Related papers: Quantum walk on a toral phase space
This note introduces some examples of quantum random walks in d-dimensional Eucilidean space and proves the weak convergence of their rescaled n-step densities. One of the examples is called the Plancherel quantum walk because the "quantum…
We characterize quantumness of the so-called quantum walks (whose dynamics is governed by quantum mechanics) by introducing two computable measures which are stronger than the variance of the walker's position probability distribution. The…
We study a spin-1/2-particle moving on a one dimensional lattice subject to disorder induced by a random, space-dependent quantum coin. The discrete time evolution is given by a family of random unitary quantum walk operators, where the…
We study one-dimensional quantum walk with four internal degrees of freedom resulted from two entangled qubits. We will demonstrate that the entanglement between the qubits and its corresponding coin operator enable one to steer the…
We report on a discrete-time quantum walk that uses the momentum of ultra-cold rubidium-87 atoms as the walk space and two internal atomic states as the coin degree of freedom. Each step of the walk consists of a coin toss (a microwave…
We investigate the ballistic spreading behavior of the one-dimensional discrete time quantum walks whose time evolution is driven by any balanced quantum coin. We obtain closed-form expressions for the long-time variance of position of…
We consider discrete-time nearest-neighbor quantum walks on random environments in one dimension. Using the method based on a path counting, we present both quenched and annealed weak limit theorems for the quantum walk.
Quantum walks have emerged as an interesting alternative to the usual circuit model for quantum computing. While still universal for quantum computing, the quantum walk model has very different physical requirements, which lends itself more…
Quantum random walks have been much studied recently, largely due to their highly nonclassical behavior. In this paper, we study one possible route to classical behavior for the discrete quantum random walk on the line: the use of multiple…
The symmetries associated with discrete-time quantum walks (DTQWs) and the flexibilities in controlling their dynamical parameters allow to create a large number of topological phases. An interface in position space, which separates two…
Quantum and random walks have been shown to be equivalent in the following sense: a time-dependent random walk can be constructed such that its vertex distribution at all time instants is identical to the vertex distribution of any…
This work investigates a discrete-time quantum walk on a one-dimensional lattice driven by three entangled coins, each initialized via a Hadamard operator. The walker moves only when all three coins yield identical outcomes (HHH or TTT),…
We present the first robust implementation of a coined quantum walk over five steps using only passive optical elements. By employing a fiber network loop we keep the amount of required resources constant as the walker's position Hilbert…
One goal in the quantum-walk research is the exploitation of the intrinsic quantum nature of multiple walkers, in order to achieve the full computational power of the model. Here we study the behaviour of two non-interacting particles…
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…
Quantum walks are quantum counterparts of random walks and their probability distributions are different from each other. A quantum walker distributes on a Hilbert space and it is observed at a location with a probability. The finding…
Although quantum walks exhibit peculiar properties that distinguish them from random walks, classical behavior can be recovered in the asymptotic limit by destroying the coherence of the pure state associated to the quantum system. Here I…
Quantum walk (QW) utilizes its internal quantum states to decide the displacement, thereby introducing single-particle entanglement between the internal and positional degrees of freedom. By simulating three variants of QW with the…
We analyze two families of three-state quantum walks which show the localization effect. We focus on the role of the initial coin state and its coherence in controlling the properties of the quantum walk. In particular, we show that the…
We provide an explanation of recent experimental results of Xue et al., where full revivals in a time-dependent quantum walk model with a periodically changing coin are found. Using methods originally developed for "electric" walks with a…