  We study $N$ qubits having infinite-range Ising interaction and subjected to
periodic pulse of external magnetic field. We solve the cases of $N=5$ to $11$
qubits analytically, finding its eigensystem, the dynamics of the entanglement
for various initial states, and the unitary evolution operator. These
quantities shows signatures of quantum integrability. For the general case of
$N>11$ qubits, we provide a conjecture on quantum integrability based on the
numerical evidences like degenerate spectrum, and the exact periodic nature of
the time-evolved unitary evolution operator and the entanglement dynamics.
Using linear entropy we show that for class of initial unentangled state the
entanglement displays periodically maximum and zero values.
