Some of us have been reading Michael Nielsen's paper on a geometric approach to using quantum lower bounds (in brief, the construction of a Finsler metric on $SU(2^n)$ such that the geodesic distance from $I$ to an element $U$ is a lower bound on the number of gates in a quantum circuit that computes $U$). I was wondering if there were concrete examples of problems where this program led to a lower bound that came close to, matched or beat prior lower bounds obtained by other means ? 
Lower bounds for quantum circuits using the geodesic framework
quantum computing