# An adaptive variational algorithm for exact molecular simulations on a quantum computer

## TL;DR

This paper introduces an adaptive variational algorithm for quantum molecular simulations that systematically builds an accurate wavefunction ansatz, outperforming traditional methods in circuit depth and accuracy on near-term quantum hardware.

## Contribution

The paper presents a novel adaptive variational algorithm that constructs the wavefunction ansatz dynamically, improving accuracy and efficiency over fixed-ansatz methods.

## Key findings

- Outperforms unitary coupled cluster in accuracy and circuit depth
- Generates small-parameter, shallow-depth circuits
- Shows promise for exact molecular simulations on near-term quantum hardware

## Abstract

Quantum simulation of chemical systems is one of the most promising near-term applications of quantum computers. The variational quantum eigensolver, a leading algorithm for molecular simulations on quantum hardware, has a serious limitation in that it typically relies on a pre-selected wavefunction ansatz that results in approximate wavefunctions and energies. Here we present an arbitrarily accurate variational algorithm that instead of fixing an ansatz upfront, this algorithm grows it systematically one operator at a time in a way dictated by the molecule being simulated. This generates an ansatz with a small number of parameters, leading to shallow-depth circuits. We present numerical simulations, including for a prototypical strongly correlated molecule, which show that our algorithm performs much better than a unitary coupled cluster approach, in terms of both circuit depth and chemical accuracy. Our results highlight the potential of our adaptive algorithm for exact simulations with present-day and near-term quantum hardware.