That would be very surprising. They show in this work that their problem is complete for the complexity class BQP. That means that if you can solve it on a classical computer (analog or not) in polynomial time you get (for free) classical polynomial-time algorithms for solving a bunch of problems we don't currently have classical poly-time algorithms for.

Most surpisingly this would include the hidden subgroup problem and hence give you a classical poly-time algorithm for integer factorization.