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This technique is scalable to large systems through the use of a matrix product operator representation of the reference time evolution propagator. Our optimization routine is applied to various spin chains and fermionic systems described by the transverse-field Ising Hamiltonian, the Heisenberg Hamiltonian, and the spinful Fermi-Hubbard Hamiltonian. In these cases, our approach achieves a relative error improvement of up to four orders of magnitude for systems of 50 qubits, although our method is also applicable to larger systems. Furthermore, we demonstrate the versatility of our method by applying it to molecular systems, specifically lithium hydride, achieving an error improvement of up to eight orders of magnitude. This proof of concept highlights the potential of our approach for broader applications in quantum simulations.<\/jats:p>","DOI":"10.22331\/q-2025-08-27-1833","type":"journal-article","created":{"date-parts":[[2025,8,27]],"date-time":"2025-08-27T11:08:41Z","timestamp":1756292921000},"page":"1833","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":6,"title":["Riemannian quantum circuit optimization based on matrix product operators"],"prefix":"10.22331","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6707-044X","authenticated-orcid":false,"given":"Isabel Nha Minh","family":"Le","sequence":"first","affiliation":[{"name":"Technical University of Munich, School of Computation, Information and Technology, Boltzmannstr. 3, 85748 Garching, Germany"},{"name":"Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, 80799 Munich, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-5775-9730","authenticated-orcid":false,"given":"Shuo","family":"Sun","sequence":"additional","affiliation":[{"name":"Technical University of Munich, School of Computation, Information and Technology, Boltzmannstr. 3, 85748 Garching, Germany"},{"name":"Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, 80799 Munich, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6386-0230","authenticated-orcid":false,"given":"Christian B.","family":"Mendl","sequence":"additional","affiliation":[{"name":"Technical University of Munich, School of Computation, Information and Technology, Boltzmannstr. 3, 85748 Garching, Germany"},{"name":"Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, 80799 Munich, Germany"},{"name":"Technical University of Munich, Institute for Advanced Study, Lichtenbergstr. 2a, 85748 Garching, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"9598","published-online":{"date-parts":[[2025,8,27]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Richard P Feynman. ``Simulating physics with computers''. 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