Related papers: Formal languages analysed by quantum walks
We show that a quantum state transfer, previously studied as a continuous time process in networks of interacting spins, can be achieved within the model of discrete time quantum walks with position dependent coin. We argue that due to…
A quantum computer, i.e. utilizing the resources of quantum physics, superposition of states and entanglement, could furnish an exponential gain in computing time. A simulation using such resources is called a quantum simulation. The…
Quantum walks have emerged as an interesting approach to quantum information processing, exhibiting many unique properties compared to the analogous classical random walk. Here we introduce a model for a discrete-time quantum walk with…
Quantum walks, both discrete (coined) and continuous time, on a general graph of N vertices with undirected edges are reviewed in some detail. The resource requirements for implementing a quantum walk as a program on a quantum computer are…
Quantum walks are referred to as quantum analogs to random walks in mathematics. They have been studied as quantum algorithms in quantum information for quantum computers. There are two types of quantum walks. One is the discrete-time…
Quantum walks with one-dimensional translational symmetry are important for quantum algorithms, where the speed-up of the diffusion speed can be reached if long-range couplings are added. Our work studies a scheme of a ring under the strong…
A quantum walk is a time-homogeneous quantum-mechanical process on a graph defined by analogy to classical random walk. The quantum walker is a particle that moves from a given vertex to adjacent vertices in quantum superposition. Here we…
In this paper we focus our attention on a particle that follows a unidirectional quantum walk, an alternative version of the nowadays widespread discrete-time quantum walk on a line. Here the walker at each time step can either remain in…
The development of quantum algorithms based on quantum versions of random walks is placed in the context of the emerging field of quantum computing. Constructing a suitable quantum version of a random walk is not trivial: pure quantum…
It is demonstrated that in gate-based quantum computing architectures quantum walk is a natural mathematical description of quantum gates. It originates from field-matter interaction driving the system, but is not attached to specific qubit…
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…
Quantum walk is one of the main tools for quantum algorithms. Defined by analogy to classical random walk, a quantum walk is a time-homogeneous quantum process on a graph. Both random and quantum walks can be defined either in continuous or…
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…
High-dimensional quantum systems can offer extended possibilities and multiple advantages while developing advanced quantum technologies. In this paper, we propose a class of quantum-walk architecture networks that admit the efficient…
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 walks are a promising framework for developing quantum algorithms and quantum simulations. They represent an important test case for the application of quantum computers. Here we present different forms of discrete-time quantum…
In some of the earliest work on quantum mechanical computers, Feynman showed how to implement universal quantum computation by the dynamics of a time-independent Hamiltonian. I show that this remains possible even if the Hamiltonian is…
This article aims to provide an introductory survey on quantum random walks. Starting from a physical effect to illustrate the main ideas we will introduce quantum random walks, review some of their properties and outline their striking…
We investigate quantum walks in multiple dimensions with different quantum coins. We augment the model by assuming that at each step the amplitudes of the coin state are multiplied by random phases. This model enables us to study in detail…
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…