Multivariate Krawtchouk polynomials and quantum walks on the associated graphs
Hiroshi Miki · Open Collections · 2019
It is known that Krawtchouk polynomials play a central role in the analysis of (continuous-time) quantum walk on hypercube. Such walk also gives the spin lattice Hamiltonian where perfect state transfer occurs. In this talk (or presentation), we will start with multivariate Krawtchouk polynomials. We will introduce the associated graph and show that some spin lattice Hamiltonian in multi-dimension can be described as projections of quantum walk on this graph. In the model, fractional revival in addition to perfect state transfer is shown to take place. This is based on the joint-work with Satoshi Tsujimoto and Luc Vinet.