  We present an algorithm that given any $n$-vertex, $m$-edge, rank $r$
hypergraph constructs a spectral sparsifier with $O(n \varepsilon^{-2} \log n
\log r)$ hyperedges in nearly-linear $\widetilde{O}(mr)$ time. This improves in
both size and efficiency over a line of work (Bansal-Svensson-Trevisan 2019,
Kapralov-Krauthgamer-Tardos-Yoshida 2021) for which the previous best size was
$O(\min\{n \varepsilon^{-4} \log^3 n,nr^3 \varepsilon^{-2} \log n\})$ and
runtime was $\widetilde{O}(mr + n^{O(1)})$.
  Independent Result: In an independent work, Lee (Lee 2022) also shows how to
compute a spectral hypergraph sparsifier with $O(n \varepsilon^{-2} \log n \log
r)$ hyperedges.
