Paper on transport on Cayley Graphs
Quantum random walks have been studied a lot worldwide to see if they can provide a type of quantum algorithm. One normally compares the quantum random walk with a classical drunken sailor walk (
whats this? See www.youtube.com/watch or really en.wikipedia.org/wiki/Random_walk). One set of intriguing results people found is that quantum information, when making a quantum random walk on certain types of graphs (hypercubes), can traverse the graph much much faster than the associated classical random walk. More interestingly the quantum information, which is initially concentrated on a point on the graph, eventually refocuses on the antipodal point. This means it is tranported perfectly. Such perfect transport is quite unusual in quantum mechanics. With Jim Cresser and (then), Honours Student Chris Facer, we looked a what would happen if we carefully added a few more links into the hypercbe graph. Amazingly we found that the quantum information could be made to refocus perfectly at all sorts of places in the graph! The published paper is here

- jtwamley's blog
- 483 reads
