Chaos and complexity from quantum neural network. A study with diffusion metric in machine learning

A bstract In this work, our prime objective is to study the phenomena of quantum chaos and complexity in machine learning dynamics Quantum Neural Network (QNN). Parameterized Circuits (PQCs) hybrid quantum-classical framework introduced as a universal function approximator perform optimization with Stochastic Gradient Descent (SGD). We employ statistical differential geometric approach theory QNN. The evolution parametrized unitary operators correlated trajectory parameters Diffusion metric. establish version Complexity Chaos terms physically relevant quantities, which are not only essential determining stability, but also providing very significant lower bound generalization capability explicitly prove that when system executes limit cycles or oscillations phase space, QNN maximized. Finally, we have determined on variance steady state condition using Cauchy Schwartz Inequality.