  In a quantum spin liquid, the magnetic moments of the constituent electron
spins evade classical long-range order to form an exotic state that is quantum
entangled and coherent over macroscopic length scales [1-2]. Such phases offer
promising perspectives for device applications in quantum information
technologies, and their study can reveal fundamentally novel physics in quantum
matter. Quantum spin ice is an appealing proposal of one such state, in which
the fundamental ground state properties and excitations are described by an
emergent U(1) lattice gauge theory [3-7]. This quantum-coherent regime has
quasiparticles that are predicted to behave like magnetic and electric
monopoles, along with a gauge boson playing the role of an artificial photon.
However, this emergent lattice quantum electrodynamics has proved elusive in
experiments. Here we report neutron scattering measurements of the rare-earth
pyrochlore magnet Pr$_2$Hf$_2$O$_7$ that provide evidence for a quantum spin
ice ground state. We find a quasi-elastic structure factor with pinch points -
a signature of a classical spin ice - that are partially suppressed, as
expected in the quantum-coherent regime of the lattice field theory at finite
temperature. Our result allows an estimate for the speed of light associated
with magnetic photon excitations. We also reveal a continuum of inelastic spin
excitations, which resemble predictions for the fractionalized, topological
excitations of a quantum spin ice. Taken together, these two signatures suggest
that the low-energy physics of Pr$_2$Hf$_2$O$_7$ can be described by emergent
quantum electrodynamics. If confirmed, the observation of a quantum spin ice
ground state would constitute a concrete example of a three-dimensional quantum
spin liquid - a topical state of matter which has so far mostly been explored
in lower dimensionalities.
