Relationship between differential geometry and quantum computation?

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I have just started reading about quantum computation (Quantum Computation and Quantum Information, Nielsen and Chuang).

In parallel, I have to study differential geometry for a final exam. After the standard part of it, where you must cover the basic topics, the professor lets you present a related topic (it's optional). I was wondering if I can present some connection between differential geometry and quantum computation. The most promising thing I found is a couple of articles by Howard Brandt (see for example this one.) about Riemmanian geometry.

Can anyone give me more recommendations? The two non obligatory constraints are the following:

  1. I'm a beginner at quantum computation.
  2. If the relationship has anything to do with Frobenius theorem, much better. I also like Lie algebra.

Thank you very much.