  A new quantum spin liquid (QSL) candidate material H$_{3}$LiIr$_{2}$O$_{6}$
was synthesized recently and was found not to show any magnetic order or phase
transition down to low temperatures. In this work, we study the quantum
dynamics of the hydrogen ions, i.e., protons, in this material by combining
first-principles calculations and theoretical analysis. We show that each
proton and its adjacent oxygen ions form an electric dipole. The dipole
interactions and the proton tunneling are captured by a transverse-field Ising
model with a quantum disordered paraelectric ground state. The dipole
excitations have an energy gap $\Delta_{\mathrm{d}}\simeq 60$ meV, and can be
probed by the infrared optical spectroscopy and the dielectric response. We
argue that the electric dipole fluctuations renormalize the magnetic
interactions in H$_{3}$LiIr$_{2}$O$_{6}$ and lead to a Kitaev QSL state.
