Related papers: N-dimensional alternate coined quantum walks from …
For a discrete two-state quantum walk (QW) on the half-line with a general condition at the boundary, we formulate and prove a weak limit theorem describing the terminal behavior of its transition probabilities. In this context,…
We propose a variation of the quantum walk on a circle in phase space by conjoining the Hadamard coin flip with simultaneous displacement of the walker's location in phase space and show that this generalization is a proper quantum walk…
Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a…
We study quantum walk on a ladder with combination of conventional and split-step protocols. The two components of the walk resulting from periodic boundary conditions can be made to have three kinds of probability distributions. Two of…
Quantum random walks (QRWs) are random processes in which the resulting probability density of the "walker" state, whose movement is governed by a "coin" state, is described in a non-classical manner. Previously, Q-plates have been used to…
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 extend the scheme of quantum teleportation by quantum walks introduced by Wang et al. (2017). First, we introduce the mathematical definition of the accomplishment of quantum teleportation by this extended scheme. Secondly, we show a…
We propose a quantum-electrodynamics scheme for implementing the discrete-time, coined quantum walk with the walker corresponding to the phase degree of freedom for a quasi-magnon field realized in an ensemble of nitrogen-vacancy centres in…
In this paper we investigate one dimensional quantum walks with two-step memory, which can be viewed as an extension of quantum walks with one-step memory. We develop a general formula for the amplitudes of the two-step-memory walk with…
The discrete time quantum walk which is a quantum counterpart of random walk plays important roles in the theory of quantum information theory. In the present paper, we focus on discrete time quantum walks viewed as quantization of random…
We provide an algorithm that factorizes one-dimensional quantum walks into a protocol of two basic operations: A fixed conditional shift that transports particles between cells and suitable coin operators that act locally in each cell. This…
We propose a new multi-dimensional discrete-time quantum walk (DTQW), whose continuum limit is an extended multi-dimensional Dirac equation, which can be further mapped to the Schr\"{o}dinger equation. We show in two ways that our DTQW is…
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…
Quantum random walks are shown to have non-intuitive dynamics, which makes them an attractive area of study for devising quantum algorithms for well-known classical problems as well as those arising in the field of quantum computing. In…
Discrete-time quantum walks, quantum generalizations of classical random walks, provide a framework for quantum information processing, quantum algorithms and quantum simulation of condensed matter systems. The key property of quantum…
We investigate the quantum versions of a one-dimensional random walk, whose corresponding Markov Chain is of order 2. This corresponds to the walk having a memory of up to two previous steps. We derive the amplitudes and probabilities for…
Properties of the probability distribution generated by a discrete-time quantum walk, such as the number of peaks it contains, depend strongly on the choice of the initial condition. In the present paper we discuss from this point of view…
We present a discrete-time, one-dimensional quantum walk based on the entanglement between the momentum of ultracold rubidium atoms (the walk space) and two internal atomic states (the "coin" degree of freedom). Our scheme is highly…
Quantum walks, both discrete (coined) and continuous time, form the basis of several recent quantum algorithms. Here we use numerical simulations to study the properties of discrete, coined quantum walks. We investigate the variation in the…
Quantum walk (QW) provides a versatile tool to study fundamental physics and also to make a variety of practical applications. We here start with the recent idea of {\it nonlinear} QW and show that introducing {\it nonlinearity} to QW can…