# Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets

## TL;DR

This paper demonstrates a hardware-efficient variational quantum eigensolver capable of solving small molecule and quantum magnetism problems with up to six qubits, showing promising results for quantum computational chemistry and physics.

## Contribution

The authors introduce a tailored variational quantum eigensolver optimized for specific hardware interactions, enabling the study of larger molecular and magnetic systems on current quantum devices.

## Key findings

- Successful experimental optimization of six-qubit Hamiltonian problems
- Accurate determination of ground state energies for molecules up to BeH2
- Agreement between experimental results and noisy simulation models

## Abstract

Quantum computers can be used to address molecular structure, materials science and condensed matter physics problems, which currently stretch the limits of existing high-performance computing resources. Finding exact numerical solutions to these interacting fermion problems has exponential cost, while Monte Carlo methods are plagued by the fermionic sign problem. These limitations of classical computational methods have made even few-atom molecular structures problems of practical interest for medium-sized quantum computers. Yet, thus far experimental implementations have been restricted to molecules involving only Period I elements. Here, we demonstrate the experimental optimization of up to six-qubit Hamiltonian problems with over a hundred Pauli terms, determining the ground state energy for molecules of increasing size, up to BeH2. This is enabled by a hardware-efficient variational quantum eigensolver with trial states specifically tailored to the available interactions in our quantum processor, combined with a compact encoding of fermionic Hamiltonians and a robust stochastic optimization routine. We further demonstrate the flexibility of our approach by applying the technique to a problem of quantum magnetism. Across all studied problems, we find agreement between experiment and numerical simulations with a noisy model of the device. These results help elucidate the requirements for scaling the method to larger systems, and aim at bridging the gap between problems at the forefront of high-performance computing and their implementation on quantum hardware.