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In this work, we introduce a new hybrid approach that finds the eigenenergies by collecting real-time measurements and post-processing them using the machinery of dynamic mode decomposition (DMD). From the perspective of quantum dynamics, we establish that our approach can be formally understood as a stable variational method on the function space of observables available from a quantum many-body system. We also provide strong theoretical and numerical evidence that our method converges rapidly even in the presence of a large degree of perturbative noise, and show that the method bears an isomorphism to robust matrix factorization methods developed independently across various scientific communities. Our numerical benchmarks on spin and molecular systems demonstrate an accelerated convergence and a favorable resource reduction over state-of-the-art algorithms. The DMD-centric strategy can systematically mitigate noise and stands out as a leading hybrid quantum-classical eigensolver.<\/jats:p>","DOI":"10.22331\/q-2025-08-27-1836","type":"journal-article","created":{"date-parts":[[2025,8,27]],"date-time":"2025-08-27T13:50:08Z","timestamp":1756302608000},"page":"1836","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":2,"title":["Estimating Eigenenergies from Quantum Dynamics: A Unified Noise-Resilient Measurement-Driven Approach"],"prefix":"10.22331","volume":"9","author":[{"given":"Yizhi","family":"Shen","sequence":"first","affiliation":[{"name":"Applied Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA"}]},{"given":"Daan","family":"Camps","sequence":"additional","affiliation":[{"name":"National Energy Research Scientific Computing Center, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA"}]},{"given":"Aaron","family":"Szasz","sequence":"additional","affiliation":[{"name":"Applied Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA"}]},{"given":"Siva","family":"Darbha","sequence":"additional","affiliation":[{"name":"Applied Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA"},{"name":"National Energy Research Scientific Computing Center, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA"}]},{"given":"Katherine","family":"Klymko","sequence":"additional","affiliation":[{"name":"National Energy Research Scientific Computing Center, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA"}]},{"given":"David B.","family":"Williams--Young","sequence":"additional","affiliation":[{"name":"Applied Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA"}]},{"given":"Norm M.","family":"Tubman","sequence":"additional","affiliation":[{"name":"NASA Ames Research Center, Moffett Field, CA 94035, USA"}]},{"given":"Roel Van","family":"Beeumen","sequence":"additional","affiliation":[{"name":"Applied Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA"}]}],"member":"9598","published-online":{"date-parts":[[2025,8,27]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Leon Balents. ``Spin liquids in frustrated magnets''. 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