Analyzing variational quantum landscapes with information content

npj Quantum Information, vol. 10

Abstract

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 way to analyze variational quantum algorithms in a data-driven fashion well-suited for near-term quantum computers.

Authors 3

1. Adrián Pérez-Salinas corresponding Aachen Instituut-Lorentz 〈aQaL〉 Applied Quantum Algorithms

   Leiden University

   Affiliation as printed

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

   〈aQaL〉 Applied Quantum Algorithms, Universiteit Leiden, Leiden, Netherlands

2. Hao Wang corresponding Aachen 〈aQaL〉 Applied Quantum Algorithms

   Leiden University

   Affiliation as printed

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

   〈aQaL〉 Applied Quantum Algorithms, Universiteit Leiden, Leiden, Netherlands

3. Xavier Bonet-Monroig corresponding Aachen Instituut-Lorentz 〈aQaL〉 Applied Quantum Algorithms

   Leiden University

   Affiliation as printed

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

   〈aQaL〉 Applied Quantum Algorithms, Universiteit Leiden, Leiden, Netherlands