Quantum Topology Seminar
Louis H Kauffman
UIC, NSU
Searching for a Quantum Algorithm for Khovanov Homology
Abstract: This talk will discuss our search for a quantum algorithm for Khovanov Homology.
The project began a long time ago with the speaker and more recently with Nadia Shirakova and Sam Lomonaco.
It remains in an unfinished state. The problem is how could a quantum black box efficiently produce the chain complex for Khovanov homology
from the combinatorial input data of a knot or quantum knot? Once we have such data, it is possible to apply combinatorial Hodge Theory and the
phase estimation methods of Lloyd and Zanardi to compute ranks of homology groups. But how can a quantum black box know the chain complex?
Thursday February 25, 2021 at 12:00 PM in Zoom