Analyzing variational quantum landscapes with information content

TL;DR

This paper introduces an information content framework to analyze variational quantum landscapes, linking it to gradient norms, and validates the approach through numerical studies of barren plateau problems, aiding near-term quantum algorithm analysis.

Contribution

It establishes a connection between information content and gradient norms in variational quantum landscapes, providing analytical bounds and a data-driven analysis method.

Findings

Derived bounds on gradient estimators using information content

Validated the approach with numerical scaling analysis of barren plateaus

Provided a new analytical tool for near-term quantum algorithm assessment

Abstract

The parameters of the quantum circuit in a variational quantum algorithm induce a landscape that contains the relevant information regarding its optimization hardness. In this work we investigate such landscapes through the lens of information content, a measure of the variability between points in parameter space. Our major contribution connects the information content to the average norm of the gradient, for which we provide robust analytical bounds on its estimators. This result holds for any (classical or quantum) variational landscape. We validate the analytical understating by numerically studying the scaling of the gradient in an instance of the barren plateau problem. In such instance we are able to estimate the scaling pre-factors in the gradient. Our work provides a new way to analyze variational quantum algorithms in a data-driven fashion well-suited for near-term quantum computers.