Benchmarking of different optimizers in the VQAs for applications in quantum chemistry

What is it about?

Classical optimizers play a crucial role in determining the accuracy and convergence of variational quantum algorithms; leading algorithms use a near-term quantum computer to solve the ground state properties of molecules, simulate the dynamics of different quantum systems, and so on. In the literature, many optimizers, each having its own architecture, have been employed expediently for different applications. In this work, we consider a few popular and efficacious optimizers and assess their performance in variational quantum algorithms for applications in quantum chemistry in a realistic noisy setting. We benchmark the optimizers with critical analysis based on quantum simulations of simple molecules, such as hydrogen, lithium hydride, beryllium hydride, water, and hydrogen fluoride. The errors in the ground state energy, dissociation energy, and dipole moment are the parameters used as yardsticks. All the simulations were carried out with an ideal quantum circuit simulator, a noisy quantum circuit simulator, and finally, a noisy simulator with noise embedded from the IBM Cairo quantum device to understand the performance of the classical optimizers in ideal and realistic quantum environments.

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Photo by Fractal Hassan on Unsplash

Photo by Fractal Hassan on Unsplash

Why is it important?

An optimizer plays one of the most crucial parts in any variational quantum algorithm as it determines the overall efficiency of the employed algorithm, both in terms of accuracy and convergence speed. The performance of an optimizer depends partly on the quantum hardware (or the simulator being used) and partly on the problem at hand. Currently, a wide variety of optimizers are available for end users. They can be broadly classified into the following three categories: (a) gradient-based optimizers require evaluation of the gradient of the cost function for optimization, (b) gradient-free optimizers do not require the gradient evaluation, and (c) quantum-hardware-specific optimizers, where the gradient evaluation requires some quantum architecture. The availability of multiple options leads to confusion in the choice of proper optimizers for measurement-specific or otherwise overall performance. In that respect, a benchmarking of the optimizers specific to quantum chemistry applications is essential. Similar benchmarking studies are also available in the literature on variational quantum linear solvers, quantum machine learning (QML) problems, complex network analyses, and a few others. There exist very few benchmarking studies on quantum chemistry problems, where only a few specific gradient-free optimizers were considered. The aim of the present work is to provide a comparative performance analysis of some of the commonly used classical optimizers in the variational quantum algorithms based on different applications related to quantum chemistry.