Related papers: Controlling quantum walks with coin eigenstates

We have recently proposed a two-dimensional quantum walk where the requirement of a higher dimensionality of the coin space is substituted with the alternance of the directions in which the walker can move [C. Di Franco, M. Mc Gettrick, and…

A connection between the asymptotic behavior of the open quantum walk and the spectrum of a generalized quantum coins is studied. For the case of simultaneously diagonalizable transition operators an exact expression for probability…

We introduce an analytically treatable spin decoherence model for quantum walk on a line that yields the exact position probability distribution of an unbiased classical random walk at all-time scales. This spin decoherence model depicts a…

We show analytically that particle trapping appears in a quantum process called "quantum walk", in which the particle moves macroscopically correlating to the inner states. It has been well known that a particle in the ``Hadamard walk" with…

We obtain some rigorous results on limit theorems for quantum walks driven by many coins introduced by Brun et al. in the long time limit. The results imply that whether the behavior of a particle is quantum or classical depends on the…

We address the performance of a coin-biased quantum walk as a generator for non-classical position states of the walker. We exploit a phenomenon of coherent localisation in the position space --- resulting from the choice of small values of…

Quantum walks constitute a rich area of quantum information science, where multipartite entanglement plays a central role in the dynamics and scalability of quantum advantage over classical simulators. In this work, we study the…

The position density of a "particle" performing a continuous-time quantum walk on the integer lattice, viewed on length scales inversely proportional to the time t, converges (as t tends to infinity) to a probability distribution that…

We show that quantum walks interpolate between a coherent `wave walk' and a random walk depending on how strongly the walker's coin state is measured; i.e., the quantum walk exhibits the quintessentially quantum property of complementarity,…

We study the effect of random scattering in quantum walks on a finite graph and compare it with the effect of repeated measurements. To this end, a constructive approach is employed by introducing a localized and a delocalized basis for the…

Entanglement is a key resource in many quantum information applications and achieving high values independently of the initial conditions is an important task. Here we address the problem of generating highly entangled states in a discrete…

Quantum walks and random walks bear similarities and divergences. One of the most remarkable disparities affects the probability of finding the particle at a given location: typically, almost a flat function in the first case and a…

We present numerical study of a model of quantum walk in periodic potential on the line. We take the simple view that different potentials affect differently the way the coin state of the walker is changed. For simplicity and definiteness,…

Absorption of two-state coined quantum walks on a finite line with two sinks located at $N$ and $-N$ is investigated. Elaborating on the results of Konno et al., J. Phys. A: Math. Gen. 36 241 (2003), we derive closed formulas for the…

For a discrete two-state quantum walk (QW) on the half-line with a general condition at the boundary, we formulate and prove a weak limit theorem describing the terminal behavior of its transition probabilities. In this context,…

We demonstrate a coined quantum walk over ten steps in a one-dimensional network of linear optical elements. By applying single-point phase defects, the translational symmetry of an ideal standard quantum walk is broken resulting in…

We simulate various topological phenomena in condense matter, such as formation of different topological phases, boundary and edge states, through two types of quantum walk with step-dependent coins. Particularly, we show that…

It is demonstrated that in gate-based quantum computing architectures quantum walk is a natural mathematical description of quantum gates. It originates from field-matter interaction driving the system, but is not attached to specific qubit…

We describe quantum controllability under the influences of the quantum decoherence induced by the quantum control itself. It is shown that, when the controller is considered as a quantum system, it will entangle with its controlled system…

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),…