Forward and Backward Mappings for Quantum Graphical Models

Explore an invited conference talk from TQC 2024 that delves into the forward and backward mapping problems within quantum graphical models. Learn how quantum states generalize classical probability distributions and understand the complexities of deriving mean parameters from model parameters in forward mapping, including the challenges of approximating partition functions. Discover quantum belief propagation techniques for one-dimensional systems and variational methods like Markov entropy decomposition. Examine the backward mapping problem's relationship to Hamiltonian learning, and understand the quantum iterative scaling (QIS) algorithm that transforms backward mapping into sequential forward mapping problems. Study the convergence proof for QIS, its advantages over gradient descent methods, and learn how quasi-Newton methods can enhance both QIS and gradient descent algorithms for improved efficiency. Delivered at the 19th Conference on the Theory of Quantum Computation, Communication and Cryptography at OIST, Japan, this comprehensive presentation bridges theoretical quantum information science with practical computational approaches.