Rydberg atoms with principal quantum number n >> 1 have exaggerated atomic
properties including dipole-dipole interactions that scale as n^4 and radiative
lifetimes that scale as n^3. It was proposed a decade ago to take advantage of
these properties to implement quantum gates between neutral atom qubits. The
availability of a strong, long-range interaction that can be coherently turned
on and off is an enabling resource for a wide range of quantum information
tasks stretching far beyond the original gate proposal. Rydberg enabled
capabilities include long-range two-qubit gates, collective encoding of
multi-qubit registers, implementation of robust light-atom quantum interfaces,
and the potential for simulating quantum many body physics. We review the
advances of the last decade, covering both theoretical and experimental aspects
of Rydberg mediated quantum information processing.Comment: accepted version, to appear in Rev. Mod. Phys., 40 figures
