An Introduction to Variational Quantum Eigensolver Applied to Chemistry

TL;DR

This paper introduces the Variational Quantum Eigensolver (VQE) as a promising quantum algorithm for simulating molecular systems, highlighting its potential advantages and discussing its complexity and implementation challenges.

Contribution

It provides an overview of applying VQE to chemistry, explaining its fundamentals, integration with quantum mechanics, and analyzing its computational complexity and practical challenges.

Findings

VQE can potentially outperform classical methods in molecular simulations.

The paper discusses the algorithm's spatial and temporal complexity.

It highlights the feasibility of VQE given current quantum hardware limitations.

Abstract

Quantum mechanics has introduced a new theoretical framework for the study of molecules, enabling the prediction of properties and dynamics through the solution of the Schr\"odinger equation applied to these systems. However, solving this equation is computationally expensive, which has led to the development of various mathematical frameworks and computational methods designed to balance the available resources with the desired level of accuracy. In particular, quantum computers have emerged as a promising technology with the potential to address these problems more efficiently in the coming decades, whether through reductions in memory, time, and energy consumption, $\textit{i. e.}$, reductions in computational complexity or by enhancing precision. This research field is known as Quantum Simulation. Given the current technological limitations of quantum computers, Variational Quantum Algorithms (VQAs), especially the Variational Quantum Eigensolver (VQE), stand out as a feasible approach to demonstrating advantages over classical methods in the near term. This feasibility arises from their lower demand for quantum gates and the reduced depth of the circuits required for their implementation. In this work, we present the application of quantum mechanics to the study of molecules, provide an introduction to the fundamentals of quantum computing, and explore the integration of these fields by employing the VQE in molecular simulations. Finally, we discuss the spatial and temporal complexity associated with the algorithm, highlighting its implications and challenges.