An analogue of the Riemann Hypothesis via quantum walks

TL;DR

This paper explores a quantum walk-based analogue of the Riemann Hypothesis, using the Konno-Sato theorem to analyze graphs like complete, cycle, and star graphs.

Contribution

It introduces a novel quantum walk framework to formulate an analogue of the Riemann Hypothesis and provides specific examples on various graph types.

Findings

Quantum walk analogue of the Riemann Hypothesis proposed

Examples on complete, cycle, and star graphs analyzed

Connections to the Konno-Sato theorem established

Abstract

We consider an analogue of the well-known Riemann Hypothesis based on quantum walks on graphs with the help of the Konno-Sato theorem. Furthermore, we give some examples for complete, cycle, and star graphs.