Analyzing variational quantum landscapes with information content

arXiv (Cornell University)

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.

Authors 3

1. Adrián Pérez-Salinas
2. Hao Wang Aachen

   Leiden University

   Affiliation as printed

   Applied Quantum Algorithms , Universiteit Leiden

   LIACS , Universiteit Leiden , Niels Bohrweg 1 , 2333 CA Leiden , Netherlands

3. Xavier Bonet-Monroig Aachen Instituut-Lorentz

   Leiden University

   Affiliation as printed

   Instituut-Lorentz , Universiteit Leiden , Niels Bohrweg 2 , 2333 CA Leiden , Netherlands