  Ground state energy estimation in physical, chemical, and materials sciences
is one of the most promising applications of quantum computing. 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.
