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Ground state energy estimation in physical, chemical, and materials sciencesis one of the most promising applications of quantum computing. In this work,we introduce a new hybrid approach that finds the eigenenergies by collectingreal-time measurements and post-processing them using the machinery of dynamicmode decomposition (DMD). From the perspective of quantum dynamics, weestablish that our approach can be formally understood as a stable variationalmethod on the function space of observables available from a quantum many-bodysystem. We also provide strong theoretical and numerical evidence that ourmethod converges rapidly even in the presence of a large degree of perturbativenoise, and show that the method bears an isomorphism to robust matrixfactorization methods developed independently across various scientificcommunities. Our numerical benchmarks on spin and molecular systems demonstratean accelerated convergence and a favorable resource reduction overstate-of-the-art algorithms. The DMD-centric strategy can systematicallymitigate noise and stands out as a leading hybrid quantum-classicaleigensolver.

Estimating Eigenenergies from Quantum Dynamics: A Unified Noise-Resilient Measurement-Driven Approach