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

TL;DR

This paper presents a noise-resilient, measurement-driven hybrid quantum-classical method for estimating eigenenergies in quantum systems, demonstrating rapid convergence and resource efficiency over existing algorithms.

Contribution

It introduces a novel approach combining quantum measurements with dynamic mode decomposition, providing a stable, noise-tolerant variational method for eigenenergy estimation.

Findings

Method converges rapidly even with high noise levels

Demonstrates resource reduction compared to state-of-the-art algorithms

Shows effectiveness on spin and molecular systems

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.