# Quantum inverse iteration algorithm for programmable quantum simulators

## TL;DR

This paper introduces a quantum inverse iteration algorithm that estimates ground state properties of quantum systems using programmable quantum devices, leveraging Fourier approximation and Hamiltonian dynamics.

## Contribution

It presents a novel quantum inverse iteration method that utilizes Fourier approximation to implement Hamiltonian inverses on quantum hardware, enabling ground state estimation.

## Key findings

- Successfully benchmarked on quantum chemistry examples like H2 and BeH2.
- Demonstrated applicability to material science models such as the Bose-Hubbard model.
- Shows compatibility with existing quantum devices for ground state studies.

## Abstract

We propose a quantum inverse iteration algorithm which can be used to estimate the ground state properties of a programmable quantum device. The method relies on the inverse power iteration technique, where the sequential application of the Hamiltonian inverse to an initial state prepares an approximate groundstate. To apply the inverse Hamiltonian operation, we write it as a sum of unitary evolution operators using the Fourier approximation approach. This allows to reformulate the protocol as separate measurements for the overlap of initial and propagated wavefunction. The algorithm thus crucially depends on the ability to run Hamiltonian dynamics with an available quantum device. We benchmark the performance using paradigmatic examples of quantum chemistry, corresponding to molecular hydrogen and beryllium hydride. Finally, we show its use for studying the ground state properties of relevant material science models which can be simulated with existing devices, considering an example of the Bose-Hubbard atomic simulator.