Quantum Speedups for Log-Concave Sampling from Local Structure

For a convex function $f \colon \mathbb{R}^d \to \mathbb{R}$, the problem of sampling from a distribution proportional to $e^{-f(x)}$ is called log-concave sampling. In many practical scenarios, the function $f(x)$ turns out to admit a local decomposition $f(x) = \sum_{a=1}^R ψ_a(x_{S_a})$. In this