  We study theoretically driven quantum dynamics in periodic arrays of
two-level qubits coupled to the waveguide. We demonstrate, that strongly
subradiant eigenstates of the master equation for the density matrix emerge
under strong coherent driving for arrays with the anti-Bragg periods
$d=\lambda/4,3\lambda/4$... This happens even though are no such states at low
driving powers. Thus, our findings show that in the quantum nonlinear regime
the domain of existence of subradiant states expands beyond conventional
subwavelength structures. These driven states are directly manifested in
long-living quantum correlations between the qubit excitations.
