{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T08:13:19Z","timestamp":1778487199833,"version":"3.51.4"},"publisher-location":"Cham","reference-count":32,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032225382","type":"print"},{"value":"9783032225399","type":"electronic"}],"license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"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":[],"published-print":{"date-parts":[[2026]]},"DOI":"10.1007\/978-3-032-22539-9_7","type":"book-chapter","created":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T08:06:24Z","timestamp":1778486784000},"page":"87-97","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Notes on\u00a0Quantum Computing over\u00a0Complex Geometric Algebras with\u00a0Split Signature"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2460-7571","authenticated-orcid":false,"given":"Jaroslav","family":"Hrdina","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,6,4]]},"reference":[{"key":"7_CR1","doi-asserted-by":"publisher","unstructured":"Alves, R., Hildenbrand, D., Hrdina, J., et al.: An online calculator for quantum computing operations based on geometric algebra. Adv. Appl. Clifford Algebras. 32(4) (2022). https:\/\/doi.org\/10.1007\/s00006-021-01185-w","DOI":"10.1007\/s00006-021-01185-w"},{"key":"7_CR2","doi-asserted-by":"crossref","unstructured":"Bravyi, S.B., Kitaev, A.Y.: Fermionic quantum computation. Annals of Physics. 298 (2002)","DOI":"10.1006\/aphy.2002.6254"},{"key":"7_CR3","doi-asserted-by":"publisher","unstructured":"Brde\u010dkov\u00e1, J., Hrdina, J.: Notes on the losses compensation of a three-phase power system with dc offset based on geometric algebras. Nonlinear Anal. Model. Control, 30(2) (2025). https:\/\/doi.org\/10.15388\/namc.2025.30.38965","DOI":"10.15388\/namc.2025.30.38965"},{"key":"7_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"482","DOI":"10.1007\/978-3-030-61864-3_41","volume-title":"Advances in Computer Graphics","author":"R Byrtus","year":"2020","unstructured":"Byrtus, R., Derevianko, A., Va\u0161\u00edk, P.: Outline of tube elbow detection based on GAC. In: Magnenat-Thalmann, N., Stephanidis, C., Wu, E., Thalmann, D., Sheng, B., Kim, J., Papagiannakis, G., Gavrilova, M. (eds.) CGI 2020. LNCS, vol. 12221, pp. 482\u2013491. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-61864-3_41"},{"key":"7_CR5","doi-asserted-by":"crossref","unstructured":"Cafaro, C., Mancini, S.: A geometric algebra perspective on quantum computational gates and universality in quantum computing. Adv. Appl. Clifford Algebras, 21 (2011)","DOI":"10.1007\/s00006-010-0269-x"},{"key":"7_CR6","doi-asserted-by":"crossref","unstructured":"de Lima Marquezino F., Portugal R., Lavor C.: A Primer on Quantum Computing. Springer, Cham (2019)","DOI":"10.1007\/978-3-030-19066-8"},{"key":"7_CR7","doi-asserted-by":"publisher","unstructured":"Derevianko, A., Vas\u030c\u00edk, P.: Solver-free optimal control for linear dynamical switched system by means of geometric algebra. Math. Meth. Appl. Sci. 47 (2024). https:\/\/doi.org\/10.1002\/mma.8752.","DOI":"10.1002\/mma.8752."},{"key":"7_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1007\/978-3-030-98260-7_13","volume-title":"Modelling and Simulation for Autonomous Systems","author":"A Derevianko","year":"2022","unstructured":"Derevianko, A., Lou\u010dka, P.: Search for\u00a0similarity transformation between image point clouds using geometric algebra for\u00a0conics. In: Mazal, J., Fagiolini, A., Vasik, P., Turi, M., Bruzzone, A., Pickl, S., Neumann, V., Stodola, P. (eds.) MESAS 2021. LNCS, vol. 13207, pp. 215\u2013226. Springer, Cham (2022). https:\/\/doi.org\/10.1007\/978-3-030-98260-7_13"},{"key":"7_CR9","doi-asserted-by":"crossref","unstructured":"Doran C., Lasenby A.: Geometric Algebra for Physicists. Cambridge University Press, Cambridge (2003)","DOI":"10.1017\/CBO9780511807497"},{"key":"7_CR10","doi-asserted-by":"crossref","unstructured":"Doran, C., Hestenes, D., Sommen, F., Van Acker, N.: Lie groups as spin groups. J. Math. Phys. 34 (1993)","DOI":"10.1063\/1.530050"},{"key":"7_CR11","doi-asserted-by":"publisher","unstructured":"Eryganov I., Hrdina, J.: Complex clifford algebra in repeated quantum prisoner\u2019s dilemma. Math. Meth. Appl. Sci. 47 (2024). https:\/\/doi.org\/10.1002\/mma.8694","DOI":"10.1002\/mma.8694"},{"issue":"42","key":"7_CR12","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8121\/ad7c9c","volume":"57","author":"I Eryganov","year":"2024","unstructured":"Eryganov, I., Hrdina, J., N\u00e1vrat, A.: Quantization of two- and three-player cooperative games based on QRA. J. Phys. Math. General 57(42), 425303 (2024). https:\/\/doi.org\/10.1088\/1751-8121\/ad7c9c","journal-title":"J. Phys. Math. General"},{"key":"7_CR13","doi-asserted-by":"crossref","unstructured":"Flitney A. P., Abbott D.: An introduction to quantum game theory. Fluctuation Noise Lett. 2 (2002)","DOI":"10.1142\/S0219477502000981"},{"key":"7_CR14","doi-asserted-by":"crossref","unstructured":"Gutoski, G., Watrous, J.: Toward a general theory of quantum games. In: Proceedings of the Thirty-Ninth Annual ACM Symposium on Theory of Computing (2007)","DOI":"10.1145\/1250790.1250873"},{"key":"7_CR15","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-31794-1","volume-title":"Foundations of Geometric Algebra Computing","author":"D Hildenbrand","year":"2013","unstructured":"Hildenbrand, D.: Foundations of Geometric Algebra Computing. Springer, Heidelberg (2013)"},{"key":"7_CR16","doi-asserted-by":"publisher","unstructured":"Hildenbrand, D., Hrdina, J., N\u00e1vrat, A., Vas\u030c\u00edk, P.: Local controllability of snake robots based on CRA, theory and practice. Adv. Appl. Clifford Algebras, 30(1) (2020). https:\/\/doi.org\/10.1007\/s00006-019-1022-8","DOI":"10.1007\/s00006-019-1022-8"},{"key":"7_CR17","doi-asserted-by":"publisher","unstructured":"Hitzer, E., Lavor, C., Hildenbrand, D. : Current survey of clifford geometric algebra applications. Math. Methods Appl. Sci. 1\u201331 (2022). https:\/\/doi.org\/10.1002\/mma.8316","DOI":"10.1002\/mma.8316"},{"key":"7_CR18","doi-asserted-by":"publisher","unstructured":"Hitzer, E., Kamarianakis, M., Papagiannakis, G., Vas\u030c\u00edk, P.: Survey of new applications of geometric algebra. Math. Methods Appl. Sci. 1\u201317 (2023). https:\/\/doi.org\/10.1002\/mma.9575.","DOI":"10.1002\/mma.9575."},{"key":"7_CR19","doi-asserted-by":"publisher","unstructured":"Hrdina, J., N\u00e1vrat, A.: Binocular computer vision based on conformal geometric algebra Adv. Appl. Clifford Algebras 27 (2017). https:\/\/doi.org\/10.1007\/s00006-017-0764-4","DOI":"10.1007\/s00006-017-0764-4"},{"key":"7_CR20","doi-asserted-by":"publisher","unstructured":"Hrdina, J., N\u00e1vrat, A., Va\u0161\u00edk, P.: Geometric algebra for conics. Adv. Appl. Clifford Algebras, 28(66) (2018). https:\/\/doi.org\/10.1007\/s00006-018-0879-2","DOI":"10.1007\/s00006-018-0879-2"},{"key":"7_CR21","doi-asserted-by":"publisher","unstructured":"Hrdina, J., N\u00e1vrat, A., Va\u0161\u00edk, P.: Fitting in geometric algebra setting. Adv. Appl. Clifford Algebras. 29(72) (2019). https:\/\/doi.org\/10.1007\/s00006-019-0989-5","DOI":"10.1007\/s00006-019-0989-5"},{"key":"7_CR22","doi-asserted-by":"publisher","unstructured":"Hrdina, J., Navrat, A., Vasik, P.: Quantum computing based on complex clifford algebras. Quantum Inf. Process. 21 (2022). https:\/\/doi.org\/10.1007\/s11128-022-03648-w","DOI":"10.1007\/s11128-022-03648-w"},{"key":"7_CR23","doi-asserted-by":"publisher","unstructured":"Hrdina, J., Hildenbrand, D., N\u00e1vrat, A., et. al.: Quantum register algebra: the mathematical language for quantum computing. Quantum Inf. Process. 22 (2023). https:\/\/doi.org\/10.1007\/s11128-023-04086-y","DOI":"10.1007\/s11128-023-04086-y"},{"key":"7_CR24","volume-title":"Clifford Algebra and Spinors","author":"P Lounesto","year":"2006","unstructured":"Lounesto, P.: Clifford Algebra and Spinors. Cambridge University Press, Cambridge (2006)"},{"key":"7_CR25","doi-asserted-by":"crossref","unstructured":"Tilly, J., Chen, H., Cao, S., et al.: The variational quantum eigensolver: a review of methods and best practices. Phys. Rep. 986 (2022)","DOI":"10.1016\/j.physrep.2022.08.003"},{"key":"7_CR26","doi-asserted-by":"publisher","first-page":"24591","DOI":"10.1109\/ACCESS.2023.3254299","volume":"11","author":"F Casado-Machado","year":"2023","unstructured":"Casado-Machado, F., Mart\u00ednez-Ramos, J.L., Barrag\u00e1n-Villarejo, M., Maza-Ortega, J.M.: Reduced reference frame transformation assessment in unbalanced three-phase four-wire systems. IEEE Access. 11, 24591\u201324603 (2023). https:\/\/doi.org\/10.1109\/ACCESS.2023.3254299","journal-title":"IEEE Access."},{"key":"7_CR27","doi-asserted-by":"publisher","unstructured":"Montoya, F.G., Eid, A.H.: Formulating the geometric foundation of Clarke, Park, and FBD transformations by means of Clifford\u2019s geometric algebra. Math. Methods Appl. Sci. 45(8) (2022). https:\/\/doi.org\/10.1002\/mma.8038","DOI":"10.1002\/mma.8038"},{"key":"7_CR28","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1007\/s00190-024-01854-1","volume":"98","author":"J Ventura","year":"2024","unstructured":"Ventura, J., et al.: A novel geometric method based on conformal geometric algebra applied to the resection problem in two and three dimensions. J. Geod. 98, 47 (2024). https:\/\/doi.org\/10.1007\/s00190-024-01854-1","journal-title":"J. Geod."},{"key":"7_CR29","volume-title":"Geometric Fundamentals of Robotics","author":"JM Selig","year":"2005","unstructured":"Selig, J.M.: Geometric Fundamentals of Robotics, 2nd edn. Springer, New York (2005)","edition":"2"},{"key":"7_CR30","doi-asserted-by":"publisher","unstructured":"Stodola, M., Hrdina,\u00a0J.: Higher order geometric algebras and their implementations using bott periodicity. Adv. Appl. Clifford Algebras 34(44) (2024). https:\/\/doi.org\/10.1007\/s00006-024-01346-7","DOI":"10.1007\/s00006-024-01346-7"},{"key":"7_CR31","doi-asserted-by":"crossref","unstructured":"Vaz, Jr., J., da Rocha, Jr R.: An Introduction to Clifford Algebras and Spinors. Oxford (2016)","DOI":"10.1093\/acprof:oso\/9780198782926.001.0001"},{"key":"7_CR32","unstructured":"Ventura, J., et al.: On the fitting of three-phase voltage curves with ellipses using geometric algebra for conics. In: Proceedings - ICREPQ (2024)"}],"container-title":["Lecture Notes in Computer Science","Empowering Novel Geometric Algebra for Graphics and Engineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-032-22539-9_7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T08:06:34Z","timestamp":1778486794000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-22539-9_7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"ISBN":["9783032225382","9783032225399"],"references-count":32,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-22539-9_7","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026]]},"assertion":[{"value":"4 June 2026","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"The authors have no competing interests to declare that\u00a0are relevant to the content of this article","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Disclosure of Interests"}},{"value":"ENGAGE","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Workshop on Empowering Novel Geometric Algebra for Graphics and Engineering","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Hong Kong","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"China","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2025","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"14 July 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"14 July 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"15","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"engage2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/www.cgs-network.org\/cgi25\/engage-workshop-2025\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}