  The pyrochlore material Nd$_2$Zr$_2$O$_7$ with an "all-in-all-out" (AIAO)
magnetic order shows novel quantum moment fragmentation with gapped flat
dynamical spin ice modes. The parameterized spin Hamiltonian with a dominant
frustrated ferromagnetic transverse term reveals a proximity to a U(1) spin
liquid. Here we study magnetic excitations of Nd$_2$Zr$_2$O$_7$ above the
ordering temperature ($T_\text{N}$) using high-energy-resolution inelastic
neutron scattering. We find strong spin ice correlations at zero energy with
the disappearance of gapped magnon excitations of the AIAO order. It seems that
the gap to the dynamical spin ice closes above $T_\text{N}$ and the system
enters a quantum spin ice state competing with and suppressing the AIAO order.
Classical Monte Carlo, molecular dynamics and quantum boson calculations
support the existence of a Coulombic phase above $T_\text{N}$. Our findings
relate the magnetic ordering of Nd$_2$Zr$_2$O$_7$ with the Higgs mechanism and
provide explanations for several previously reported experimental features.
