Related papers: Continuum Limits of Lazy Open Quantum Walks
We treat a quantum walk (QW) on the line whose quantum coin at each vertex tends to be the identity as the distance goes to infinity. We obtain a limit theorem that this QW exhibits localization with not an exponential but a "power-law"…
Describing a particle in an external electromagnetic field is a basic task of quantum mechanics. The standard scheme for this is known as "minimal coupling", and consists of replacing the momentum operators in the Hamiltonian by modified…
Propagation in quantum walks is revisited by showing that very general 1D discrete-time quantum walks with time- and space-dependent coefficients can be described, at the continuous limit, by Dirac fermions coupled to electromagnetic…
We introduce and solve from first principles a continuous-time quantum walk with absorption generated by a Lindblad boundary sink of arbitrary strength. Tracing out the sink maps the problem onto a non-Hermitian tight-binding Hamiltonian…
The evolution of a closed quantum system is described by a unitary operator generated by a Hermitian Hamiltonian. However, when certain degrees of freedom are coupled to an environment, the relevant dynamics can be captured by non-unitary…
We study a generalized Hadamard walk in one dimension with three inner states. The particle governed by the three-state quantum walk moves, in superposition, both to the left and to the right according to the inner state. In addition to…
We study the evolution of a random walker on a conservative dynamic random environment composed of independent particles performing simple symmetric random walks, generalizing results of [16] to higher dimensions and more general transition…
We propose categories of $1$-dimensional and multi-dimensional quantum walks. In the categories, an object is a quantum walk, and a morphism is an intertwining operator between two quantum walks. The new framework enables us to discuss…
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…
Quantum walk research has mainly focused on evolutions due to repeated applications of time-independent unitary coin operators. However, the idea of controlling the single particle evolution using time-dependent unitary coins has still been…
Discrete-time quantum walks (DTQWs) in random artificial electric and gravitational fields are studied analytically and numerically. The analytical computations are carried by a new method which allows a direct exact analytical…
We revisit the one dimensional discrete time quantum walk with 3 states and the Grover coin. We derive analytic expressions for observed the localization, an long time approximation for the probability density function (PDF). We also…
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…
We study the noisy dynamics of periodically driven, discrete-step quantum walks in a one-dimensional photonic lattice. We find that in the bulk, temporal noise that is constant within a Floquet period leads to decoherence-free momentum…
In this paper, a study on discrete-time coined quantum walks on the line is presented. Clear mathematical foundations are still lacking for this quantum walk model. As a step towards this objective, the following question is being…
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…
We introduce and analyze a one-dimensional quantum walk with two time-independent rotations on the coin. We study the influence on the property of quantum walk due to the second rotation on the coin. Based on the asymptotic solution in the…
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…
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…
In the framework of quantum open systems, that is, simple quantum systems coupled to quantum baths, our aim is to characterize those actions of the quantum environment which give rise to dynamics dictated by classical noises. First, we…