Tall stems. Tiny little 'leaves' ... seems more like a succulent than a cactus. But which one?
Hi Stephen, based on your picture I'm going to say that this is one of the many Euphorbia, which by the way are poisonous, so when dealing with it, please use caution as the sap is caustic and can cause eye damage and contact dermatitis.
I'm not sure if the leaves actually are burgundy colored, as they appear in the picture, so that makes me wonder if this is a particular variety that has that type of coloration; I've included a link to one that looks similar.