Quantum walks with memory on cycles

TL;DR

This paper explores quantum walks on cycles with 1-step memory, deriving probability distributions and analyzing how memory influences quantum walk behavior compared to memoryless models.

Contribution

It introduces a formula for probability distributions in quantum walks with memory and compares their properties to traditional memoryless quantum walks.

Findings

Derived explicit formulas for probability distributions with memory

Identified differences between memory and memoryless quantum walks

Analyzed the impact of memory on walk properties

Abstract

We study the model of quantum walks on cycles enriched by the addition of 1-step memory. We provide a formula for the probability distribution and the time-averaged limiting probability distribution of the introduced quantum walk. Using the obtained results, we discuss the properties of the introduced model and the difference in comparison to the memoryless model.