","first-page":"020305","DOI":"10.1088\/1674-1056\/22\/2\/020305","volume":"22.2","author":"Y-H Ji","year":"2013","unstructured":"Ji Y-H, Liu Y-M (2013) Investigations into quantum correlation of coupled qubits in a squeezed vacuum reservoir. Chin Phys B 22.2:020305","journal-title":"Chin Phys B"},{"key":"96_CR48","doi-asserted-by":"crossref","unstructured":"Jordan TF (2009) .. In: Journal of Physics: Conference Series, vol 196 . IOP Publishing, p 012010","DOI":"10.1088\/1742-6596\/196\/1\/012010"},{"key":"96_CR49","doi-asserted-by":"publisher","first-page":"055803","DOI":"10.1103\/PhysRevA.72.055803","volume":"72","author":"A Joshi","year":"2005","unstructured":"Joshi A, Hassan SS, Xiao M (2005) Controlling subluminal to superluminal behavior of group velocity with squeezed reservoir. Phys Rev A 72:055803","journal-title":"Phys Rev A"},{"key":"96_CR50","unstructured":"Jozsa R (1997) Entanglement and quantum computation. arXiv:9707034"},{"key":"96_CR51","doi-asserted-by":"publisher","first-page":"1762","DOI":"10.1007\/s10701-020-00319-7","volume":"50.12","author":"A Khrennikov","year":"2020","unstructured":"Khrennikov A (2020) Quantum versus classical entanglement: eliminating the issue of quantum nonlocality. Found Phys 50.12:1762\u20131780","journal-title":"Found Phys"},{"key":"96_CR52","doi-asserted-by":"publisher","first-page":"033063","DOI":"10.1103\/PhysRevResearch.1.033063","volume":"1.3","author":"N Killoran","year":"2019","unstructured":"Killoran N, et al. (2019) Continuous-variable quantum neural networks. Physical Review Research 1.3:033063","journal-title":"Physical Review Research"},{"key":"96_CR53","unstructured":"Kingma DP, Ba J (2014) Adam: A method for stochastic optimization. arXiv:1412.6980"},{"key":"96_CR54","doi-asserted-by":"publisher","first-page":"205503","DOI":"10.1088\/0953-4075\/43\/20\/205503","volume":"43","author":"A Kowalewska-Kud\u0142aszyk","year":"2010","unstructured":"Kowalewska-Kud\u0142aszyk A, Leo\u0144ski W (2010) Squeezed vacuum reservoir effect for entanglement decay in the nonlinear quantum scissor system. Journal of Physics B. Atomic, molecular and optical physics 43:205503","journal-title":"Journal of Physics B. Atomic, molecular and optical physics"},{"key":"96_CR55","doi-asserted-by":"publisher","first-page":"042307","DOI":"10.1103\/PhysRevA.78.042307","volume":"78.4","author":"B Kraus","year":"2008","unstructured":"Kraus B, et al. (2008) Preparation of entangled states by quantum Markov processes. Phys Rev A 78.4:042307","journal-title":"Phys Rev A"},{"key":"96_CR56","doi-asserted-by":"publisher","first-page":"080503","DOI":"10.1103\/PhysRevLett.107.080503","volume":"107.8","author":"H Krauter","year":"2011","unstructured":"Krauter H, et al. (2011) Entanglement generated by dissipation and steady state entanglement of two macroscopic objects. Phys Rev Lett 107.8:080503","journal-title":"Phys Rev Lett"},{"key":"96_CR57","unstructured":"Levine Y, Yakira D, Cohen N, Shashua A (2017) Deep learning and quantum entanglement: Fundamental connections with implications to network design. arXiv:1704.01552"},{"key":"96_CR58","doi-asserted-by":"publisher","first-page":"415","DOI":"10.1038\/nature12801","volume":"504","author":"Y Lin","year":"2013","unstructured":"Lin Y, Gaebler J, Reiter F, Tan TR, Bowler R, S\u00f8rensen A, Leibfried D, Wineland DJ (2013) Dissipative production of a maximally entangled steady state of two quantum bits. Nature 504:415","journal-title":"Nature"},{"key":"96_CR59","first-page":"M34","volume":"2014","author":"Y Lin","year":"2014","unstructured":"Lin Y, Gaebler J, Reiter F, Tan TR, Bowler R, S\u00f8rensen A, Leibfried D, Wineland D, Collaboration N et al (2014) . APS March Meeting Abstracts 2014:M34\u2013012","journal-title":"APS March Meeting Abstracts"},{"key":"96_CR60","doi-asserted-by":"publisher","first-page":"280","DOI":"10.1364\/OPTICA.443302","volume":"9.3","author":"NB Lingaraju","year":"2022","unstructured":"Lingaraju NB, et al. (2022) Bell state analyzer for spectrally distinct photons. Optica 9.3:280\u2013283","journal-title":"Optica"},{"key":"96_CR61","unstructured":"Lloyd S, et al. (2020) Quantum embeddings for machine learning. arXiv:2001.03622"},{"key":"96_CR62","doi-asserted-by":"publisher","first-page":"012315","DOI":"10.1103\/PhysRevA.98.012315","volume":"98","author":"S Lu","year":"2018","unstructured":"Lu S, Huang S, Li K, Li J, Chen J, Lu D, Ji Z, Shen Y, Zhou D, Zeng B (2018) Separability-entanglement classifier via machine learning. Phys Rev A 98:012315","journal-title":"Phys Rev A"},{"key":"96_CR63","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s41534-018-0081-3","volume":"4","author":"Y-C Ma","year":"2018","unstructured":"Ma Y-C, Yung M-H (2018) Transforming Bells inequalities into state classifiers with machine learning. npj Quantum Information 4:1","journal-title":"npj Quantum Information"},{"key":"96_CR64","volume-title":"Information theory inference and learning algorithms","author":"DJ MacKay","year":"2003","unstructured":"MacKay DJ, Mac Kay DJ et al (2003) Information theory inference and learning algorithms. Cambridge University Press, Cambridge"},{"key":"96_CR65","doi-asserted-by":"publisher","first-page":"200501","DOI":"10.1103\/PhysRevLett.114.200501","volume":"114","author":"E Magesan","year":"2015","unstructured":"Magesan E, Gambetta JM, C\u00f3rcoles AD, Chow JM (2015) Machine learning for discriminating quantum measurement trajectories and improving readout. Phys Rev Lett 114:200501","journal-title":"Phys Rev Lett"},{"key":"96_CR66","doi-asserted-by":"crossref","unstructured":"Malouf R (2002) A comparison of algorithms for maximum entropy parameter estimation. COLING-02: The 6th conference on natural language learning 2002 (CoNLL-2002)","DOI":"10.3115\/1118853.1118871"},{"key":"96_CR67","doi-asserted-by":"publisher","first-page":"340","DOI":"10.22331\/q-2020-10-09-340","volume":"4","author":"A Mari","year":"2020","unstructured":"Mari A, Bromley TR, Izaac J, Schuld M, Killoran N (2020) Transfer learning in hybrid classical-quantum neural networks. Quantum 4:340","journal-title":"Quantum"},{"key":"96_CR68","doi-asserted-by":"publisher","first-page":"042329","DOI":"10.1103\/PhysRevA.83.042329","volume":"83.4","author":"L Memarzadeh","year":"2011","unstructured":"Memarzadeh L, Mancini S (2011) Stationary entanglement achievable by environment-induced chain links. Phys Rev A 83.4:042329","journal-title":"Phys Rev A"},{"key":"96_CR69","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1007\/s42484-019-00007-4","volume":"1.3-4","author":"R Mengoni","year":"2019","unstructured":"Mengoni R, Di Pierro A (2019) Kernel methods in quantum machine learning. Quantum Machine Intelligence 1.3-4:65\u201371","journal-title":"Quantum Machine Intelligence"},{"key":"96_CR70","doi-asserted-by":"publisher","first-page":"44","DOI":"10.1016\/j.cpc.2017.06.011","volume":"220","author":"K Michielsen","year":"2017","unstructured":"Michielsen K, Nocon M, Willsch D, Jin F, Lippert T, De Raedt H (2017) Benchmarking gate-based quantum computers. Comput Phys Commun 220:44","journal-title":"Comput Phys Commun"},{"key":"96_CR71","doi-asserted-by":"publisher","first-page":"070502","DOI":"10.1103\/PhysRevLett.99.070502","volume":"99","author":"A Mizel","year":"2007","unstructured":"Mizel A, Lidar DA, Mitchell M (2007) Simple proof of equivalence between adiabatic quantum computation and the circuit model. Physical review letters 99:070502","journal-title":"Physical review letters"},{"key":"96_CR72","doi-asserted-by":"publisher","first-page":"030503","DOI":"10.1088\/2058-9565\/aab822","volume":"3","author":"N Moll","year":"2018","unstructured":"Moll N, Barkoutsos P, Bishop LS, Chow JM, Cross A, Egger DJ, Filipp S, Fuhrer A, Gambetta JM, Ganzhorn M et al (2018) Quantum optimization using variational algorithms on near-term quantum devices. Quantum Science and Technology 3:030503","journal-title":"Quantum Science and Technology"},{"key":"96_CR73","unstructured":"Narayanan A (1999) Quantum computing for beginners. In: Proceedings of the 1999 congress on evolutionary computation-CEC99 (Cat. No. 99TH8406), vol 3. IEEE"},{"key":"96_CR74","doi-asserted-by":"crossref","unstructured":"Nielsen MA, Chuang I (2002) Quantum computation and quantum information, 558\u2013559. Published in the United States of America by Cambridge University Press, New York","DOI":"10.1119\/1.1463744"},{"key":"96_CR75","unstructured":"Nielson MA, Chuang IL (2000) Quantum computation and quantum information. Published in the United States of America by Cambridge University Press, New York"},{"key":"96_CR76","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1038\/s41586-020-2170-7","volume":"580.7803","author":"L Petit","year":"2020","unstructured":"Petit L, Eenink H, Russ M, Lawrie W, Hendrickx N, Philips S, Clarke J, Vandersypen L, Veldhorst M (2020) Universal quantum logic in hot silicon qubits. Nature 580.7803:355\u2013359","journal-title":"Nature"},{"key":"96_CR77","doi-asserted-by":"publisher","first-page":"197901","DOI":"10.1103\/PhysRevLett.88.197901","volume":"88.19","author":"MB Plenio","year":"2002","unstructured":"Plenio MB, Huelga SF (2002) Entangled light from white noise. Phys Rev Lett 88.19:197901","journal-title":"Phys Rev Lett"},{"key":"96_CR78","doi-asserted-by":"crossref","unstructured":"Rabanal P, Rodr\u00edguez I, Rubio F (2007) Using river formation dynamics to design heuristic algorithms. In: International conference on unconventional computation. Springer, pp 163\u2013177","DOI":"10.1007\/978-3-540-73554-0_16"},{"key":"96_CR79","doi-asserted-by":"publisher","first-page":"1213","DOI":"10.1103\/RevModPhys.78.1213","volume":"78","author":"MI Rabinovich","year":"2006","unstructured":"Rabinovich MI, Varona P, Selverston AI, Abarbanel HD (2006) Dynamical principles in neuroscience. Rev Mod Phys 78:1213","journal-title":"Rev Mod Phys"},{"key":"96_CR80","doi-asserted-by":"publisher","first-page":"032301","DOI":"10.1103\/PhysRevA.61.032301","volume":"61","author":"A Rau","year":"2000","unstructured":"Rau A (2000) Manipulating two-spin coherences and qubit pairs. Phys Rev A 61:032301","journal-title":"Phys Rev A"},{"key":"96_CR81","doi-asserted-by":"publisher","first-page":"412002","DOI":"10.1088\/1751-8113\/42\/41\/412002","volume":"42","author":"A Rau","year":"2009","unstructured":"Rau A (2009) Algebraic characterization of X-states in quantum information. Journal of physics a: Mathematical and theoretical 42:412002","journal-title":"Journal of physics a: Mathematical and theoretical"},{"key":"96_CR82","doi-asserted-by":"publisher","unstructured":"Scala F, et al. (2022) Quantum variational learning for entanglement witnessing. In: 2022 International Joint Conference on Neural Networks (IJCNN), Padua, Italy. https:\/\/doi.org\/10.1109\/IJCNN55064.2022.9892080, pp 1\u20138","DOI":"10.1109\/IJCNN55064.2022.9892080"},{"key":"96_CR83","doi-asserted-by":"publisher","first-page":"270503","DOI":"10.1103\/PhysRevLett.127.270503","volume":"127.27","author":"AW Schlimgen","year":"2021","unstructured":"Schlimgen AW et al (2021) Quantum simulation of open quantum systems using a unitary decomposition of operators. Phys Rev Lett 127.27:270503","journal-title":"Phys Rev Lett"},{"key":"96_CR84","doi-asserted-by":"publisher","first-page":"032308","DOI":"10.1103\/PhysRevA.101.032308","volume":"101.3","author":"M Schuld","year":"2020","unstructured":"Schuld M, et al. (2020) Circuit-centric quantum classifiers. Phys Rev A 101.3:032308","journal-title":"Phys Rev A"},{"key":"96_CR85","doi-asserted-by":"publisher","first-page":"040504","DOI":"10.1103\/PhysRevLett.122.040504","volume":"122.4","author":"M Schuld","year":"2019","unstructured":"Schuld M, Killoran N (2019) Quantum machine learning in feature hilbert spaces. Physical review letters 122.4:040504","journal-title":"Physical review letters"},{"key":"96_CR86","doi-asserted-by":"publisher","first-page":"2567","DOI":"10.1007\/s11128-014-0809-8","volume":"13","author":"M Schuld","year":"2014","unstructured":"Schuld M, Sinayskiy I, Petruccione F (2014) The quest for a quantum neural network. Quantum Inf Process 13:2567","journal-title":"Quantum Inf Process"},{"key":"96_CR87","doi-asserted-by":"crossref","unstructured":"Scully MO, Zubairy MS (1999) Quantum optics","DOI":"10.1119\/1.19344"},{"key":"96_CR88","doi-asserted-by":"publisher","first-page":"441","DOI":"10.1038\/nphoton.2017.93","volume":"11","author":"Y Shen","year":"2017","unstructured":"Shen Y, Harris NC, Skirlo S, Prabhu M, Baehr-Jones T, Hochberg M, Sun X, Zhao S, Larochelle H, Englund D et al (2017) Deep learning with coherent nanophotonic circuits. Nature photonics 11:441","journal-title":"Nature photonics"},{"key":"96_CR89","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s42005-021-00784-0","volume":"5","author":"SE Smart","year":"2022","unstructured":"Smart SE, Hu Z, Kais S, Mazziotti DA (2022) . Communications Physics 5:1","journal-title":"Communications Physics"},{"key":"96_CR90","doi-asserted-by":"publisher","first-page":"060902","DOI":"10.1063\/1.5100160","volume":"4","author":"S Takeda","year":"2019","unstructured":"Takeda S, Furusawa A (2019) . APL Photonics 4:060902","journal-title":"APL Photonics"},{"key":"96_CR91","doi-asserted-by":"publisher","first-page":"5259","DOI":"10.1098\/rsta.2011.0485","volume":"370","author":"F Ticozzi","year":"2012","unstructured":"Ticozzi F, Viola L (2012) Stabilizing entangled states with quasi-local quantum dynamical semigroups. Philosophical Transactions of the Royal Society A Mathematical, Physical and Engineering Sciences 370:5259","journal-title":"Philosophical Transactions of the Royal Society A Mathematical, Physical and Engineering Sciences"},{"key":"96_CR92","doi-asserted-by":"publisher","first-page":"080502","DOI":"10.1103\/PhysRevLett.122.080502","volume":"122","author":"S Touzard","year":"2019","unstructured":"Touzard S, Kou A, Frattini N, Sivak V, Puri S, Grimm A, Frunzio L, Shankar S, Devoret M (2019) Gated conditional displacement readout of superconducting qubits. Phys Rev Lett 122: 080502","journal-title":"Phys Rev Lett"},{"key":"96_CR93","doi-asserted-by":"publisher","first-page":"012316","DOI":"10.1103\/PhysRevA.64.012316","volume":"64.1","author":"F Verstraete","year":"2001","unstructured":"Verstraete F, Audenaert K, De Moor B (2001) Maximally entangled mixed states of two qubits. Phys Rev A 64.1:012316","journal-title":"Phys Rev A"},{"key":"96_CR94","doi-asserted-by":"publisher","first-page":"633","DOI":"10.1038\/nphys1342","volume":"5","author":"F Verstraete","year":"2009","unstructured":"Verstraete F, Wolf MM, Ignacio Cirac J (2009) Quantum computation and quantum-state engineering driven by dissipation. Nat Phys 5:633","journal-title":"Nat Phys"},{"key":"96_CR95","doi-asserted-by":"publisher","first-page":"4277","DOI":"10.1103\/PhysRevA.40.4277","volume":"40","author":"RF Werner","year":"1989","unstructured":"Werner RF (1989) Quantum states with Einstein-Podolsky-Rosen correlations admitting a hiddenvariable model. Phys Rev A 40:4277","journal-title":"Phys Rev A"},{"key":"96_CR96","doi-asserted-by":"crossref","unstructured":"Wiseman HM, Milburn GJ (2009) Quantum measurement and control. Cambridge University Press","DOI":"10.1017\/CBO9780511813948"},{"key":"96_CR97","doi-asserted-by":"publisher","first-page":"1198","DOI":"10.1007\/s10773-016-3262-x","volume":"56","author":"S-X Wu","year":"2017","unstructured":"Wu S-X, Yu C-S (2017) The precision of parameter estimation for dephasing model under squeezed reservoir. Int J Theor Phys 56:1198","journal-title":"Int J Theor Phys"},{"key":"96_CR98","doi-asserted-by":"publisher","first-page":"043615","DOI":"10.1103\/PhysRevA.98.043615","volume":"98.4","author":"Y Yanay","year":"2018","unstructured":"Yanay Y, Clerk AA (2018) Reservoir engineering of bosonic lattices using chiral symmetry and localized dissipation. Phys Rev A 98.4:043615","journal-title":"Phys Rev A"},{"key":"96_CR99","doi-asserted-by":"publisher","first-page":"190401","DOI":"10.1103\/PhysRevLett.123.190401","volume":"123.19","author":"M Yang","year":"2019","unstructured":"Yang M, et al. (2019) Experimental simultaneous learning of multiple nonclassical correlations. Phys Rev Lett 123.19:190401","journal-title":"Phys Rev Lett"},{"key":"96_CR100","doi-asserted-by":"publisher","first-page":"033041","DOI":"10.1088\/1367-2630\/ab7598","volume":"22","author":"Z Yang","year":"2020","unstructured":"Yang Z, Zhang X (2020) Entanglement-based quantum deep learning. New J Phys 22:033041","journal-title":"New J Phys"},{"key":"96_CR101","doi-asserted-by":"publisher","first-page":"022334","DOI":"10.1103\/PhysRevA.78.022334","volume":"78","author":"Y Yeo","year":"2008","unstructured":"Yeo Y (2008) Local noise can enhance two-qubit teleportation. Phys Rev A 78:022334","journal-title":"Phys Rev A"},{"key":"96_CR102","doi-asserted-by":"publisher","first-page":"140404","DOI":"10.1103\/PhysRevLett.93.140404","volume":"93","author":"T Yu","year":"2004","unstructured":"Yu T, Eberly J (2004) Finite-time disentanglement via spontaneous emission. Phys Rev Lett 93:140404","journal-title":"Phys Rev Lett"},{"key":"96_CR103","doi-asserted-by":"publisher","first-page":"140403","DOI":"10.1103\/PhysRevLett.97.140403","volume":"97","author":"T Yu","year":"2006","unstructured":"Yu T, Eberly J (2006) Quantum open system theory: bipartite aspects. Phys Rev Lett 97:140403","journal-title":"Phys Rev Lett"},{"key":"96_CR104","doi-asserted-by":"publisher","first-page":"651","DOI":"10.1023\/A:1026656110699","volume":"37","author":"M Zak","year":"1998","unstructured":"Zak M, Williams CP (1998) Quantum neural nets. Int J Theor Phys 37:651","journal-title":"Int J Theor Phys"},{"key":"96_CR105","first-page":"021041","volume":"7","author":"S Zeytino\u011flu","year":"2017","unstructured":"Zeytino\u011flu S, \u0130mamo\u0121lu A, Huber S (2017) Engineering matter interactions using squeezed vacuum. Phys Rev X 7:021041","journal-title":"Phys Rev X"},{"key":"96_CR106","doi-asserted-by":"publisher","first-page":"062315","DOI":"10.1103\/PhysRevA.66.062315","volume":"66.6","author":"Y-S Zhang","year":"2002","unstructured":"Zhang Y-S, et al. (2002) Experimental preparation of the Werner state via spontaneous parametric down-conversion. Phys Rev A 66.6:062315","journal-title":"Phys Rev A"},{"key":"96_CR107","doi-asserted-by":"publisher","first-page":"240502","DOI":"10.1103\/PhysRevLett.98.240502","volume":"98.24","author":"B Zhao","year":"2007","unstructured":"Zhao B, Chen Z-B, Chen Y-A, Schmiedmayer J, Pan J-W (2007) Robust creation of entanglement between remote memory qubits. Phys Rev Lett 98.24:240502","journal-title":"Phys Rev Lett"},{"key":"96_CR108","doi-asserted-by":"publisher","first-page":"020402","DOI":"10.1103\/PhysRevLett.126.020402","volume":"126","author":"S Zippilli","year":"2021","unstructured":"Zippilli S, Vitali D (2021) Dissipative engineering of Gaussian entangled states in harmonic lattices with a single-site squeezed reservoir. Phys Rev Lett 126:020402","journal-title":"Phys Rev Lett"},{"key":"96_CR109","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s42484-020-00033-7","volume":"3","author":"C Zoufal","year":"2021","unstructured":"Zoufal C, Lucchi A, Woerner S (2021) Variational quantum Boltzmann machines. Quantum Machine Intelligence 3:1","journal-title":"Quantum Machine Intelligence"}],"container-title":["Quantum Machine Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s42484-023-00096-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s42484-023-00096-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s42484-023-00096-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,19]],"date-time":"2023-06-19T04:02:51Z","timestamp":1687147371000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s42484-023-00096-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,25]]},"references-count":109,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2023,6]]}},"alternative-id":["96"],"URL":"https:\/\/doi.org\/10.1007\/s42484-023-00096-2","relation":{"has-preprint":[{"id-type":"doi","id":"10.21203\/rs.3.rs-2034606\/v1","asserted-by":"object"}]},"ISSN":["2524-4906","2524-4914"],"issn-type":[{"value":"2524-4906","type":"print"},{"value":"2524-4914","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2,25]]},"assertion":[{"value":"5 September 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 January 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 February 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":"Not applicable","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"<!--Emphasis Type='Bold' removed-->Ethics approval and consent to participate"}},{"value":"Not applicable","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"<!--Emphasis Type='Bold' removed-->Consent for publication"}},{"value":"Not applicable","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"<!--Emphasis Type='Bold' removed-->Human and animal ethics"}},{"value":"The author declares no competing interests.","order":5,"name":"Ethics","group":{"name":"EthicsHeading","label":"<!--Emphasis Type='Bold' removed-->Conflict of interest"}}],"article-number":"13"}}