Alexander the Great's empire is a reasonable contender, I think. He inherited the Kingdom of Macedonia upon the death of his father in 336, became Pharoah of Egypt in 332, and king of Persia in 330. Having, within the space of six years, conquered what was the Persian empire, brought almost all of Greece under his control, and began to campaign beyond the borders of the Persian empire towards India, seven years later, at the time of his death, the empire fell apart, and was divided up among his various generals.
So we can say seven years as an upper bound for the shortest empire in history. I'm sure there are significantly shorter ones, but I can't think of any obviously at the moment.
I'm removing this question because it's essentially unanswerable. 'Collapse' isn't a hard and fast term, so any answer is just going to be opinion.