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Rapid Mixing of Parallel Kac's Walk: From Spheres to Stiefel Manifolds
Kac's walk is a classical local random walk whose action on a single real unit vector in dimension $d$ mixes in total variation in $Θ(d\log d)$ sequential steps~\cite{PS17}. Lu, Qin, Song, Yao, and Zhao introduced a parallel version of Kac's walk that mixes a single quantum state in $O(\log d)$ roun
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