  H$_3$S is believed to the most possible high-temperature superconducting
($T_{\text{c}}$) phase of hydrogen sulfide at $\sim$200 GPa. It's isotope
substitution of hydrogen (H) by deuterium (D), however, shows an anomalous
$T_{\text{c}}$ decrease of $\sim$100 K at 140 to 160 GPa, much larger than the
Bardeen-Cooper-Schrieffer theory prediction. Using ab initio path-integral
molecular dynamics (PIMD), we show that the nuclear quantum effects (NQEs)
influence the structures of H$_3$S and D$_3$S differently at finite
temperatures and the interval when H$_3$S possesses the symmetric high
$T_{\text{c}}$ structure while D$_3$S does not is in agreement with, though
their absolute values are lower than experiments. This is consistent with an
earlier theoretical study using the stochastic self-consistent harmonic
approximation method in descriptions of the nuclei at 0 K.The remaining
discrepancy can be substantially improved when the electronic structures are
calculated using a hybrid function. Our study presents a simple picture to
interpret the isotope dependent of $T_{\text{c}}$ and emphasizes the quantum
nature in the high-pressure hydrogen sulfide system.
