Discrete-Time Quantum Walk - Dynamics and Applications

TL;DR

This dissertation explores the dynamics of discrete-time quantum walks, optimizing their properties, analyzing noise effects, and applying them to quantum phase transitions and entanglement creation in physical systems.

Contribution

It introduces new optimization methods for quantum walks, examines symmetry and noise effects, and proposes novel applications in quantum phase control and entanglement generation.

Findings

Optimized quantum walk using SU(2) coin operations.

Analyzed noise and topology effects on quantum walk dynamics.

Proposed quantum walk applications in optical lattice control and entanglement creation.

Abstract

This dissertation presents investigations on dynamics of discrete-time quantum walk and some of its applications. Quantum walks has been exploited as an useful tool for quantum algorithms in quantum computing. Beyond quantum computational purposes, it has been used to explain and control the dynamics in various physical systems. In order to use the quantum walk to its fullest potential, it is important to know and optimize the properties purely due to quantum dynamics and in presence of noise. Various studies of its dynamics in the absence and presence of noise have been reported. We propose new approaches to optimize the dynamics, discuss symmetries and effect of noise on the quantum walk. Making use of its properties, we propose the use of quantum walk as an efficient new tool for various applications in physical systems and quantum information processing. In the first and second part of this dissertation, we discuss evolution process of the quantum walks, propose and demonstrate the optimization of discrete-time quantum walk using quantum coin operation from SU(2) group and discuss some of its properties. We investigate symmetry operations and environmental effects on dynamics of the walk on a line and an n-cycle highlighting the interplay between noise and topology. Using the properties and behavior of quantum walk discussed in part two, in part three we propose the application of quantum walk to realize quantum phase transition in optical lattice, that is to efficiently control and redistribute ultracold atoms in optical lattice. We also discuss the implementation scheme. Another application we consider is creation of spatial entanglement using quantum walk on a quantum many body system.