Sampling from Spherical Spin Glasses in Total Variation via Algorithmic Stochastic Localization

We consider the problem of algorithmically sampling from the Gibbs measure of a mixed $p$-spin spherical spin glass. We give a polynomial-time algorithm that samples from the Gibbs measure up to vanishing total variation error, for any model whose mixture satisfies $$ ξ''(s) < \frac{1}{(1-s)^2}, \