{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,8]],"date-time":"2026-05-08T15:48:51Z","timestamp":1778255331231,"version":"3.51.4"},"reference-count":84,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T00:00:00Z","timestamp":1648598400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"We propose a quantum representation of binary classification trees with binary features based on a probabilistic approach. By using the quantum computer as a processor for probability distributions, a probabilistic traversal of the decision tree can be realized via measurements of a quantum circuit. We describe how tree inductions and the prediction of class labels of query data can be integrated into this framework. An on-demand sampling method enables predictions with a constant number of classical memory slots, independent of the tree depth. We experimentally study our approach using both a quantum computing simulator and actual IBM quantum hardware. To our knowledge, this is the first realization of a decision tree classifier on a quantum device.<\/jats:p>","DOI":"10.22331\/q-2022-03-30-676","type":"journal-article","created":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T16:39:43Z","timestamp":1648658383000},"page":"676","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":21,"title":["Representation of binary classification trees with binary features by quantum circuits"],"prefix":"10.22331","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7479-3339","authenticated-orcid":false,"given":"Raoul","family":"Heese","sequence":"first","affiliation":[{"name":"Fraunhofer ITWM, 67663 Kaiserslautern, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0737-7604","authenticated-orcid":false,"given":"Patricia","family":"Bickert","sequence":"additional","affiliation":[{"name":"Fraunhofer ITWM, 67663 Kaiserslautern, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2171-8639","authenticated-orcid":false,"given":"Astrid Elisa","family":"Niederle","sequence":"additional","affiliation":[{"name":"BASF SE, 67063 Ludwigshafen, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2022,3,30]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"S.B. Kotsiantis ``Decision trees: a recent overview'' Artif Intell Rev 39, 261-283 (2013).","DOI":"10.1007\/s10462-011-9272-4"},{"key":"1","unstructured":"O.Z. Maimonand L. Rokach ``Data Mining With Decision Trees: Theory And Applications'' World Scientific Publishing Company (2014)."},{"key":"2","doi-asserted-by":"crossref","unstructured":"L. Breiman ``Classification and Regression Trees'' CRC Press (2017).","DOI":"10.1201\/9781315139470"},{"key":"3","doi-asserted-by":"publisher","unstructured":"Laurent Hyafiland Ronald L. Rivest ``Constructing optimal binary decision trees is NP-complete'' Information Processing Letters 5, 15\u201317 (1976).","DOI":"10.1016\/0020-0190(76)90095-8"},{"key":"4","doi-asserted-by":"publisher","unstructured":"Dimitris Bertsimasand Jack Dunn ``Optimal classification trees'' Machine Learning 106, 1039\u20131082 (2017).","DOI":"10.1007\/s10994-017-5633-9"},{"key":"5","unstructured":"Arman Zharmagambetov, Suryabhan Singh Hada, Miguel \u00c1. Carreira-Perpi\u00f1\u00e1n, and Magzhan Gabidolla, ``An Experimental Comparison of Old and New Decision Tree Algorithms'' (2020)."},{"key":"6","doi-asserted-by":"publisher","unstructured":"J.R. Quinlan ``Induction of decision trees'' Machine Learning 1, 81\u2013706 (1986).","DOI":"10.1007\/BF00116251"},{"key":"7","doi-asserted-by":"publisher","unstructured":"Jacob Biamonte, Peter Wittek, Nicola Pancotti, Patrick Rebentrost, Nathan Wiebe, and Seth Lloyd, ``Quantum machine learning'' Nature 549, 195\u2013202 (2017).","DOI":"10.1038\/nature23474"},{"key":"8","doi-asserted-by":"publisher","unstructured":"Edward Farhiand Sam Gutmann ``Quantum computation and decision trees'' Phys. Rev. A 58, 915\u2013928 (1998).","DOI":"10.1103\/PhysRevA.58.915"},{"key":"9","doi-asserted-by":"publisher","unstructured":"Songfeng Luand Samuel L. Braunstein ``Quantum decision tree classifier'' Quantum Information Processing 13, 757\u2013770 (2014).","DOI":"10.1007\/s11128-013-0687-5"},{"key":"10","doi-asserted-by":"publisher","unstructured":"Maria Schuld, Ilya Sinayskiy, and Francesco Petruccione, ``An introduction to quantum machine learning'' Contemporary Physics 56, 172\u2013185 (2015).","DOI":"10.1080\/00107514.2014.964942"},{"key":"11","unstructured":"Kamil Khadiev, Ilnaz Mannapov, and Liliya Safina, ``The Quantum Version Of Classification Decision Tree Constructing Algorithm C5.0'' (2019)."},{"key":"12","doi-asserted-by":"publisher","unstructured":"Vittorio Giovannetti, Seth Lloyd, and Lorenzo Maccone, ``Quantum Random Access Memory'' Physical Review Letters 100 (2008).","DOI":"10.1103\/physrevlett.100.160501"},{"key":"13","unstructured":"Iordanis Kerenidisand Anupam Prakash ``Quantum Recommendation Systems'' (2016)."},{"key":"14","unstructured":"Howard Barnum, M Saks, and M Szegedy, ``Quantum Decision Trees and Semidefinite Programming'' (2001)."},{"key":"15","doi-asserted-by":"publisher","unstructured":"Harry Buhrmanand Ronald de Wolf ``Complexity measures and decision tree complexity: a survey'' Theoretical Computer Science 288, 21\u201343 (2002) Complexity and Logic.","DOI":"10.1016\/S0304-3975(01)00144-X"},{"key":"16","doi-asserted-by":"publisher","unstructured":"Yaoyun Shi ``Entropy lower bounds for quantum decision tree complexity'' Information Processing Letters 81, 23\u201327 (2002).","DOI":"10.1016\/S0020-0190(01)00191-0"},{"key":"17","doi-asserted-by":"publisher","unstructured":"Salman Beigiand Leila Taghavi ``Quantum Speedup Based on Classical Decision Trees'' Quantum 4, 241 (2020).","DOI":"10.22331\/q-2020-03-02-241"},{"key":"18","doi-asserted-by":"publisher","unstructured":"Cristian S. Calude, Michael J. Dinneen, Monica Dumitrescu, and Karl Svozil, ``Experimental evidence of quantum randomness incomputability'' Physical Review A 82 (2010).","DOI":"10.1103\/physreva.82.022102"},{"key":"19","doi-asserted-by":"publisher","unstructured":"Johannes Koflerand Anton Zeilinger ``Quantum Information and Randomness'' European Review 18, 469\u2013480 (2010).","DOI":"10.1017\/s1062798710000268"},{"key":"20","doi-asserted-by":"publisher","unstructured":"Sourabh Katoch, Sumit Singh Chauhan, and Vijay Kumar, ``A review on genetic algorithm: past, present, and future'' Multimedia Tools and Applications 80, 8091\u20138126 (2021).","DOI":"10.1007\/s11042-020-10139-6"},{"key":"21","doi-asserted-by":"publisher","unstructured":"Guang Hao Low, Theodore J. Yoder, and Isaac L. Chuang, ``Quantum inference on Bayesian networks'' Phys. Rev. A 89, 062315 (2014).","DOI":"10.1103\/PhysRevA.89.062315"},{"key":"22","doi-asserted-by":"publisher","unstructured":"Sima E. Borujeni, Nam H. Nguyen, Saideep Nannapaneni, Elizabeth C. Behrman, and James E. Steck, ``Experimental evaluation of quantum Bayesian networks on IBM QX hardware'' 2020 IEEE International Conference on Quantum Computing and Engineering (QCE) 372\u2013378 (2020).","DOI":"10.1109\/QCE49297.2020.00053"},{"key":"23","doi-asserted-by":"publisher","unstructured":"Michael de Oliveiraand Luis Soares Barbosa ``Quantum Bayesian Decision-Making'' Foundations of Science (2021).","DOI":"10.1007\/s10699-021-09781-6"},{"key":"24","doi-asserted-by":"publisher","unstructured":"S. Akers ``Binary Decision Diagrams'' IEEE Transactions on Computers 27, 509\u2013516 (1978).","DOI":"10.1109\/TC.1978.1675141"},{"key":"25","doi-asserted-by":"publisher","unstructured":"Foster Provostand Pedro Domingos ``Tree Induction for Probability-Based Ranking'' Machine Learning 52, 199\u2013215 (2003).","DOI":"10.1023\/A:1024099825458"},{"key":"26","unstructured":"Melanie Mitchell ``An Introduction to Genetic Algorithms'' MIT Press, Cambridge (1999)."},{"key":"27","unstructured":"Alvaro H. C. Correia, Robert Peharz, and Cassio de Campos, ``Joints in Random Forests'' (2020)."},{"key":"28","doi-asserted-by":"crossref","unstructured":"M. A. Nielsenand I. L. Chuang ``Quantum Computation and Quantum Information: 10th Anniversary Edition'' Cambridge University Press (2010).","DOI":"10.1017\/CBO9780511976667"},{"key":"29","unstructured":"Lov Groverand Terry Rudolph ``Creating superpositions that correspond to efficiently integrable probability distributions'' (2002)."},{"key":"30","doi-asserted-by":"publisher","unstructured":"Maris Ozols, Martin Roetteler, and J\u00e9r\u00e9mie Roland, ``Quantum rejection sampling'' Proceedings of the 3rd Innovations in Theoretical Computer Science Conference on - ITCS'12 (2012).","DOI":"10.1145\/2090236.2090261"},{"key":"31","doi-asserted-by":"crossref","unstructured":"Maria Schuldand Francesco Petruccione ``Supervised Learning with Quantum Computers'' Springer International Publishing (2018).","DOI":"10.1007\/978-3-319-96424-9"},{"key":"32","doi-asserted-by":"crossref","unstructured":"Mikko M\u00f6tt\u00f6nen, Juha J. Vartiainen, Ville Bergholm, and Martti M. Salomaa, ``Transformation of Quantum States Using Uniformly Controlled Rotations'' Quantum Info. Comput. 5, 467\u2013473 (2005).","DOI":"10.26421\/QIC5.6-5"},{"key":"33","doi-asserted-by":"publisher","unstructured":"V.V. Shende, S.S. Bullock, and I.L. Markov, ``Synthesis of quantum-logic circuits'' IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 25, 1000\u20131010 (2006).","DOI":"10.1109\/tcad.2005.855930"},{"key":"34","doi-asserted-by":"publisher","unstructured":"Martin Pleschand \u010caslav Brukner ``Quantum-state preparation with universal gate decompositions'' Physical Review A 83 (2011).","DOI":"10.1103\/physreva.83.032302"},{"key":"35","doi-asserted-by":"publisher","unstructured":"Yuval R. Sanders, Guang Hao Low, Artur Scherer, and Dominic W. Berry, ``Black-Box Quantum State Preparation without Arithmetic'' Physical Review Letters 122 (2019).","DOI":"10.1103\/physrevlett.122.020502"},{"key":"36","doi-asserted-by":"crossref","unstructured":"Johannes Bausch ``Fast Black-Box Quantum State Preparation'' (2021).","DOI":"10.22331\/q-2022-08-04-773"},{"key":"37","doi-asserted-by":"publisher","unstructured":"Pierre-Luc Dallaire-Demersand Nathan Killoran ``Quantum generative adversarial networks'' Physical Review A 98 (2018).","DOI":"10.1103\/physreva.98.012324"},{"key":"38","doi-asserted-by":"publisher","unstructured":"Marcello Benedetti, Erika Lloyd, Stefan Sack, and Mattia Fiorentini, ``Parameterized quantum circuits as machine learning models'' Quantum Science and Technology 4, 043001 (2019).","DOI":"10.1088\/2058-9565\/ab4eb5"},{"key":"39","doi-asserted-by":"publisher","unstructured":"Ling Hu, Shu-Hao Wu, Weizhou Cai, Yuwei Ma, Xianghao Mu, Yuan Xu, Haiyan Wang, Yipu Song, Dong-Ling Deng, Chang-Ling Zou, and Luyan Sun, ``Quantum generative adversarial learning in a superconducting quantum circuit'' Science Advances 5 (2019).","DOI":"10.1126\/sciadv.aav2761"},{"key":"40","doi-asserted-by":"publisher","unstructured":"Christa Zoufal, Aur\u00e9lien Lucchi, and Stefan Woerner, ``Quantum Generative Adversarial Networks for learning and loading random distributions'' npj Quantum Information 5, 103 (2019).","DOI":"10.1038\/s41534-019-0223-2"},{"key":"41","doi-asserted-by":"publisher","unstructured":"Adriano Barenco, Charles H. Bennett, Richard Cleve, David P. DiVincenzo, Norman Margolus, Peter Shor, Tycho Sleator, John A. Smolin, and Harald Weinfurter, ``Elementary gates for quantum computation'' Physical Review A 52, 3457\u20133467 (1995).","DOI":"10.1103\/physreva.52.3457"},{"key":"42","doi-asserted-by":"publisher","unstructured":"Israel F. Araujo, Daniel K. Park, Francesco Petruccione, and Adenilton J. da Silva, ``A divide-and-conquer algorithm for quantum state preparation'' Scientific Reports 11, 6329 (2021).","DOI":"10.1038\/s41598-021-85474-1"},{"key":"43","unstructured":"Xiaoming Sun, Guojing Tian, Shuai Yang, Pei Yuan, and Shengyu Zhang, ``Asymptotically Optimal Circuit Depth for Quantum State Preparation and General Unitary Synthesis'' (2021)."},{"key":"44","doi-asserted-by":"crossref","unstructured":"Xiao-Ming Zhang, Man-Hong Yung, and Xiao Yuan, ``Low-depth Quantum State Preparation'' (2021).","DOI":"10.1103\/PhysRevResearch.3.043200"},{"key":"45","doi-asserted-by":"crossref","unstructured":"Ji Liu, Luciano Bello, and Huiyang Zhou, ``Relaxed Peephole Optimization: A Novel Compiler Optimization for Quantum Circuits'' (2020).","DOI":"10.1109\/CGO51591.2021.9370310"},{"key":"46","doi-asserted-by":"publisher","unstructured":"Laxmidhar Biswal, Debjyoti Bhattacharjee, Anupam Chattopadhyay, and Hafizur Rahaman, ``Techniques for fault-tolerant decomposition of a multicontrolled Toffoli gate'' Physical Review A 100 (2019).","DOI":"10.1103\/physreva.100.062326"},{"key":"47","doi-asserted-by":"publisher","unstructured":"Mehdi Saeediand Massoud Pedram ``Linear-depth quantum circuits forn-qubit Toffoli gates with no ancilla'' Physical Review A 87 (2013).","DOI":"10.1103\/physreva.87.062318"},{"key":"48","doi-asserted-by":"publisher","unstructured":"Manabendra Nath Bera, Antonio Ac\u00edn, Marek Ku\u015b, Morgan W Mitchell, and Maciej Lewenstein, ``Randomness in quantum mechanics: philosophy, physics and technology'' Reports on Progress in Physics 80, 124001 (2017).","DOI":"10.1088\/1361-6633\/aa8731"},{"key":"49","doi-asserted-by":"publisher","unstructured":"M. Cerezo, Andrew Arrasmith, Ryan Babbush, Simon C. Benjamin, Suguru Endo, Keisuke Fujii, Jarrod R. McClean, Kosuke Mitarai, Xiao Yuan, Lukasz Cincio, and Patrick J. Coles, ``Variational Quantum Algorithms'' (2020).","DOI":"10.1038\/s42254-021-00348-9"},{"key":"50","doi-asserted-by":"publisher","unstructured":"W. Zhai, P. Kelly, and W.-B. Gong, ``Genetic algorithms with noisy fitness'' Mathematical and Computer Modelling 23, 131\u2013142 (1996).","DOI":"10.1016\/0895-7177(96)00068-4"},{"key":"51","doi-asserted-by":"publisher","unstructured":"Donald A. Sofge ``Toward a Framework for Quantum Evolutionary Computation'' 2006 IEEE Conference on Cybernetics and Intelligent Systems 1\u20136 (2006).","DOI":"10.1109\/ICCIS.2006.252360"},{"key":"52","doi-asserted-by":"publisher","unstructured":"Gexiang Zhang ``Quantum-inspired evolutionary algorithms: a survey and empirical study'' Journal of Heuristics 17, 303\u2013351 (2011).","DOI":"10.1007\/s10732-010-9136-0"},{"key":"53","doi-asserted-by":"publisher","unstructured":"Rafael Lahoz-Beltra ``Quantum Genetic Algorithms for Computer Scientists'' Computers 5 (2016).","DOI":"10.3390\/computers5040024"},{"key":"54","doi-asserted-by":"publisher","unstructured":"Harper R. Grimsley, Sophia E. Economou, Edwin Barnes, and Nicholas J. Mayhall, ``An adaptive variational algorithm for exact molecular simulations on a quantum computer'' Nature Communications 10, 3007 (2019).","DOI":"10.1038\/s41467-019-10988-2"},{"key":"55","unstructured":"Arthur G. Rattew, Shaohan Hu, Marco Pistoia, Richard Chen, and Steve Wood, ``A Domain-agnostic, Noise-resistant, Hardware-efficient Evolutionary Variational Quantum Eigensolver'' (2020)."},{"key":"56","doi-asserted-by":"crossref","unstructured":"L. Franken, B. Georgiev, S. Muecke, M. Wolter, N. Piatkowski, and C. Bauckhage, ``Gradient-free quantum optimization on NISQ devices'' (2021).","DOI":"10.1109\/CEC55065.2022.9870269"},{"key":"57","doi-asserted-by":"publisher","unstructured":"Andrew Arrasmith, M. Cerezo, Piotr Czarnik, Lukasz Cincio, and Patrick J. Coles, ``Effect of barren plateaus on gradient-free optimization'' (2020).","DOI":"10.22331\/q-2021-10-05-558"},{"key":"58","unstructured":"David W. Aha ``Tic-Tac-Toe Endgame Data Set'' (1991) accessed June 2021."},{"key":"59","unstructured":"Dheeru Duaand Casey Graff ``UCI Machine Learning Repository'' (2017)."},{"key":"60","doi-asserted-by":"publisher","unstructured":"``Qiskit: An Open-source Framework for Quantum Computing'' (2019).","DOI":"10.5281\/zenodo.2562110"},{"key":"61","unstructured":"F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay, ``Scikit-learn: Machine Learning in Python'' Journal of Machine Learning Research 12, 2825\u20132830 (2011)."},{"key":"62","doi-asserted-by":"publisher","unstructured":"John Preskill ``Quantum Computing in the NISQ era and beyond'' Quantum 2, 79 (2018).","DOI":"10.22331\/q-2018-08-06-79"},{"key":"63","unstructured":"IBM ``IBM Quantum'' (2021)."},{"key":"64","doi-asserted-by":"publisher","unstructured":"Ryan LaRose ``Overview and Comparison of Gate Level Quantum Software Platforms'' Quantum 3, 130 (2019).","DOI":"10.22331\/q-2019-03-25-130"},{"key":"65","doi-asserted-by":"publisher","unstructured":"Andrew W. Cross, Lev S. Bishop, Sarah Sheldon, Paul D. Nation, and Jay M. Gambetta, ``Validating quantum computers using randomized model circuits'' Physical Review A 100 (2019).","DOI":"10.1103\/physreva.100.032328"},{"key":"66","doi-asserted-by":"publisher","unstructured":"Leo Breiman ``Random Forests'' Machine Learning 45, 5\u201332 (2001).","DOI":"10.1023\/A:1010933404324"},{"key":"67","unstructured":"Chin-Yao Chang, Eric Jones, and Peter Graf, ``On Quantum Computing for Mixed-Integer Programming'' (2020)."},{"key":"68","doi-asserted-by":"publisher","unstructured":"Jin-Kao Kochenberger, Fred Glover, Mark Lewis, Zhipeng L\u00fc, Haibo Wang, and Yang Wang, ``The unconstrained binary quadratic programming problem: a survey'' Journal of Combinatorial Optimization 28, 58\u201381 (2014).","DOI":"10.1007\/s10878-014-9734-0"},{"key":"69","unstructured":"Ehsan Zahedinejadand Arman Zaribafiyan ``Combinatorial Optimization on Gate Model Quantum Computers: A Survey'' (2017)."},{"key":"70","doi-asserted-by":"publisher","unstructured":"C. E. Shannon ``A mathematical theory of communication'' The Bell System Technical Journal 27, 379\u2013423 (1948).","DOI":"10.1002\/j.1538-7305.1948.tb01338.x"},{"key":"71","unstructured":"T.M. Coverand J.A. Thomas ``Elements of Information Theory'' Wiley (2012)."},{"key":"72","unstructured":"Nisha Saini ``Review of Selection Methods in Genetic Algorithms'' International Journal of Engineering and Computer Science 6, 22261\u201322263 (2017)."},{"key":"73","doi-asserted-by":"publisher","unstructured":"G. Cowan ``Statistics'' Oxford University Press (2020).","DOI":"10.1093\/ptep\/ptaa104"},{"key":"74","doi-asserted-by":"crossref","unstructured":"Jerzy Neyman ``A selection of early statistical papers'' University of California Press (1967).","DOI":"10.1525\/9780520327016"},{"key":"75","unstructured":"Niek J. Boumanand Serge Fehr ``Sampling in a Quantum Population, and Applications'' (2012)."},{"key":"76","doi-asserted-by":"publisher","unstructured":"Lawrence D. Brown, T. Tony Cai, and Anirban DasGupta, ``Interval Estimation for a Binomial Proportion'' Statistical Science 16, 101\u2013133 (2001).","DOI":"10.1214\/ss\/1009213286"},{"key":"77","unstructured":"Abdullah Ash Saki, Mahabubul Alam, and Swaroop Ghosh, ``Study of Decoherence in Quantum Computers: A Circuit-Design Perspective'' (2019)."},{"key":"78","doi-asserted-by":"publisher","unstructured":"G. Lindblad ``On the generators of quantum dynamical semigroups'' Communications in Mathematical Physics 48, 119\u2013130 (1976).","DOI":"10.1007\/BF01608499"},{"key":"79","doi-asserted-by":"publisher","unstructured":"B. M. Villegas-Mart\u00ednez, F. Soto-Eguibar, and H. M. Moya-Cessa, ``Application of Perturbation Theory to a Master Equation'' Advances in Mathematical Physics 2016, 9265039 (2016).","DOI":"10.1155\/2016\/9265039"},{"key":"80","unstructured":"Kamil Khadievand Liliya Safina ``The Quantum Version of Random Forest Model for Binary Classification Problem'' YRID-2020: International Workshop on Data Mining and Knowledge Engineering 30\u201335 (2020)."},{"key":"81","doi-asserted-by":"publisher","unstructured":"Maria Schuldand Francesco Petruccione ``Quantum ensembles of quantum classifiers'' Scientific Reports 8, 2772 (2018).","DOI":"10.1038\/s41598-018-20403-3"},{"key":"82","unstructured":"Zeke Xieand Issei Sato ``A Quantum-Inspired Ensemble Method and Quantum-Inspired Forest Regressors'' (2017)."},{"key":"83","doi-asserted-by":"publisher","unstructured":"Mohsen Shahhosseiniand Guiping Hu ``Improved Weighted Random Forest for Classification Problems'' Progress in Intelligent Decision Science 42\u201356 (2021).","DOI":"10.1007\/978-3-030-66501-2_4"}],"container-title":["Quantum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/quantum-journal.org\/papers\/q-2022-03-30-676\/pdf\/","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2023,1,30]],"date-time":"2023-01-30T23:46:39Z","timestamp":1675122399000},"score":1,"resource":{"primary":{"URL":"https:\/\/quantum-journal.org\/papers\/q-2022-03-30-676\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,30]]},"references-count":84,"URL":"https:\/\/doi.org\/10.22331\/q-2022-03-30-676","archive":["CLOCKSS"],"relation":{},"ISSN":["2521-327X"],"issn-type":[{"value":"2521-327X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,3,30]]},"article-number":"676"}}