<p>Some of us have been reading <a href="https://cstheory.stackexchange.com/questions/9304/lower-bounds-for-quantum-circuits-using-the-geodesic-framework">Michael Nielsen's paper</a> on a geometric approach to using quantum lower bounds (in brief, the construction of a Finsler metric on <span class="math-container">$SU(2^n)$</span> such that the geodesic distance from <span class="math-container">$I$</span> to an element <span class="math-container">$U$</span> is a lower bound on the number of gates in a quantum circuit that computes <span class="math-container">$U$</span>).</p>
<p>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 ?</p>
<p>One example that Joe Fitzsimmons provided is <a href="http://arxiv.org/abs/0705.0378" rel="nofollow noreferrer">this paper on optimal transfer rates in spin chains</a>. While it's a good example of the &quot;spirit&quot; of the original idea, I'm specifically looking for methods that use Nielsen's program to provide <strong>lower bounds</strong>.</p>

CC BY-SA 3.0
2011-12-12T19:36:49.830Z
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 ...
Alex 'qubeat'
CC BY-SA 3.0
2015-05-17T15:22:01.637Z
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!
Greg Kuperberg
CC BY-SA 3.0
2015-05-19T17:09:35.407Z
ok that's very weird !
Suresh Venkat
<quantum-computing>
Lower bounds for quantum circuits using the geodesic framework
Suresh Venkat
# Lower bounds for quantum circuits using the geodesic framework

(Asked by: username_0 on 2011-12-07)

Some of us have been reading [Michael Nielsen's paper](https://cstheory.stackexchange.com/questions/9304/lower-bounds-for-quantum-circuits-using-the-geodesic-framework) 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](http://arxiv.org/abs/0705.0378). 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**.

**Tags:** quantum-computing
> **Comments:**
> **username_1**: 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 ...  
> **username_2**: 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!  
> **username_0**: ok that's very weird !  

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## 0 answers

