# Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz

## TL;DR

This paper advances quantum algorithms for molecular energy calculations by optimizing the UCC ansatz in VQE, reducing circuit depth, and introducing an efficient gradient computation method, demonstrated on a hydrogen system.

## Contribution

It presents new strategies to lower circuit depth and an analytical gradient method for VQE with UCC, enhancing efficiency and accuracy in quantum molecular simulations.

## Key findings

- Reduced circuit depth without significant accuracy loss
- Efficient analytical gradient computation reduces sampling costs
- Successful simulation of a strongly correlated hydrogen system

## Abstract

The variational quantum eigensolver (VQE) algorithm combines the ability of quantum computers to efficiently compute expectation values with a classical optimization routine in order to approximate ground state energies of quantum systems. In this paper, we study the application of VQE to the simulation of molecular energies using the unitary coupled cluster (UCC) ansatz. We introduce new strategies to reduce the circuit depth for the implementation of UCC and improve the optimization of the wavefunction based on efficient classical approximations of the cluster amplitudes. Additionally, we propose an analytical method to compute the energy gradient that reduces the sampling cost for gradient estimation by several orders of magnitude compared to numerical gradients. We illustrate our methodology with numerical simulations for a system of four hydrogen atoms that exhibit strong correlation and show that the circuit depth of VQE using a UCC ansatz can be reduced without introducing significant loss of accuracy in the final wavefunctions and energies.

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Source: https://tomesphere.com/paper/1701.02691