{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,15]],"date-time":"2025-12-15T14:16:04Z","timestamp":1765808164621,"version":"build-2065373602"},"reference-count":43,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,1,27]],"date-time":"2023-01-27T00:00:00Z","timestamp":1674777600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"QuantERA","award":["731473","2020-22"],"award-info":[{"award-number":["731473","2020-22"]}]},{"name":"the University of Catania","award":["731473","2020-22"],"award-info":[{"award-number":["731473","2020-22"]}]},{"name":"National Quantum Science and Technology Institute (NQSTI)","award":["731473","2020-22"],"award-info":[{"award-number":["731473","2020-22"]}]},{"name":"4. Scienze e Tecnologie Quantistiche","award":["731473","2020-22"],"award-info":[{"award-number":["731473","2020-22"]}]},{"name":"ICSC\u2014Centro Nazionale di Ricerca in High-Performance Computing, Big Data, and Quantum Computing","award":["731473","2020-22"],"award-info":[{"award-number":["731473","2020-22"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Quantum state processing is one of the main tools of quantum technologies. While real systems are complicated and\/or may be driven by non-ideal control, they may nevertheless exhibit simple dynamics approximately confined to a low-energy Hilbert subspace. Adiabatic elimination is the simplest approximation scheme allowing us to derive in certain cases an effective Hamiltonian operating in a low-dimensional Hilbert subspace. However, these approximations may present ambiguities and difficulties, hindering a systematic improvement of their accuracy in larger and larger systems. Here, we use the Magnus expansion as a systematic tool to derive ambiguity-free effective Hamiltonians. We show that the validity of the approximations ultimately leverages only on a proper coarse-graining in time of the exact dynamics. We validate the accuracy of the obtained effective Hamiltonians with suitably tailored fidelities of quantum operations.<\/jats:p>","DOI":"10.3390\/e25020234","type":"journal-article","created":{"date-parts":[[2023,1,30]],"date-time":"2023-01-30T03:56:27Z","timestamp":1675050987000},"page":"234","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Coarse-Grained Effective Hamiltonian via the Magnus Expansion for a Three-Level System"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3313-7906","authenticated-orcid":false,"given":"Nicola","family":"Macr\u00ec","sequence":"first","affiliation":[{"name":"Dipartimento di Fisica e Astronomia \u201cEttore Majorana\u201d, Universit\u00e0 di Catania, 95123 Catania, Italy"},{"name":"Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Catania, 95123 Catania, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9704-7304","authenticated-orcid":false,"given":"Luigi","family":"Giannelli","sequence":"additional","affiliation":[{"name":"Dipartimento di Fisica e Astronomia \u201cEttore Majorana\u201d, Universit\u00e0 di Catania, 95123 Catania, Italy"},{"name":"CNR-IMM, UoS Universit\u00e0, 95123 Catania, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9929-3768","authenticated-orcid":false,"given":"Elisabetta","family":"Paladino","sequence":"additional","affiliation":[{"name":"Dipartimento di Fisica e Astronomia \u201cEttore Majorana\u201d, Universit\u00e0 di Catania, 95123 Catania, Italy"},{"name":"Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Catania, 95123 Catania, Italy"},{"name":"CNR-IMM, UoS Universit\u00e0, 95123 Catania, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5842-2677","authenticated-orcid":false,"given":"Giuseppe","family":"Falci","sequence":"additional","affiliation":[{"name":"Dipartimento di Fisica e Astronomia \u201cEttore Majorana\u201d, Universit\u00e0 di Catania, 95123 Catania, Italy"},{"name":"Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Catania, 95123 Catania, Italy"},{"name":"CNR-IMM, UoS Universit\u00e0, 95123 Catania, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1655","DOI":"10.1098\/rsta.2003.1227","article-title":"Quantum technology: The second quantum revolution","volume":"361","author":"Dowling","year":"2003","journal-title":"Philos. 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