{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T13:35:33Z","timestamp":1762522533283,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2020,12,6]],"date-time":"2020-12-06T00:00:00Z","timestamp":1607212800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Agencia Estatal de Investigacion Espa\u00f1a. \u201cPrograma Estatal de I+D+i Orientada a los Retos de la Sociedad\u201d.","award":["RTI2018-094614-B-I00"],"award-info":[{"award-number":["RTI2018-094614-B-I00"]}]},{"name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades Espa\u00f1a","award":["PGC2018-093854-B-I00"],"award-info":[{"award-number":["PGC2018-093854-B-I00"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper we investigate how the relationship with a subordinate who reports to him influences the alignment of an Industry 4.0 leader. We do this through the implementation of quantum circuits that represent decision networks. In fact, through the quantum simulation of strategic organizational design configurations (QSOD) through five hundred simulations of quantum circuits, we conclude that there is an influence of the subordinate on the leader that resembles that of a harmonic under-damped oscillator around the value of 50% probability of alignment for the leader. Likewise, we have observed a fractal behavior in this type of relationship, which seems to conjecture that there is an exchange of energy between the two agents that oscillates with greater or lesser amplitude depending on certain parameters of interdependence. Fractality in this QSOD context allows for a quantification of these complex dynamics and its pervasive effect offers robustness and resilience to the two-qubit interaction.<\/jats:p>","DOI":"10.3390\/s20236977","type":"journal-article","created":{"date-parts":[[2020,12,7]],"date-time":"2020-12-07T21:37:42Z","timestamp":1607377062000},"page":"6977","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Industry 4.0 Quantum Strategic Organizational Design Configurations. The Case of Two Qubits: One Reports to One"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2423-1474","authenticated-orcid":false,"given":"Javier","family":"Villalba-Diez","sequence":"first","affiliation":[{"name":"Hochschule Heilbronn, Fakult\u00e4t Management und Vertrieb, Campus Schw\u00e4bisch Hall, 74523 Schw\u00e4bisch Hall, Germany"},{"name":"Complex Systems Group, Escuela T\u00e9cnica Superior de Ingenieros Agr\u00f3nomos, Universidad Polit\u00e9cnica de Madrid, Av. Puerta de Hierro 2, 28040 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3949-8232","authenticated-orcid":false,"given":"Rosa Mar\u00eda","family":"Benito","sequence":"additional","affiliation":[{"name":"Complex Systems Group, Escuela T\u00e9cnica Superior de Ingenieros Agr\u00f3nomos, Universidad Polit\u00e9cnica de Madrid, Av. Puerta de Hierro 2, 28040 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4373-603X","authenticated-orcid":false,"given":"Juan Carlos","family":"Losada","sequence":"additional","affiliation":[{"name":"Complex Systems Group, Escuela T\u00e9cnica Superior de Ingenieros Agr\u00f3nomos, Universidad Polit\u00e9cnica de Madrid, Av. Puerta de Hierro 2, 28040 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Villalba-Diez, J., and Zheng, X. (2020). Quantum Strategic Organizational Design: Alignment in Industry 4.0 Complex-Networked Cyber-Physical Lean Management Systems. Sensors, 20.","DOI":"10.3390\/s20205856"},{"key":"ref_2","unstructured":"Nielsen, T.D., and Jensen, F.V. (2009). Bayesian Networks and Decision Graphs, Springer. [2nd ed.]."},{"key":"ref_3","unstructured":"Nielsen, M.A., and Chuang, I. (2010). Quantum Computation and Quantum Information, Cambridge University Press."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1145\/3402127.3402131","article-title":"Quantum Computing: A New Software Engineering Golden Age","volume":"45","author":"Piattini","year":"2020","journal-title":"SIGSOFT Softw. Eng. Notes"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1109\/TEM.2015.2424156","article-title":"Improving manufacturing operational performance by standardizing process management","volume":"62","year":"2015","journal-title":"Trans. Eng. Manag."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Villalba-Diez, J., Ordieres-Mer\u00e9, J., and Nuber, G. (2015, January 7\u20138). The HOSHIN KANRI TREE. Cross-Plant Lean Shopfloor Management. 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Empowering Leaders to Operationalize Lean Structural Networks","volume":"55","author":"Jimenez","year":"2016","journal-title":"Procedia CIRP"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Villalba-Diez, J. (2017). The HOSHIN KANRI FOREST. Lean Strategic Organizational Design, CRC Press, Taylor and Francis Group LLC. [1st ed.].","DOI":"10.1201\/9781315155814"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Villalba-Diez, J. (2017). The Lean Brain Theory. Complex Networked Lean Strategic Organizational Design, CRC Press, Taylor and Francis Group LLC.","DOI":"10.1201\/9781315155814-2"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Villalba-Diez, J., Zheng, X., Schmidt, D., and Molina, M. (2019). Characterization of Industry 4.0 Lean Management Problem-Solving Behavioral Patterns Using EEG Sensors and Deep Learning. Sensors, 19.","DOI":"10.3390\/s19132841"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Schmidt, D., Villalba Diez, J., Ordieres-Mer\u00e9, J., Gevers, R., Schwiep, J., and Molina, M. (2020). Industry 4.0 Lean Shopfloor Management Characterization Using EEG Sensors and Deep Learning. Sensors, 20.","DOI":"10.3390\/s20102860"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"10243","DOI":"10.1088\/0305-4470\/34\/47\/324","article-title":"Geometry of entangled states, Bloch spheres and Hopf fibrations","volume":"34","author":"Mosseri","year":"2001","journal-title":"J. Phys. Math. Gen."},{"key":"ref_15","unstructured":"Van Rossum, G. (1995). Python Tutorial, Technical Report CS-R9526, Centrum voor Wiskunde en Informatica (CWI)."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Wille, R., Meter, R.V., and Naveh, Y. (2019, January 25\u201329). IBM\u2019s Qiskit Tool Chain: Working with and Developing for Real Quantum Computers. Proceedings of the 2019 Design, Automation Test in Europe Conference Exhibition (DATE), Florence, Italy. ISSN 1558-1101.","DOI":"10.23919\/DATE.2019.8715261"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/23\/6977\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:41:41Z","timestamp":1760179301000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/23\/6977"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,6]]},"references-count":16,"journal-issue":{"issue":"23","published-online":{"date-parts":[[2020,12]]}},"alternative-id":["s20236977"],"URL":"https:\/\/doi.org\/10.3390\/s20236977","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2020,12,6]]}}}