Estimating Eigenenergies from Quantum Dynamics: A Unified Noise-Resilient Measurement-Driven Approach
1Applied Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
2National Energy Research Scientific Computing Center, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
3NASA Ames Research Center, Moffett Field, CA 94035, USA
| Published: | 2025-08-27, volume 9, page 1836 |
| Editor: | Jin-Peng Liu |
| Eprint: | arXiv:2306.01858v5 |
| Doi: | https://doi.org/10.22331/q-2025-08-27-1836 |
| Citation: | Quantum 9, 1836 (2025). |
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Abstract
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.
Popular summary
ODMD extracts the target energy from real-time evolution of a prepared initial state with provably rapid convergence. Numerical tests on systems from condensed matter physics and quantum chemistry show that ODMD converges faster and more reliably than state-of-the-art methods. Our theoretical analysis and illustrative numerical simulations establish ODMD as a natural, efficient approach for ground state energy estimation, relevant to a broad audience in many-body physics, quantum information, and dynamical systems.
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