Learnability and expressibility of variational quantum circuit: VC and PAC-Bayesian theory

Abstract

Variational quantum circuit algorithm is suggested as a machine learning paradigm to utilize the power of Noisy Intermediate-Scale Quantum hardware. Recent efforts lead to better theoretical understanding of the expressibility and generalization ability of quantum circuits. In this work, we compare our previous results on the quantum circuit learnability based on VC theory to some preliminary results based on PAC-Bayesian method. Some recent developments based on other generalization bounds due to other research groups are also reviewed and discussed.