Effects of One-particle Reduced Density Matrix Optimization in Variational Quantum Eigensolvers

TL;DR

This paper explores optimizing the one-particle reduced density matrix within VQE to enhance the accuracy of molecular properties and energies, demonstrating significant improvements especially with the GateFabric ansatz.

Contribution

It introduces a two-step optimization algorithm that enforces 1-RDM convergence in VQE, improving molecular property predictions beyond energy optimization alone.

Findings

Optimizing 1-RDM improves electronic property accuracy.

Significant energy and property improvements with GateFabric ansatz.

Little effect on energy for k-UpCCGSD due to already close energies.

Abstract

The variational quantum eigensolver (VQE) is a promising method for simulating molecular systems on near-term quantum computers. This approach employs energy estimation; however, other relevant molecular properties can be extracted from the one-particle reduced density matrix (1-RDM) generated by VQE. The accuracy of these properties strongly depends on the reliability and convergence of the 1-RDM, which is not guaranteed by energy-only optimization. Thus, we investigate the effect of optimizing the 1-RDM within VQE to improve the accuracy of both the energy and molecular properties. A two-step algorithm was implemented that optimizes the energy and 1-RDM by incorporating a penalty term in the cost function to enforce the convergence of the 1-RDM. The first step focuses on energy minimization, while in the second step, a weighted penalty is added to the cost function to promote simultaneous improvement of the energy and 1-RDM. This approach was tested and validated for the k-UpCCGSD and GateFabric ans\"atzes with active spaces (4,4) and (2,2), respectively. k-UpCCGSD produces energies close to CISD, so optimizing 1-RDM has little effect on the energy but significantly improves electronic properties such as electron density, dipole moments, and atomic charges. GateFabric initially shows higher energy deviations from CISD, but optimizing 1-RDM substantially improves both the energy accuracy and the quality of 1-RDM. These results demonstrate that simultaneous optimization of energy and 1-RDM is an effective strategy to improve the accuracy of energies and molecular properties in variational quantum algorithms.