Quantum computation of eigenvalues within target intervals

There is widespread interest in calculating the energy spectrum of a Hamiltonian, for example to analyze optical spectra and energy deposition by ions in materials. In this study, we propose a quantum algorithm that samples the set of energies within a target energy-interval without requiring good approximations of the target energy-eigenstates. We discuss the implementation of direct and iterative amplification protocols and give resource and runtime estimates. We illustrate initial applications by amplifying excited states on molecular hydrogen.

Automated summary

The study introduces a quantum algorithm that samples the set of energies within a target energy-interval without the need for good approximations of the target energy-eigenstates. Initial applications involve amplifying excited states on molecular hydrogen, with resource and runtime estimates provided for direct and iterative amplification protocols.