Analyzing variational quantum landscapes with information content

• DOI: 10.48550/arxiv.2303.16893
• Publication Date: 2023-01-01
• Authors: Adrián Pérez-Salinas; Hao Wang; Xavier Bonet-Monroig
• Keywords: Content (measure theory)

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