Quantum Physics Stochastic Neural Networks (QPNN)

In this paper we introduce a framework of Quantum Probability (QP) as a generalized probability theory under limited information. We show that the proposed QP includes the Classical Probability (CP) as a particular case. Moreover, QP is linked to the classical mechanics through the concepts of action, Lagrangian and Hamiltonian. Starting from our QP formalism we sketch the formulation of Quantum Physics Neural Networks (QPNN) able to take into account limited information and model uncertainty. Relations with statistical physics and Ising model, Reduced Boltzmann Machines (RBM) and Deep Belief Networks (DBN) are discussed. It is also discussed their connection with Quantum Imprecise Bayesian Network (QIBN), recently proposed for sustainability and resilience of socio-ecological technical systems under uncertainty.