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Ants, like many other animals, use visual memory to follow extended routes through complex environments, but it is unknown how their small brains implement this capability. The mushroom body neuropils have been identified as a crucial memory circuit in the insect brain, but their function has mostly been explored for simple olfactory association tasks. We show that a spiking neural model of this circuit originally developed to describe fruitfly (Drosophila melanogaster) olfactory association, can also account for the ability of desert ants (Cataglyphis velox) to rapidly learn visual routes through complex natural environments. We further demonstrate that abstracting the key computational principles of this circuit, which include one-shot learning of sparse codes, enables the theoretical storage capacity of the ant mushroom body to be estimated at hundreds of independent images.