Physica A Quantum walks with memory on cycles

h i g h l i g h t s • Model of quantum walks with memory on a cyclic graph. • Analysis of limiting probability distribution. • Comparison of the models with the memoryless case. a r t i c l e i n f o b s t r a c t 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