  The calculation of nuclear electromagnetic sum rules by directly
diagonalizing the nuclear Hamiltonian in a large basis is numerically
challenging and has not been performed for $A>2$ nuclei. With the significant
progress of high performance computing, we show that calculating sum rules
using numerous discretized continuum states obtained by directly diagonalizing
the ab initio no-core shell model Hamiltonian is achievable numerically.
Specifically, we calculate the $^{4}$He electric dipole ($E1$) polarizability,
that is an inverse energy weighted sum rule, employing the Daejeon16 $NN$
interaction. We demonstrate that the calculations are numerically tractable as
the dimension of the basis increases and are convergent. Our results for the
$^{4}$He electric dipole polarizability are consistent with the most recent
experimental data and are compared with those of other theoretical studies
employing different techniques and various interactions.
