Related papers: Exploring Topological Phases With Quantum Walks
Many phenomena in solid-state physics can be understood in terms of their topological properties. Recently, controlled protocols of quantum walks are proving to be effective simulators of such phenomena. Here we report the realization of a…
There are presently two models for quantum walks on graphs. The "coined" walk uses discrete time steps, and contains, besides the particle making the walk, a second quantum system, the coin, that determines the direction in which the…
Quantum walks constitute a versatile platform for simulating transport phenomena on discrete graphs including topological material properties while providing a high control over the relevant parameters at the same time. To experimentally…
In a recent detailed research program we proposed to study the complex physics of topological phases by an all optical implementation of a discrete-time quantum walk. The main novel ingredient proposed for this study is the use of…
The topology of a single-particle band structure plays a fundamental role in understanding a multitude of physical phenomena. Motivated by the connection between quantum walks and such topological band structures, we demonstrate that a…
Quantum walks function as essential means to implement quantum simulators, allowing one to study complex and often directly inaccessible quantum processes in controllable systems. In this contribution, the notion of a driven Gaussian…
Quantum walk serves as a versatile tool for universal quantum computing and algorithmic research. However, the implementation of discrete-time quantum walks (DTQWs) with superconducting circuits is still constrained by some limitations such…
Quantum walks are a promising framework that can be used to both understand and implement quantum information processing tasks. The quantum stochastic walk is a recently developed framework that combines the concept of a quantum walk with…
The discrete time quantum walk defined as a quantum-mechanical analogue of the discrete time random walk have recently been attracted from various and interdisciplinary fields. In this review, the weak limit theorem, that is, the asymptotic…
The quantum walk (QW) is the term given to a family of algorithms governing the evolution of a discrete quantum system and as such has a founding role in the study of quantum computation. We contribute to the investigation of QW phenomena…
We study quantum transport on finite discrete structures and we model the process by means of continuous-time quantum walks. A direct and effective comparison between quantum and classical walks can be attained based on the average…
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…
Inspired by the classical phenomenon of random walk, the concept of quantum walk has emerged recently as a powerful platform for the dynamical simulation of complex quantum systems, entanglement production and universal quantum computation.…
The capability to generate and manipulate quantum states in high-dimensional Hilbert spaces is a crucial step for the development of quantum technologies, from quantum communication to quantum computation. One-dimensional quantum walk…
Quantum walks are standard tools for searching graphs for marked vertices, and they often yield quadratic speedups over a classical random walk's hitting time. In some exceptional cases, however, the system only evolves by sign flips,…
Signaled by non-analyticities in the time evolution of physical observables, dynamic quantum phase transitions (DQPTs) emerge in quench dynamics of topological systems and possess an interesting geometric origin captured by dynamic…
I propose to study the complex physics of topological phases by an all optical implementation of a discrete-time quantum walk. The main novel ingredient is the use of parametric amplifiers in the random network which can in turn be used to…
We introduce the driven discrete time quantum walk, where walkers are added during the walk instead of only at the beginning. This leads to interference in walker number and very different dynamics when compared to the original quantum…
In this letter we introduce the concept of a driven quantum walk. This work is motivated by recent theoretical and experimental progress that combines quantum walks and parametric down- conversion, leading to fundamentally different…
We propose an experimental realization of discrete quantum random walks using neutral atoms trapped in optical lattices. The random walk is taking place in position space and experimental implementation with present day technology --even…