  We present SQDFT: a large-scale parallel implementation of the Spectral
Quadrature (SQ) method for $\mathcal{O}(N)$ Kohn-Sham Density Functional Theory
(DFT) calculations at high temperature. Specifically, we develop an efficient
and scalable finite-difference implementation of the infinite-cell
Clenshaw-Curtis SQ approach, in which results for the infinite crystal are
obtained by expressing quantities of interest as bilinear forms or sums of
bilinear forms, that are then approximated by spatially localized
Clenshaw-Curtis quadrature rules. We demonstrate the accuracy of SQDFT by
showing systematic convergence of energies and atomic forces with respect to SQ
parameters to reference diagonalization results, and convergence with
discretization to established planewave results, for both metallic and
insulating systems. We further demonstrate that SQDFT achieves excellent strong
and weak parallel scaling on computer systems consisting of tens of thousands
of processors, with near perfect $\mathcal{O}(N)$ scaling with system size and
wall times as low as a few seconds per self-consistent field iteration.
Finally, we verify the accuracy of SQDFT in large-scale quantum molecular
dynamics simulations of aluminum at high temperature.
