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.

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    $\begingroup$ I could suggest to see "introduction" sections to papers such as arxiv.org/abs/1009.5968 and arxiv.org/abs/quant-ph/0603160 for list of references and some terms ... $\endgroup$ Commented Dec 12, 2011 at 19:36
  • $\begingroup$ This was apparently posted to some other SE site as a crosspost of a CS theory question, which then got merged back with CS theory! $\endgroup$ Commented May 17, 2015 at 15:22
  • $\begingroup$ ok that's very weird ! $\endgroup$ Commented May 19, 2015 at 17:09


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