  We investigate the structural and thermodynamic properties of high-pressure
ice by incorporating quantum anharmonicity at a non-perturbative level. Quantum
fluctuations reduce the critical pressure of the phase transition between phase
VIII (with asymmetric H-bonds) and phase X (with symmetric H-bonds) by 65 GPa
from its classical value of 116 GPa at 0K. Moreover, quantum effects make it
temperature-independent over a wide temperature range (0K-300K), in agreement
with experimental estimates obtained through vibrational spectroscopy and in
striking contrast to the strong temperature dependence found in the classical
approximation. The equation of state shows fingerprints of the transition in
accordance with experimental evidence. Additionally, we demonstrate that,
within our approach, proton disorder in phase VII has a negligible impact on
the occurrence of phase X. Finally, we reproduce with high accuracy the 10 GPa
isotope shift due to the hydrogen-to-deuterium substitution.
