This shrub like cactus is an unknown species of Cylindropuntia. The way to tell members of the Cylindropuntia genus is by their cylindrical stems. The stem shape can almost guarantee inclusion in the genus. However, species identity is often difficult to pinpoint because this genus easily hybridizes.
I’m surprised at the fast growth rate of this cactus. I purchased it in April as a small two-inch high specimen in a four-inch pot, and it has grown to its present size of 10 inches high in this short time. Although I’ve only watered it a couple of times in the past six months, it is thriving. Many cacti, especially Cylindropuntia, including those in pots, do not need much water at all.
Unlike many species in this genus, the segmented stems of this cactus do not easily separate. Also, there are no paper-like sheaths on the spines, so I don't think it is a Cholla. Perhaps when it blooms, I will have another clue as to its species.