Abstract

The Variational Quantum Eigensolver (VQE) has emerged as a transformative approach in quantum computing, providing a practical means to tackle complex quantum systems. This chapter delves into the essential components and strategies for enhancing VQE performance, focusing on key areas such as hybrid optimization techniques, quantum circuit design, and measurement efficiency. By integrating classical and quantum resources, hybrid optimization methods significantly improve convergence rates while reducing the computational burden on quantum devices. The chapter explores the design of quantum circuits, emphasizing the importance of selecting appropriate variational ansätze to achieve optimal results. Challenges related to Hamiltonian simulation and measurement are critically examined, alongside innovative solutions to mitigate noise and enhance measurement fidelity. Through these comprehensive insights, this chapter aims to illuminate the potential of VQE in advancing quantum machine learning applications across diverse scientific domains.

Introduction

The Variational Quantum Eigensolver (VQE) has emerged as a pivotal algorithm in the realm of quantum computing, particularly for addressing the complexities inherent in quantum chemistry and many-body physics [1,2]. As a hybrid algorithm, VQE leverages both quantum and classical computing resources to efficiently estimate the ground state energies of quantum systems [3]. This methodology capitalizes on the strengths of current noisy intermediate-scale quantum (NISQ) devices, which are characterized by their limited qubit count and error rates [4,5]. By combining variational techniques with quantum measurements, VQE provides a promising avenue for exploring the quantum landscape, ultimately aiming to unlock new insights into chemical reactions, materials properties, and more[6,7,8,9].

One of the core strengths of VQE lies in its adaptability to various quantum systems [10]. The algorithm can be tailored to accommodate a wide range of Hamiltonians, allowing researchers to investigate diverse physical phenomena [11,12]. For instance, the ability to incorporate different ansätze, or parameterized quantum circuits, enhances the flexibility of VQE, enabling it to represent complex quantum states more accurately [13]. This adaptability was crucial in the quest for reliable quantum simulations, as it allows researchers to fine-tune their approaches based on the specific characteristics of the system under study [14]. Consequently, VQE stands out as a versatile tool for both theoretical investigations and practical applications in quantum chemistry and beyond [15].