Note that this is an oracle result, which has about zero relevance to anything in our universe (because oracles don't exist in our universe). It is of purely theoretical interest to complexity theorists.

In our universe it remains unknown if there are problems that can be solved efficiently by a quantum computer but not by any classical algorithm. It is known that BQP is contained in P^#P, so proving such a result would require separating P from P^#P, which is probably nearly as difficult as separating P from NP.