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Free keywords:
High Energy Physics - Theory, hep-th, Condensed Matter, Disordered Systems and Neural Networks, cond-mat.dis-nn,Computer Science, Learning, cs.LG,Nonlinear Sciences, Chaotic Dynamics, nlin.CD,Quantum Physics, quant-ph
Abstract:
In this work, our prime objective is to study the phenomena of quantum chaos
and complexity in the machine learning dynamics of Quantum Neural Network
(QNN). A Parameterized Quantum Circuits (PQCs) in the hybrid quantum-classical
framework is introduced as a universal function approximator to perform
optimization with Stochastic Gradient Descent (SGD). We employ a statistical
and differential geometric approach to study the learning theory of QNN. The
evolution of parametrized unitary operators is correlated with the trajectory
of parameters in the Diffusion metric. We establish the parametrized version of
Quantum Complexity and Quantum Chaos in terms of physically relevant
quantities, which are not only essential in determining the stability, but also
essential in providing a very significant lower bound to the generalization
capability of QNN. We explicitly prove that when the system executes limit
cycles or oscillations in the phase space, the generalization capability of QNN
is maximized. Moreover, a lower bound on the optimization rate is determined
using the well known Maldacena Shenker Stanford (MSS) bound on the Quantum
Lyapunov exponent.
