Institute for Quantum Information (IQI) Weekly Seminar
Two little results in topology, motivated by quantum computation
Quantum computation has taken much from the scientific fields it sprouted from. Occasionally, it has also given back. I will discuss two recent results, both of which employ basic methods and ideas from quantum computation to prove a new theorem about low-dimensional topology. In the first result, we show the existence of 3-manifold diagrams which cannot be made ``very thin'' via local transformations. The key to the proof is establishing the #P-hardness of certain 3-manifold invariants, which we achieve via an application of the Solovay-Kitaev universality theorem with exponential precision. In the second result, we prove a relationship between the distinguishing power of a link invariant, and the entangling power of the linear operator that describes braiding. More precisely, we show that link invariants derived from non-entangling solutions to the Yang-Baxter equation are trivial.
The former is joint work with Catharine Lo (Caltech), and the latter is joint work with Stephen Jordan and Michael Jarett (UMD).
Contact: Jackie O'Sullivan at 626.395.4964 email@example.com