  Spin liquids are highly correlated yet disordered states formed by the
entanglement of magnetic dipoles$^1$. Theories typically define such states
using gauge fields and deconfined quasiparticle excitations that emerge from a
simple rule governing the local ground state of a frustrated magnet. For
example, the '2-in-2-out' ice rule for dipole moments on a tetrahedron can lead
to a quantum spin ice in rare-earth pyrochlores - a state described by a
lattice gauge theory of quantum electrodynamics$^{2-4}$. However, f-electron
ions often carry multipole degrees of freedom of higher rank than dipoles,
leading to intriguing behaviours and 'hidden' orders$^{5-6}$. Here we show that
the correlated ground state of a Ce$^{3+}$-based pyrochlore, Ce$_2$Sn$_2$O$_7$,
is a quantum liquid of magnetic octupoles. Our neutron scattering results are
consistent with the formation of a fluid-like state of matter, but the
intensity distribution is weighted to larger scattering vectors, which
indicates that the correlated degrees of freedom have a more complex
magnetization density than that typical of magnetic dipoles in a spin liquid.
The temperature evolution of the bulk properties in the correlated regime below
1 Kelvin is well reproduced using a model of dipole-octupole doublets on a
pyrochlore lattice$^{7-8}$. The nature and strength of the octupole-octupole
couplings, together with the existence of a continuum of excitations attributed
to spinons, provides further evidence for a quantum ice of octupoles governed
by a '2-plus-2-minus' rule. Our work identifies Ce$_2$Sn$_2$O$_7$ as a unique
example of a material where frustrated multipoles form a 'hidden' topological
order, thus generalizing observations on quantum spin liquids to multipolar
phases that can support novel types of emergent fields and excitations.
