A promising route to realize entangled magnetic states combines geometrical frustration with quantum-tunneling effects. Spin-ice materials are canonical examples of frustration, and Ising spins in a transverse magnetic field are the simplest many-body model of quantum tunneling. In this talk, I shall show that the recently discovered tripod kagome lattice material Ho₃Mg₂Sb₃O₁₄ unites an ice-like magnetic degeneracy with quantum-tunneling terms generated by an intrinsic splitting of the Ho³⁺ ground-state doublet. Using neutron scattering and thermodynamic experiments, we observe a symmetry-breaking transition at T* ~ 0.32 K to a remarkable quantum state with three peculiarities: a macroscopic degeneracy of ice-like microstates; a fragmentation of the spin into periodic and aperiodic components; and persistent spin fluctuations down to 0.12 K. A model incorporating the interplay of frustration and quantum dynamics is necessary to explain our scattering data. Our results establish Ho₃Mg₂Sb₃O₁₄ realizes quantum kagome ice, a frustrated Ising model with an intrinsic homogeneous transverse field.