Full variance bounds beyond averaged input and target states

Derive asymptotic bounds for the full gradient variance of the Quantum Simplified Graph Convolutional Network, including the spread over input and target states rather than only its average over those states.

Background

The trainability analysis primarily evaluates the expected gradient variance averaged over possible input and target states. The paper notes that obtaining bounds for the full variance additionally requires controlling the spread across those states, and that a standard-deviation approximation may not be valid because the spread need not be symmetric.