Benchmarking VQE Configurations: Architectures, Initializations, and Optimizers for Silicon Ground State Energy

TL;DR

This paper systematically benchmarks different VQE configurations, including architectures, initializations, and optimizers, for estimating the silicon atom's ground-state energy, providing insights into optimal settings for quantum chemical simulations.

Contribution

It offers a structured benchmark of VQE configurations, highlighting the impact of initialization and optimizer choices on performance for complex quantum chemistry problems.

Findings

Initialization significantly affects stability and convergence.

Adaptive optimizers outperform conventional methods.

Chemically inspired ansatz improves accuracy and convergence.

Abstract

Quantum computing presents a promising path toward precise quantum chemical simulations, particularly for systems that challenge classical methods. This work investigates the performance of the Variational Quantum Eigensolver (VQE) in estimating the ground-state energy of the silicon atom, a relatively heavy element that poses significant computational complexity. Within a hybrid quantum-classical optimization framework, we implement VQE using a range of ansatz, including Double Excitation Gates, ParticleConservingU2, UCCSD, and k-UpCCGSD, combined with various optimizers such as gradient descent, SPSA, and ADAM. The main contribution of this work lies in a systematic methodological exploration of how these configuration choices interact to influence VQE performance, establishing a structured benchmark for selecting optimal settings in quantum chemical simulations. Key findings show that parameter initialization plays a decisive role in the algorithm's stability, and that the combination of a chemically inspired ansatz with adaptive optimization yields superior convergence and precision compared to conventional approaches.