We propose a protocol for quantum non-demolition photon counting which uses a Rydberg array as a measurement apparatus. Our protocol consists of (I) photon storage, (II) an observation phase comprised of a series of Rabi flops to a Rydberg state and measurements, and (III) retrieval of the stored photons. A detectable signal of the photon number $n$ is provided by the collective enhancement of the Rabi frequency by a factor of $\sqrt{n}$. Our protocol can be used to distill Fock states from arbitrary initial states and to perform photonic state discrimination. We confirm that it is robust to experimentally realistic noise.
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