Related papers: An appropriate candidate for exact distribution of…
A connection between the asymptotic behavior of the open quantum walk and the spectrum of a generalized quantum coins is studied. For the case of simultaneously diagonalizable transition operators an exact expression for probability…
Quantum walks are powerful kernels in quantum computing protocols that possess strong capabilities in speeding up various simulation and optimisation tasks. One striking example is given by quantum walkers evolving on glued trees for their…
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…
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…
We consider a discrete-time random walk on the nodes of an unbounded hexagonal lattice. We determine the probability generating functions, the transition probabilities and the relevant moments. The convergence of the stochastic process to a…
We study scattering quantum walks on highly symmetric graphs and use the walks to solve search problems on these graphs. The particle making the walk resides on the edges of the graph, and at each time step scatters at the vertices. All of…
We study quantum walks on general graphs from the point of view of scattering theory. For a general finite graph we choose two vertices and attach one half line to each. We are interested in walks that proceed from one half line, through…
In this paper, we derive the distribution of a two-dimensional (complex) random walk in which the angle of each step is restricted to a subset of the circle. This setting appears in various domains, such as in over-the-air computation in…
We propose a class of models of random walks in a random environment where an exact solution can be given for a stationary distribution. The tool is the detailed balance equations.
We address the question of symmetries of an important type of quantum walks. We introduce all the necessary definitions and provide a rigorous formulation of the problem. Using a thorough analysis, we reach the complete answer by presenting…
Suzuki's split-step quantum walk on the one-dimensional integer lattice can be naturally viewed as a chirally symmetric quantum walk. Given the unitary time-evolution of such a chirally symmetric quantum walk, we can separately introduce…
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…
By pursuing the deep relation between the one-dimensional Dirac equation and quantum walks, the physical role of quantum interference in the latter is explained. It is shown that the time evolution of the probability density of a quantum…
This note describes recent results on the localization properties of Random Quantum Walks on the d-dimensional lattice in a regime analogous to the large disorder regime by means of the Fractional Moments Method adapted to the unitary…
We present a comprehensive classification of one-dimensional coined quantum walks on the infinite line, focusing on the spatial probability distributions they induce. Building on prior results, we identify all initial coin states that lead…
We realize a pair of simultaneous ten-step one-dimensional quantum walks with two walkers sharing coins, which we prove is analogous to the ten-step two-dimensional quantum walk with a single walker holding a four-dimensional coin. Our…
In this short note, we study quantum walks (QWs) on one dimensional lattice $\delta \mathbb{Z}$. Following Hong-Yang, we prove Strichartz estimates for QWs independent of the lattice width $\delta$.
We discuss an efficient physical realization of topological quantum walks on a finite lattice. The $N$-point lattice is realized with $\log_2 N$ qubits, and the quantum circuit utilizes a number of quantum gates which is polynomial in the…
We consider the problem of finding a desired item out of $N$ items arranged on the sites of a two-dimensional lattice of size $\sqrt{N} \times \sqrt{N}$. The previous quantum walk based algorithms take $O(\sqrt{N}\log N)$ steps to solve…
We prove new mixing rate estimates for the random walks on homogeneous spaces determined by a probability distribution on a finite group $G$. We introduce the switched random walk determined by a finite set of probability distributions on…