He might be referring to this: http://arxiv.org/pdf/0811.3171v3.pdf

So, if the question you want to ask is "what is some property of the solution of the (sparse) set of linear equations" rather than wanting to know the (inherently O(n)) solution itself, you can get exponential speedup.

Well yes, that's one problem with quantum computing. Writing data to those qubits and reading the computed results is getting you back to square one.