Related papers: Open Quantum Random Walks
A quantum particle evolving by Schr\"odinger's equation contains, from the kinetic energy of the particle, a term in its Hamiltonian proportional to Laplace's operator. In discrete space, this is replaced by the discrete or graph Laplacian,…
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…
Lazy quantum walks were presented by Andrew M. Childs to prove that the continuous-time quantum walk is a limit of the discrete-time quantum walk [Commun.Math.Phys.294,581-603(2010)]. In this paper, we discuss properties of lazy quantum…
Quantum walks, the quantum analogue of the classical random walk, have been shown to underpin quantum algorithms for fluid dynamics. We propose the quantum half-adder gate method for quantum walks as a good benchmark algorithm, specifically…
Quantum walks with long-range steps $R^{-\gamma}$ ($R$ being the distance between sites) on a discrete line behave in similar ways for all $\gamma\geq2$. This is in contrast to classical random walks, which for $\gamma >3$ belong to a…
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…
Dynamical phase transitions in the relaxation behavior of stochastic quantum walks are investigated, focusing on systems where coherent unitary evolution is periodically interrupted by dephasing. This interplay leads to a classicalization…
The concept of open quantum walks (OQW), quantum walks exclusively driven by the interaction with the external environment, is reviewed. OQWs are formulated as discrete completely positive maps on graphs. The basic properties of OQWs are…
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…
We define a random walk on the set of primitive points of $\mathbb{Z}^d$. We prove that for walks generated by measures satisfying mild conditions these walks are recurrent in a strong sense. That is, we show that the associated Markov…
We construct a quantum random walk algorithm, based on the Dirac operator instead of the Laplacian. The algorithm explores multiple evolutionary branches by superposition of states, and does not require the coin toss instruction of…
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…
Classical and quantum walks on some finite paths are introduced. It is shown that these walks have explicit solutions given in terms of exceptional Krawtchouk polynomials and their properties are explored. In particular, fractional revival…
Quantum walks are expected to provide useful algorithmic tools for quantum computation. This paper introduces absorbing probability and time of quantum walks and gives both numerical simulation results and theoretical analyses on Hadamard…
This paper presents a realistic, stochastic, and local model that reproduces nonrelativistic quantum mechanics (QM) results without using its mathematical formulation. The proposed model only uses integer-valued quantities and operations on…
We introduce a model of a quantum walk on a graph in which a particle jumps between neighboring nodes and interacts with independent spins sitting on the edges. Entanglement propagates with the walker. We apply this model to the case of a…
We study the motion of M particles performing a quantum walk on the line. Under various conditions on the initial coin states for quantum walkers controlled by the Hadamard operator, we give theoretical criterion to observe the quantum…
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…
Quantum random walks represent a powerful tool for the implementation of various quantum algorithms. We consider a convolution problem for the graphs which provide quantum and classical random walks. We suggest a new method for lattices and…
We investigate a tight binding quantum walk on a graph. Repeated stroboscopic measurements of the position of the particle yield a measured "trajectory", and a combination of classical and quantum mechanical properties for the walk are…