ORQVIZ: Visualizing High-Dimensional Landscapes in Variational Quantum Algorithms

TL;DR

This paper introduces ORQVIZ, a software tool that adapts visualization techniques from deep learning to analyze high-dimensional loss landscapes in Variational Quantum Algorithms, aiding understanding and design of quantum circuits.

Contribution

It presents a novel open-source Python package, orqviz, for visualizing high-dimensional VQA landscapes, including techniques like PCA, Hessians, and elastic band algorithms, with applications to multiple VQA types.

Findings

Visualization verifies previous observations about VQAs.

Insights into the impact of noise on loss landscapes.

Enhanced understanding of VQA optimization challenges.

Abstract

Variational Quantum Algorithms (VQAs) are promising candidates for finding practical applications of near to mid-term quantum computers. There has been an increasing effort to study the intricacies of VQAs, such as the presence or absence of barren plateaus and the design of good quantum circuit ans\"atze. Many of these studies can be linked to the loss landscape that is optimized as part of the algorithm, and there is high demand for quality software tools for flexibly studying these loss landscapes. In our work, we collect a variety of techniques that have been used to visualize the training of deep artificial neural networks and apply them to visualize the high-dimensional loss landscapes of VQAs. We review and apply the techniques to three types of VQAs: the Quantum Approximate Optimization Algorithm, the Quantum Circuit Born Machine, and the Variational Quantum Eigensolver. Additionally, we investigate the impact of noise due to finite sampling in the estimation of loss functions. For each case, we demonstrate how our visualization techniques can verify observations from past studies and provide new insights. This work is accompanied by the release of the open-source Python package $\textit{orqviz}$, which provides code to compute and flexibly plot 1D and 2D scans, Principal Component Analysis scans, Hessians, and the Nudged Elastic Band algorithm. $\textit{orqviz}$ enables flexible visual analysis of high-dimensional VQA landscapes and can be found at: $\textbf{github.com/zapatacomputing/orqviz}$.