This paper presents a novel CNN-based architecture, referred to as Q-Net, to learn local feature descriptors that are useful for matching image patches from two different spectral bands. Given correctly matched and non-matching cross-spectral image pairs, a quadruplet network is trained to map input image patches to a common Euclidean space, regardless of the input spectral band. Our approach is inspired by the recent success of triplet networks in the visible spectrum, but adapted for cross-spectral scenarios, where, for each matching pair, there are always two possible non-matching patches: one for each spectrum. Experimental evaluations on a public cross-spectral VIS-NIR dataset shows that the proposed approach improves the state-of-the-art. Moreover, the proposed technique can also be used in mono-spectral settings, obtaining a similar performance to triplet network descriptors, but requiring less training data.