Related papers: Properties of Open Quantum Walks on $\mathbb{Z}$

We consider two independent quantum walks on separate lines augmented by partial or full swapping of coins after each step. For classical random walks, swapping or not swapping coins makes little difference to the random walk…

We consider asymptotic behaviour of a Hadamard walk on a cycle. For a walk which starts with a state in which all the probability is concentrated on one node, we find the explicit formula for the limiting distribution and discuss its…

Quantum walks, both discrete (coined) and continuous time, form the basis of several quantum algorithms and have been used to model processes such as transport in spin chains and quantum chemistry. The enhanced spreading and mixing…

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 walk (QW) is the quantum analog of the random walk. QW is an integral part of the development of numerous quantum algorithms. Hence, an in-depth understanding of QW helps us to grasp the quantum algorithms. We revisit the…

Quantum walks on graphs are ubiquitous in quantum computing finding a myriad of applications. Likewise, random walks on graphs are a fundamental building block for a large number of algorithms with diverse applications. While the…

Exploiting multi-dimensional quantum walks as feasible platforms for quantum computation and quantum simulation is attracting constantly growing attention from a broad experimental physics community. Here, we propose a two-dimensional…

Open quantum walks (OQWs) are a new type of quantum walks which are entirely driven by the dissipative interaction with external environments and are formulated as completely positive trace-preserving maps on graphs. A generalized quantum…

Theoretical and applied studies of quantum walks are abundant in quantum science and technology thanks to their relative simplicity and versatility. Here we derive closed-form expressions for the probability distribution of quantum walks on…

We study numerically the behavior of continuous-time quantum walks over networks which are topologically equivalent to square lattices. On short time scales, when placing the initial excitation at a corner of the network, we observe a fast,…

Rules for quantizing the walker+coin parts of a classical random walk are provided by treating them as interacting quantum systems. A quantum optical random walk (QORW), is introduced by means of a new rule that treats quantum or classical…

We study quantum walk on a ladder with combination of conventional and split-step protocols. The two components of the walk resulting from periodic boundary conditions can be made to have three kinds of probability distributions. Two of…

We present an idea to convert to a unitary quantum walk any open quantum walk which is defined on lattices as well as on finite graphs. This approach generalizes to the domain of open quantum walks (or quantum Markov chains) the framework…

We consider quantum walks on the cycle in the non-stationary case where the `coin' operation is allowed to change at each time step. We characterize, in algebraic terms, the set of possible state transfers and prove that, as opposed to the…

This paper presents a simple model that mimics quantum mechanics (QM) results in terms of probability fields of free particles subject to self-interference, without using Schr\"{o}dinger equation or wavefunctions. Unlike the standard QM…

We report on the possibility of controlling quantum random walks with a step-dependent coin. The coin is characterized by a (single) rotation angle. Considering different rotation angles, one can find diverse probability distributions for…

Discrete-time quantum walk in one-dimension is studied from a path-integral perspective. This enables derivation of a closed-form expression for amplitudes corresponding to any coin-position basis of the state vector of the quantum walker…

We investigate quantum walks which play an important role in the modelling of many phenomena. The detailed and thorough description is given to the discrete quantum walks on a line, where the total quantum state consists of quantum states…

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…

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…