{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T18:02:08Z","timestamp":1767895328199,"version":"3.49.0"},"reference-count":45,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,2,17]],"date-time":"2025-02-17T00:00:00Z","timestamp":1739750400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Science Foundation Graduate Research Fellowship Program","award":["DGE 2140745"],"award-info":[{"award-number":["DGE 2140745"]}]},{"name":"National Science Foundation Graduate Research Fellowship Program","award":["1R15GM128149-01"],"award-info":[{"award-number":["1R15GM128149-01"]}]},{"name":"Texas Tech University (TTU) Graduate School Fellowship","award":["DGE 2140745"],"award-info":[{"award-number":["DGE 2140745"]}]},{"name":"Texas Tech University (TTU) Graduate School Fellowship","award":["1R15GM128149-01"],"award-info":[{"award-number":["1R15GM128149-01"]}]},{"DOI":"10.13039\/100000002","name":"National Institutes of Health (NIH)","doi-asserted-by":"publisher","award":["DGE 2140745"],"award-info":[{"award-number":["DGE 2140745"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000002","name":"National Institutes of Health (NIH)","doi-asserted-by":"publisher","award":["1R15GM128149-01"],"award-info":[{"award-number":["1R15GM128149-01"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We present the first step toward the quantum computing (QC) formulation of the electron nuclear dynamics (END) method within the variational quantum simulator (VQS) scheme: END\/QC\/VQS. END is a time-dependent, variational, on-the-flight, and non-adiabatic method to simulate chemical reactions. END represents nuclei with frozen Gaussian wave packets and electrons with a single-determinantal state in the Thouless non-unitary representation. Within the hybrid quantum\/classical VQS, END\/QC\/VQS currently evaluates the metric matrix M and gradient vector V of the symplectic END\/QC equations on the QC software development kit QISKIT, and calculates basis function integrals and time evolution on a classical computer. To adapt END to QC, we substitute the Thouless non-unitary representation with Fukutome unitary representation. We derive the first END\/QC\/VQS version for pure electronic dynamics in multielectron chemical models consisting of two-electron units with fixed nuclei. Therein, Fukutome unitary matrices factorize into triads of one-qubit rotational matrices, which leads to a QC encoding of one electron per qubit. We design QC circuits to evaluate M and V in one-electron diatomic molecules. In log2-log2 plots, errors and deviations of those evaluations decrease linearly with the number of shots and with slopes = \u22121\/2. We illustrate an END\/QC\/VQS simulation with the pure electronic dynamics of H2+ We discuss the present results and future END\/QC\/QVS extensions.<\/jats:p>","DOI":"10.3390\/sym17020303","type":"journal-article","created":{"date-parts":[[2025,2,17]],"date-time":"2025-02-17T07:48:22Z","timestamp":1739778502000},"page":"303","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Toward a Quantum Computing Formulation of the Electron Nuclear Dynamics Method via Fukutome Unitary Representation"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4281-4198","authenticated-orcid":false,"given":"Juan C.","family":"Dominguez","sequence":"first","affiliation":[{"name":"Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, TX 79409-1061, USA"}]},{"given":"Ismael","family":"de Farias","sequence":"additional","affiliation":[{"name":"Department of Industrial, Manufacturing, and Systems Engineering, Texas Tech University, Lubbock, TX 79409-3061, USA"}]},{"given":"Jorge A.","family":"Morales","sequence":"additional","affiliation":[{"name":"Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, TX 79409-1061, USA"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"McWeeny, R. 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