Classical and quantum walks on paths associated with exceptional Krawtchouk polynomials

TL;DR

This paper introduces classical and quantum walks on finite paths linked to exceptional Krawtchouk polynomials, providing explicit solutions and demonstrating phenomena like fractional revival in quantum walks.

Contribution

It presents explicit solutions for walks using exceptional Krawtchouk polynomials and explores their properties, including fractional revival in quantum walks.

Findings

Explicit solutions for walks in terms of exceptional Krawtchouk polynomials

Demonstration of fractional revival in quantum walks

Analysis of properties of these walks

Abstract

Classical and quantum walks on some finite paths are introduced. It is shown that these walks have explicit solutions given in terms of exceptional Krawtchouk polynomials and their properties are explored. In particular, fractional revival is shown to take place in the corresponding quantum walks.