Related papers: Analytical solutions for quantum walks on 1D chain…
We derive the momentum space dynamic equations and state functions for one dimensional quantum walks by using linear systems and Lie group theory. The momentum space provides an analytic capability similar to that contributed by the z…
Coined quantum walks may be interpreted as the motion in position space of a quantum particle with a spin degree of freedom; the dynamics are determined by iterating a unitary transformation which is the product of a spin transformation and…
In this paper, we present a quantum Bernoulli noises approach to quantum walks on hypercubes. We first obtain an alternative description of a general hypercube and then, based on the alternative description, we find that the operators…
We study numerically the behavior of continuous-time quantum walks over networks which are topologically equivalent to square lattices. On short time scales, when placing the initial excitation at a corner of the network, we observe a fast,…
Quantum walks are a well-established model for the study of coherent transport phenomena and provide a universal platform in quantum information theory. Dynamically influencing the walker's evolution gives a high degree of flexibility for…
We introduce the Peierls substitution to a two-dimensional discrete-time quantum walk on a square lattice to examine the spreading dynamics and the coin-position entanglement in the presence of an artificial gauge field. We use the ratio of…
Quantum walk research has mainly focused on evolutions due to repeated applications of time-independent unitary coin operators. However, the idea of controlling the single particle evolution using time-dependent unitary coins has still been…
Mixing properties of discrete-time quantum walks on two-dimensional grids with torus-like boundary conditions are analyzed, focusing on their connection to the complexity of the corresponding abstract search algorithm. In particular, an…
We consider a continuous-time symmetric supercritical branching random walk on a multidimensional lattice with a finite set of the particle generation centres, i.e. branching sources. The main object of study is the evolutionary operator…
We study the localization of probability distribution in a discrete quantum random walk on an infinite chain. With a phase defect introduced in any position of the quantum random walk (QRW), we have found that the localization of the…
We solve exactly the non-equilibrium dynamics of two discrete random walkers moving in channels with transition rates $p \neq q$ that swap positions at a rate $s$. We compute exactly the joint probability distribution $P_{n,m}(t)$ for the…
We study a class of discrete-time quantum walks with inhomogeneous coins defined in [Y. Shikano and H. Katsura, Phys. Rev. E {\bf 82}, 031122 (2010)]. We establish symmetry properties of the spectrum of the evolution operator, which…
A transition of quantum walk induced by classical randomness changes the probability distribution of the walker from a two-peak structure to a single-peak one when the random parameter exceeds a critical value. We first establish the…
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…
In this expository note, we discuss spatially inhomogeneous quantum walks in one dimension and describe a genre of mathematical methods that enables one to translate information about the time-independent eigenvalue equation for the unitary…
Quantum walk (QW), which is considered as the quantum counterpart of the classical random walk (CRW), is actually the quantum extension of CRW from the single-coin interpretation. The sequential unitary evolution engenders correlation…
We present a new scheme for a discrete-time quantum walk on two- and three-dimensional lattices using a two-state particle. We use different Pauli basis as translational eigestates for different axis and show that the coin operation, which…
Quantum walks and random walks bear similarities and divergences. One of the most remarkable disparities affects the probability of finding the particle at a given location: typically, almost a flat function in the first case and a…
The switch process alternates independently between 1 and -1, with the first switch to 1 occurring at the origin. The expected value function of this process is defined uniquely by the distribution of switching times. The relation between…
Discrete-time quantum walks are considered a counterpart of random walks and the study for them has been getting attention since around 2000. In this paper, we focus on a quantum walk which generates a probability distribution splitting to…