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Lower bounds for quantum circuits using the geodesic framework

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(this question is a crosspost from cstheory. I've incorporated the one answer there into the question)

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 ?

One example that Joe Fitzsimmons provided is this paper on optimal transfer rates in spin chains. While it's a good example of the "spirit" of the original idea, I'm specifically looking for methods that use Nielsen's program to provide lower bounds.

This post has been migrated from (A51.SE)
asked Dec 7, 2011 in Theoretical Physics by suresh (1,535 points) [ no revision ]
I could suggest to see "introduction" sections to papers such as http://arxiv.org/abs/1009.5968 and http://arxiv.org/abs/quant-ph/0603160 for list of references and some terms ...

This post has been migrated from (A51.SE)

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