  $LaH_{10}$, as a member of hydrogen-rich superconductors, has a
superconducting critical temperature of 250 K at high pressures, which exhibits
the possibility of solving the long-term goal of room temperature
superconductivity. Considering the extreme pressure and low mass of hydrogen,
the nuclear quantum effects in $LaH_{10}$ should be significant and have an
impact on its various physical properties. Here, we adopt the method combines
deep-potential (DP) and quantum thermal bath (QTB), which was verified to be
able to account for quantum effects in high-accuracy large-scale molecular
dynamics simulations. Our method can actually reproduce pressure-temperature
phase diagrams of $LaH_{10}$ consistent with experimental and theoretical
results. After incorporating quantum effects, the quantum fluctuation driven
diffusion of proton is found even in the absence of thermal fluctuation near 0
K. The high mobility of proton is found to be compared to liquid, yet the
structure of $LaH_{10}$ is still rigid. These results would greatly enrich our
vision to study quantum behavior of hydrogen-rich superconductors.
