Quantum Computation of Eigenvalues within Target Intervals

TL;DR

This paper introduces a quantum algorithm for efficiently sampling eigenvalues within a specific energy range of a Hamiltonian, useful for spectral analysis without needing precise eigenstate approximations.

Contribution

It presents a novel quantum algorithm that targets eigenvalues in a specified interval, with detailed protocols and resource estimates, demonstrated on molecular hydrogen.

Findings

Effective amplification of excited states demonstrated

Resource and runtime estimates provided

Potential applications in spectral analysis and material science

Abstract

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.