Quantum state transfer and periodicity in discrete-time quantum walks under non--Markovian dephasing noise

TL;DR

This paper explores how non-Markovian dephasing noise affects quantum state transfer and periodicity in discrete-time quantum walks on various graphs, demonstrating the potential for successful state transfer despite environmental noise.

Contribution

It analyzes the impact of non-Markovian noise, specifically RTN and OUN, on quantum walk-based state transfer and periodicity across different graph topologies, highlighting noise resilience.

Findings

RTN and OUN noises enable finite-step state transfer

Non-Markovian noise can preserve periodicity in quantum walks

Feasibility of quantum state transfer in noisy environments

Abstract

In quantum communication, quantum state transfer from one location to another in a quantum network plays a prominent role, where the impact of noise could be crucial. The idea of state transfer can be fruitfully associated with quantum walk on graphs. We investigate the consequences of non-Markovian quantum noises on periodicity and state transfer induced by a discrete-time quantum walk on graphs, governed by the Grover coin operator. Different bipartite graphs, such as the path graph, cycle graph, star graph, and complete bipartite graph, present periodicity and state transfer in a discrete-time quantum walk depending on the topology of the graph. We investigate the effect of quantum non-Markovian dephasing noises, particularly quantum non-Markovian Random Telegraph Noise (RTN) and modified non-Markovian Ornstein-Uhlenbeck Noise (OUN) on state transfer and periodicity. We demonstrate how the RTN and OUN noises allow state transfer and periodicity for a finite number of steps in a quantum walk. Our investigation brings out the feasibility of state transfer in a noisy environment.