  Neutron scattering measurements on the pyrochlore magnet Ce$_2$Zr$_2$O$_7$
reveal an unusual crystal field splitting of its lowest $J$=5/2 multiplet, such
that its ground state doublet is composed of m$_J$=$\pm$3/2, giving these
doublets a dipole - octupole (DO) character with local Ising anisotropy. Its
magnetic susceptibility shows weak antiferromagnetic correlations with
$\theta_{CW}$=-0.4(2)K, leading to a naive expectation of an All-In, All-Out
ordered state at low temperatures. Instead our low energy inelastic neutron
scattering measurements show a dynamic quantum spin ice state, with suppressed
scattering near |$\textbf{Q}$|=0, and no long range order at low temperatures.
This is consistent with recent theory predicting symmetry enriched U(1) quantum
spin liquids for such DO doublets decorating the pyrochlore lattice. Finally,
we show that disorder, especially oxidation of powder samples, is important in
Ce$_2$Zr$_2$O$_7$ and could play an important role in the low temperature
behaviour of this material.
