Nearly Optimal Embeddings of Flat Tori

Ishan Agarwal, Oded Regev, Yi Tang

We show that for any $n$-dimensional lattice $\mathcal{L}\subseteq {\mathbb{R}}^n$, the torus ${\mathbb{R}}^n/\mathcal{L}$ can be embedded into Hilbert space with $O(\sqrt{n\log n})$…