Optimization of the Variational Quantum Eigensolver for Quantum Chemistry Applications

TL;DR

This paper analyzes and optimizes the variational quantum eigensolver (VQE) algorithm for quantum chemistry, focusing on reducing qubit manipulations, comparing classical and quantum methods, and providing performance-based recommendations.

Contribution

It formally justifies qubit removal in VQE and evaluates different classical and entangling methods for improved performance in quantum chemistry applications.

Findings

Qubit removal process is formally justified.

Certain classical optimization algorithms outperform others at high dimensionality.

Performance-based recommendations for entangling and optimization methods are provided.

Abstract

This work studies the variational quantum eigensolver algorithm, designed to determine the ground state of a quantum mechanical system by combining classical and quantum hardware. Methods of reducing the number of required qubit manipulations, prone to induce errors, for the variational quantum eigensolver are studied. We formally justify the qubit removal process as sketched by Bravyi, Gambetta, Mezzacapo and Temme [arXiv:1701.08213 (2017)]. Furthermore, different classical optimization and entangling methods, both gate based and native, are surveyed by computing ground state energies of H$_2$ and LiH. This paper aims to provide performance-based recommendations for entangling methods and classical optimization methods. Analyzing the VQE problem is complex, where the optimization algorithm, the method of entangling, and the dimensionality of the search space all interact. In specific cases however, concrete results can be shown, and an entangling method or optimization algorithm can be recommended over others. In particular we find that for high dimensionality (many qubits and/or entanglement depth) certain classical optimization algorithms outperform others in terms of energy error.