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

Journal of High Energy Physics

Ankan Dutta¹  Debisree Ray²  Sayantan Choudhury³ 

[1] Department of Mechanical Engineering, Jadavpur University, 700032, Kolkata, India;Department of Physics and Astronomy, Mississippi State University, 355 Lee Boulevard, 39762, Mississippi State, MS, USA;National Institute of Science Education and Research, 752050, Bhubaneswar, Odisha, India;Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, 400085, Mumbai, India;Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, 14476, Potsdam-Golm, Germany;

关键词: Stochastic Processes;    Random Systems;    Classical Theories of Gravity;    Matrix Models;   

DOI  :  10.1007/JHEP04(2021)138

来源: Springer

【 摘 要 】

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. Finally, we have determined the generalization capability bound on the variance of parameters of the QNN in a steady state condition using Cauchy Schwartz Inequality.

【 授权许可】

CC BY