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VQAs for solving the Poisson equation were recently proposed, as this method transforms the linear equation with a symmetric positive definite matrix obtained by discretizing the Poisson equation into a minimization problem. In this study, we propose a VQA for second-order linear differential equations including the Poisson equation on the basis of the referenced study, where the coefficient matrix obtained through discretization is a non-symmetric matrix. Furthermore, in our VQAs, we succeeded in decomposing the coefficient matrices arising from the periodic and the Dirichlet boundary condition into linear combinations of measurement operators and unitary matrices.<\/jats:p>","DOI":"10.2478\/qic-2025-0012","type":"journal-article","created":{"date-parts":[[2025,7,1]],"date-time":"2025-07-01T14:34:30Z","timestamp":1751380470000},"page":"232-247","source":"Crossref","is-referenced-by-count":1,"title":["Variational Quantum Algorithm for Solving Second-Order Linear Differential Equations"],"prefix":"10.2478","volume":"25","author":[{"given":"Ryo","family":"Sugaya","sequence":"first","affiliation":[{"name":"Department of Applied Physics, Graduate School of Engineering, Nagoya University , Nagoya 464-8601 , Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tomohiro","family":"Sogabe","sequence":"additional","affiliation":[{"name":"Department of Applied Physics, Graduate School of Engineering, Nagoya University , Nagoya 464-8601 , Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tomoya","family":"Kemmochi","sequence":"additional","affiliation":[{"name":"Department of Applied Physics, Graduate School of Engineering, Nagoya University , Nagoya 464-8601 , Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shao-Liang","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Applied Physics, Graduate School of Engineering, Nagoya University , Nagoya 464-8601 , Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"374","published-online":{"date-parts":[[2025,7,1]]},"reference":[{"key":"2026062620005332102_j_qic-2025-0012_ref_001","doi-asserted-by":"crossref","unstructured":"T. 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