Exploring the Cost Landscape of Variational Quantum Algorithms

Variational Quantum Algorithms (VQAs) have emerged as a promising approach to leverage the capabilities of quantum computing, even within the constraints of limited qubits and noise. Understanding their iterative process, including their cost landscapes, is necessary to optimize these algorithms. This landscape represents the interplay between the algorithm's parameters and the cost function, offering a visualization of the challenges for the optimization process. Regions known as barren plateaus and narrow gorges can impede optimization algorithms by causing gradients to vanish, leading to stalled optimization processes. Recognizing and devising strategies to circumvent these severe problems is essential for designing VQAs. For this purpose, we provide an overview of local and global metrics to support the understanding of the VQA cost landscape. Moreover, our results may serve as a baseline for further research on cost landscapes.