# Quantum Simulation of Resonant Transitions for Solving the Eigen-problem of an Effective Water Hamiltonian

## TL;DR

This paper demonstrates a quantum algorithm using a four-qubit simulator to efficiently find energy spectra and eigenstates of a water molecule's effective Hamiltonian, overcoming classical computational limitations.

## Contribution

The work introduces an experimental quantum algorithm leveraging resonant transitions to solve eigen-problems of molecular Hamiltonians with a small quantum simulator.

## Key findings

- Successfully obtained the energy spectrum of a water molecule's effective Hamiltonian.
- Demonstrated state transformation accessing large Hilbert space regions.
- Efficiently prepared specific eigenstates based on measured eigenenergies.

## Abstract

It is difficult to calculate the energy levels and eigenstates of a large physical system on a classical computer because of the exponentially growing size of the Hilbert space. In this work, we experimentally demonstrate a quantum algorithm which could solve this problem via simulated resonant transitions. Using a four-qubit quantum simulator in which two qubits are used as ancillas for control and measurement, we obtain the energy spectrum of a 2-qubit low-energy effective Hamiltonian of the water molecule. The simulated transitions allow the state of the quantum simulator to transform and access large regions of the Hilbert space, including states that have no overlap with the initial state. Furthermore, we make use of this algorithm to efficiently prepare specific eigenstates on the simulator according to the measured eigenenergies.