Related papers: Time-inhomogeneous Quantum Walks with Decoherence …
In this article we investigate the effects of shifting position decoherence, arisen from the tunneling effect in the experimental realization of the quantum walk, on the one-dimensional discreet time quantum walk. We show that in the regime…
The mixing time of a discrete-time quantum walk on the hypercube is considered. The mean probability distribution of a Markov chain on a hypercube is known to mix to a uniform distribution in time O(n log n). We show that the mean…
In all existing quantum walk models, the assumption about a pre-existing fixed background causal structure is always made and has been taken for granted. Nevertheless, in this work we will get rid of this tacit assumption especially by…
The subject of this paper is a kind of dynamical systems called quantum walks. We study one-dimensional homogeneous analytic quantum walks U. We explain how to identify the space of all the uniform intertwining operators between these…
One-dimensional discrete-time quantum walk has played an important role in development of quantum algorithms and protocols for different quantum simulations. The speedup observed in quantum walk algorithms is attributed to quantum…
The quantum and classical behaviors of two-dimensional (2D) alternative quantum walk (AQW) in the presence of decoherence have been discussed in detail. For any kinds of decoherence, the analytic expressions for the moments of position…
We discuss decoherence in discrete-time quantum walks in terms of a phenomenological model that distinguishes spin and spatial decoherence. We identify the dominating mechanisms that affect quantum walk experiments realized with neutral…
In this paper, we study discrete-time quantum walks on one-dimensional lattices. We find that the coherent dynamics depends on the initial states and coin parameters. For infinite size of lattice, we derive an explicit expression for the…
Quantum walk models have been used as an algorithmic tool for quantum computation and to describe various physical processes. This paper revisits the relationship between relativistic quantum mechanics and the quantum walks. We show the…
We study how discrete-time quantum walks behave under short-range correlated noise. By considering noise as a source of inhomogeneity of quantum gates, we introduce a primitive relaxation in the assumption of uncorrelated stochastic noise:…
We study a class of discrete-time quantum walks with inhomogeneous coins defined in [Y. Shikano and H. Katsura, Phys. Rev. E {\bf 82}, 031122 (2010)]. We establish symmetry properties of the spectrum of the evolution operator, which…
Quantum random walk in a two-dimensional lattice with randomly distributed traps is investigated. Distributions of quantum walkers are evaluated dynamically for the cases of Hadamard, Fourier, and Grover coins, and quantum to classical…
Quantum walks have a host of applications, ranging from quantum computing to the simulation of biological systems. We present an intrinsically stable, deterministic implementation of discrete quantum walks with single photons in space. The…
The theory of random walks on finite graphs is well developed with numerous applications. In quantum walks, the propagation is governed by quantum mechanical rules; generalizing random walks to the quantum setting. They have been…
We put forward a new, versatile and highly-scalable experimental setup for the realization of discrete two-dimensional quantum random walks with a single-qubit coin and tunable degree of decoherence. The proposed scheme makes use of a small…
Since a limit distribution of a discrete-time quantum walk on the line was derived in 2002, a lot of limit theorems for quantum walks with a localized initial state have been reported. On the other hand, in quantum probability theory, there…
Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a…
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…
Quantum random walks are the quantum counterpart of classical random walks, and were recently studied in the context of quantum computation. A quantum random walker is subject to self interference, leading to a remarkably different behavior…
Discrete-time quantum walks are considered a counterpart of random walks and the study for them has been getting attention since around 2000. In this paper, we focus on a quantum walk which generates a probability distribution splitting to…