The polynomial-factor hardness conjecture for the Shortest Vector Problem

Let $\mathrm{SVP}$ denote the Shortest Vector Problem on lattices, and let a polynomial-factor approximation mean an approximation within a factor bounded by a polynomial in the lattice dimension. Polynomial-factor SVP hardness conjecture. There is no polynomial-time quantum algorithm that approximates $\mathrm{SVP}$ to within polynomial factors. This is the widely believed worst-case hardness assumption underlying the cryptographic evidence for the computational hardness of continuous learning with errors.