  Periodically driven quantum many-body systems exhibit novel nonequilibrium
states such as prethermalization, discrete time crystals, and many-body
localization. Recently, the general mechanism of fractional resonances has been
proposed that leads to slowing the many-body dynamics in systems with both
$U(1)$ and parity symmetry. Here, we show that fractional resonance is stable
under local noise models. To corroborate our finding, we numerically study the
dynamics of a small-scale Bose-Hubbard model that can readily be implemented in
existing noisy intermediate-scale quantum (NISQ) devices. Our findings suggest
a possible pathway toward a stable nonequilibrium state of matter, with
potential applications of quantum memories for quantum information processing.
