  We develop a program package named QS$^{3}$ [\textipa{kj\'u:-\'es-kj\'u:b}]
based on the (thick-restart) Lanczos method for analyzing spin-1/2 XXZ-type
quantum spin models on spatially uniform/non-uniform lattices near fully
polarized states, which can be mapped to dilute hardcore Bose systems. All
calculations in QS$^{3}$, including eigenvalue problems, expectation values for
one/two-point spin operators, and static/dynamical spin structure factors, are
performed in the symmetry-adapted bases specified by the number
$N_{\downarrow}$ of down spins and the wave number $\boldsymbol{k}$ associated
with the translational symmetry without using the bit representation for
specifying spin configurations. Because of these treatments, QS$^{3}$ can
support large-scale quantum systems containing more than 1000 sites with dilute
$N_{\downarrow}$. We show the benchmark results of QS$^{3}$ for the low-energy
excitation dispersion of the isotropic Heisenberg model on the
$10\times10\times10$ cubic lattice, the static and dynamical spin structure
factors of the isotropic Heisenberg model on the $10\times10$ square lattice,
and the open-MP parallelization efficiency on the supercomputer (Ohtaka) based
on AMD Epyc 7702 installed at the Institute for the Solid State Physics (ISSP).
Theoretical backgrounds and the user interface of QS$^{3}$ are also described.
