Related papers: Quaternionic quantum walks
Coin and scattering are the two major formulations for discrete quantum walks models, each believed to have its own advantages in different applications. Although they are related in some cases, it was an open question their equivalence in…
The dimensionality of the internal coin space of discrete-time quantum walks has a strong impact on the complexity and richness of the dynamics of quantum walkers. While two-dimensional coin operators are sufficient to define a certain…
Recently, a new model of quantum walk, utilizing recycled coins, was introduced; however little is yet known about its properties. In this paper, we study its behavior on the cycle graph. In particular, we will consider its time averaged…
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…
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…
We exhibit a way to associate a quantum walk (QW) on the non-negative integers to any probability measure on the unit circle. This forces us to consider one step transitions that are not traditionally allowed. We illustrate this in the case…
History dependent discrete time quantum walks (QWs) are often studied for their lattice traversal properties. A particular model in the literature uses the state of a memory qubit at each site to record visits and to control the dynamics of…
Quantum walks are widely and successfully used to model diverse physical processes. This leads to computation of the models, to explore their properties. Quantum walks have also been shown to be universal for quantum computing. This is a…
Quantum walks (QWs) exhibit different properties compared with classical random walks (RWs), most notably by linear spreading and localization. In the meantime, random walks that replicate quantum walks, which we refer to as…
Discrete-time Quantum Walks (QWs) are transportation models of single quantum particles over a lattice. Their evolution is driven through causal and local unitary operators. QWs are a powerful tool for quantum simulation of fundamental…
A Plastic Quantum Walk admits both continuous time and continuous spacetime. The model has been recently proposed by one of the authors in \cite{molfetta2019quantum}, leading to a general quantum simulation scheme for simulating fermions in…
We study a position-dependent discrete-time quantum walk (QW) in one dimension, whose time-evolution operator is built up from two coin operators which are distinguished by phase factors from $x\geq0$ and $x\leq-1$. We call the QW the {\it…
In this paper we present closed-form expressions for the wave function that governs the evolution of the discrete-time quantum walk on a line when the coin operator is arbitrary. The formulas were derived assuming that the walker can either…
We clarify that coined quantum walk is determined by only the choice of local quantum coins. To do so, we characterize coined quantum walks on graph by disjoint Euler circles with respect to symmetric arcs. In this paper, we introduce a new…
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…
Quantum walk has been regarded as a primitive to universal quantum computation. By using the operations required to describe the single particle discrete-time quantum walk on a position space we demonstrate the realization of the universal…
Quantum state preparation in high-dimensional systems is an essential requirement for many quantum-technology applications. The engineering of an arbitrary quantum state is, however, typically strongly dependent on the experimental platform…
The theory of random walks on finite graphs is well developed with numerous applications. In quantum walks, the propagation is governed by quantum mechanical rules; generalizing random walks to the quantum setting. They have been…
We propose a novel implementation of discrete time quantum walks for a neutral atom in an array of optical microtraps or an optical lattice. We analyze a one-dimensional walk in position space, with the coin, the additional qubit degree of…
One of the unique features of discrete-time quantum walks is called trapping, meaning the inability of the quantum walker to completely escape from its initial position, albeit the system is translationally invariant. The effect is…