A Unified Theory of Barren Plateaus for Deep Parametrized Quantum Circuits

Explore a comprehensive lecture on the unified theory of barren plateaus in deep parametrized quantum circuits. Delve into the challenges faced by variational quantum computing schemes, including trainability issues caused by circuit expressiveness, input data entanglement, observable locality, and hardware noise. Discover a novel Lie algebraic theory that provides an exact expression for the loss function variance in deep parametrized quantum circuits, even in the presence of certain noise models. Understand how this framework unifies previously independent sources of barren plateaus through generalized concepts of entanglement, operator locality, and algebraic decoherence. Gain insights into the mathematical aspects of quantum learning and their implications for near-term quantum devices.