Related papers: Aperiodic Quantum Random Walks
Coherent evolution governs the behaviour of all quantum systems, but in nature it is often subjected to influence of a classical environment. For analysing quantum transport phenomena quantum walks emerge as suitable model systems. In…
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…
Discrete time (coined) quantum walks are produced by the repeated application of a constant unitary transformation to a quantum system. By recasting these walks into the setting of periodic perturbations to an otherwise freely evolving…
In this Chapter, we present some interesting properties of quantum walks on the line. We concentrate our attention in the emergence of invariance and provide some insights into the ultimate origin of the observed behavior. In the first part…
A random walk scheme, consisting of alternating phases of regular Brownian motion and L\'evy walks, is proposed as a model for run-and-tumble bacterial motion. Within the continuous-time random walk approach we obtain the long-time and…
Quantum walks are referred to as quantum analogs to random walks in mathematics. They have been studied as quantum algorithms in quantum information for quantum computers. There are two types of quantum walks. One is the discrete-time…
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…
In this note, we discuss a general definition of quantum random walks on graphs and illustrate with a simple graph the possibility of very different behavior between a classical random walk and its quantum analogue. In this graph,…
Properties of one dimensional discrete-time quantum walks are sensitive to the presence of inhomogeneities in the substrate, which can be generated by defining position dependent coin operators. Deterministic aperiodic sequences of two or…
We show that anomalous diffusion can result when the steps of a random walk are not statistically independent. We present an algorithm that counts all the possible paths of particles diffusing on random graphs with arbitrary degree…
The random walk with hyperbolic probabilities that we are introducing is an example of stochastic diffusion in a one-dimensional heterogeneous media. Although driven by site-dependent one-step transition probabilities, the process retains…
We show that the standard quantum-walk quantum-to-classical transition, characterized by ballistic-to-diffusive spreading of the walker's position, can be controlled by externally modulating the coin state. We illustrate by showing an…
Quantum transitions are described semiclassically as motions of systems along (complex) trajectories. We consider the cases when the semiclassical trajectories are unstable and find that durations of the corresponding transitions are large.…
We discuss a particular kind of quantum walk on a general graph. We affix two semi-infinite lines to a general finite graph, which we call tails. On the tails, the particle making the walk simply advances one unit at each time step, so that…
We show that particle transport in a uniform, quantum multi-baker map, is generically ballistic in the long time limit, for any fixed value of Planck's constant. However, for fixed times, the semi-classical limit leads to diffusion. Random…
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…
We study the persistent random walk of photons on a one-dimensional lattice of random transmittances. Transmittances at different sites are assumed independent, distributed according to a given probability density $f(t)$. Depending on the…
We introduce a continuous-time quantum walk on an ultrametric space corresponding to the set of p-adic integers and compute its time-averaged probability distribution. It is shown that localization occurs for any location of the ultrametric…
Quantum random walks have received much interest due to their non-intuitive dynamics, which may hold the key to a new generation of quantum algorithms. What remains a major challenge is a physical realization that is experimentally viable…
Quantum walks have been employed widely to develop new tools for quantum information processing recently. A natural quantum walk dynamics of interacting particles can be used to implement efficiently the universal quantum computation. In…