Efficient Measurement-Driven Eigenenergy Estimation with Classical Shadows

Understand

Quantum algorithms exploiting real-time evolution under a target Hamiltonian have demonstrated remarkable efficiency in extracting key spectral information.

• However, the broader potential of these methods, particularly beyond ground state calculations, is underexplored.
• In this work, we introduce the framework of multi-observable dynamic mode decomposition (MODMD), which combines the observable dynamic mode decomposition, a measurement-driven eigensolver tailored for near-term implementation, with classical shadow tomography.
• MODMD leverages random scrambling in the classical shadow technique to construct, with exponentially reduced resource requirements, a signal subspace that encodes rich spectral information.