Dynamical Transition in Controllable Quantum Neural Networks with Large Depth

Explore a 33-minute QuICS lecture examining the training dynamics of quantum neural networks and their fundamental role in quantum information science. Delve into how late-time training dynamics with quadratic loss functions can be described through generalized Lotka-Volterra equations, leading to transcritical bifurcation transitions. Learn about the duality between quantum neural tangent kernel and total error, as dynamics shift from frozen-kernel to frozen-error states. Understand the exponential convergence patterns toward fixed points and polynomial behavior at critical points through non-perturbative analytical theory using restricted Haar ensemble. Examine the Hessian-to-effective-Hamiltonian mapping and its linearly vanishing gap at transition points. Compare training convergence speeds between linear and quadratic loss functions, with experimental verification from IBM quantum devices, and explore generalizations beyond binary cases to multiple data scenarios.