{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T16:49:07Z","timestamp":1772297347813,"version":"3.50.1"},"reference-count":27,"publisher":"World Scientific Pub Co Pte Lt","issue":"09","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Geom. Methods Mod. Phys."],"published-print":{"date-parts":[[2018,9]]},"abstract":"<jats:p> Quantum splines are curves in a Hilbert space or, equivalently, in the corresponding Hilbert projective space, which generalize the notion of Riemannian cubic splines to the quantum domain. In this paper, we present a generalization of this concept to general density matrices with a Hamiltonian approach and using a geometrical formulation of quantum mechanics. Our main goal is to formulate an optimal control problem for a nonlinear system on [Formula: see text] which corresponds to the variational problem of quantum splines. The corresponding Hamiltonian equations and interpolation conditions are derived. The results are illustrated with some examples and the corresponding quantum splines are computed with the implementation of a suitable iterative algorithm. <\/jats:p>","DOI":"10.1142\/s0219887818501475","type":"journal-article","created":{"date-parts":[[2018,5,3]],"date-time":"2018-05-03T10:03:24Z","timestamp":1525341804000},"page":"1850147","source":"Crossref","is-referenced-by-count":5,"title":["A general framework for quantum splines"],"prefix":"10.1142","volume":"15","author":[{"given":"L.","family":"Abrunheiro","sequence":"first","affiliation":[{"name":"CIDMA \u2013 Center for Research and Development in Mathematics and Applications, Higher Institute of Accounting and Administration, University of Aveiro, Aveiro 3810-500, Portugal"}]},{"given":"M.","family":"Camarinha","sequence":"additional","affiliation":[{"name":"Centre for Mathematics of University of Coimbra, Department of Mathematics, University of Coimbra, Coimbra 3001-454, Portugal"}]},{"given":"J.","family":"Clemente-Gallardo","sequence":"additional","affiliation":[{"name":"Department of Theoretical Physics, Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, Edificio I+D, Mariano Esquillor s\/n, Zaragoza 50018, Spain"}]},{"given":"J. C.","family":"Cuch\u00ed","sequence":"additional","affiliation":[{"name":"Department of Agricultural and Forest Engineering, University of Lleida, Av. 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