Speaker: 苗强博士

Title: Barren Plateaus in the Riemannian Formulation and Gradient Scaling in Tensor Network Ansätze

Language: Chinese

Time & Venue: 2026.04.21 15:00-16:00 思源楼615

Abstract: Barren plateaus in the optimization task of hybrid quantum-classical algorithms, posing a significant obstacle to scalability. This report synthesizes recent theoretical advances to investigate this challenge from two complementary angles. First, by examining the problem through a Riemannian formulation, we demonstrate that barren plateaus are fundamentally equivalent to an exponential decay in the variance of cost-function differences. This geometric perspective provides a tighter analytical bound and reveals that the issue persists regardless of whether optimization is gradient-based or gradient-free. Second, we investigate the gradient scaling properties within tensor network states (TNS), specifically Matrix Product States, Tree Tensor Networks, and the Multiscale Entanglement Renormalization Ansatz. Contrary to generic quantum circuits, we prove these architectures are inherently free of barren plateaus, providing analytical guarantees for the trainability of randomly initialized states. These findings highlight the critical role of ansatz design in overcoming exponential hardness.