Selected open problems in continuous-time quantum walks

Abstract

Quantum walks on graphs are fundamental to quantum computing and have led to many interesting open problems in algebraic graph theory. This review article highlights three key classes of open problems in this domain: perfect state transfer, instantaneous uniform mixing, and average mixing matrices. In highlighting these open problems, our aim is to stimulate further research and exploration in this rapidly evolving field.

Keywords

• quantum walks
• spectral graph theory
• 05c50
• 81p45