Related papers: Quantum Walks in Weak Stochastic Gauge Fields
We introduce the quantum stochastic walk (QSW), which determines the evolution of generalized quantum mechanical walk on a graph that obeys a quantum stochastic equation of motion. Using an axiomatic approach, we specify the rules for all…
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…
The quantum walk is the quantum analogue of the well-known random walk, which forms the basis for models and applications in many realms of science. Its properties are markedly different from the classical counterpart and might lead to…
There are presently two models for quantum walks on graphs. The "coined" walk uses discrete time steps, and contains, besides the particle making the walk, a second quantum system, the coin, that determines the direction in which the…
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…
Using coordinate-free basic operators on toy Fock spaces \cite{AP}, quantum random walks are defined following the ideas in \cite{LP,AP}. Strong convergence of quantum random walks associated with bounded structure maps is proved under…
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…
The dimensionality of the internal coin space of discrete-time quantum walks has a strong impact on the complexity and richness of the dynamics of quantum walkers. While two-dimensional coin operators are sufficient to define a certain…
Quantum walks have emerged as an interesting approach to quantum information processing, exhibiting many unique properties compared to the analogous classical random walk. Here we introduce a model for a discrete-time quantum walk with…
Constructing a discrete model like a cellular automaton is a powerful method for understanding various dynamical systems. However, the relationship between the discrete model and its continuous analogue is, in general, nontrivial. As a…
Gauge invariance is one of the more important concepts in physics. We discuss this concept in connection with the unitary evolution of discrete-time quantum walks in one and two spatial dimensions, when they include the interaction with…
We investigate the dynamics of discrete-time quantum walk subject to time correlated noise. Noise is described as an unitary coin-type operator before each step, and attention is focused on the noise generated by a Gaussian Ornstein…
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…
Discrete-time quantum walks can be regarded as quantum dynamical simulators since they can simulate spatially discretized Schr\"{o}dinger, massive Dirac, and Klein-Gordon equations. Here, two different types of Fibonacci discrete-time…
A damped random walk is a stochastic process, defined by an exponential covariance matrix that behaves as a random walk for short time scales and asymptotically achieves a finite variability amplitude at long time scales. Over the last few…
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…
The discrete quantum walk in N dimensions is analyzed from the perspective of its dispersion relations. This allows understanding known properties, as well as designing new ones when spatially extended initial conditions are considered.…
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…
Quantum walks have by now been realized in a large variety of different physical settings. In some of these, particularly with trapped ions, the walk is implemented in phase space, where the corresponding position states are not orthogonal.…
We study the quenched behaviour of a perturbed version of the simple symmetric random walk on the set of integers. The random walker moves symmetrically with an exception of some randomly chosen sites where we impose a random drift. We show…