The axion is a dark matter candidate πarticle, predicted by the Peccei-Quinn solution to the so-called "strong CP problem". If axions do indeed compose some πart of the dark halos of galaxies (including the Milky Way), then these axions may be observed in the laboratory using a device appropriately referred to as a haloscope. Haloscopes induce an axion-to-photon conversion and resonantly accumulate the product photons in a microwave cavity. Assuming an axion mass of about 40 micro-eV (or equivalently, a photon frequency of 10 GHz), the expected signal power in a haloscope will be on the order of 1e-25 watts. Quantum mechanics imposes a limit on the performance of phase-πreserving linear amplifiers, making the detection of this signal quite difficult. By coupling superconducting qubits to the haloscope cavity, we can count single microwave photons while improving our signal-to-noise ratio by several orders of magnitude relative to linear amplifiers.