Related papers: Spectrum for a non-unitary one-dimensional two-sta…

Higher-order topological insulators not only exhibit exotic bulk-boundary correspondence principle, but also have an important application in quantum computing. However, they have never been achieved in quantum walk. In this paper, we…

Non-Hermiticity significantly enriches the properties of topological models, leading to exotic features such as the non-Hermitian skin effects and non-Bloch bulk-boundary correspondence that have no counterparts in Hermitian settings. Its…

In this paper, we consider stationary measures of discrete-time three-state quantum walks including the Fourier and Grover walks in the one-dimensional lattice. We give non-uniform stationary measures by solving the corresponding eigenvalue…

One goal in the quantum-walk research is the exploitation of the intrinsic quantum nature of multiple walkers, in order to achieve the full computational power of the model. Here we study the behaviour of two non-interacting particles…

Quantum versions of random walks on the line and the cycle show a quadratic improvement over classical random walks in their spreading rates and mixing times respectively. Non-unitary quantum walks can provide a useful optimisation of these…

Quantum walks of interacting particles may display non-trivial features due to the interplay between the statistical nature and the many-body interactions associated to them. We analyze the quantum walk of interacting defects on top of an…

We examine the completeness of bi-orthogonal sets of eigenfunctions for non-Hermitian Hamiltonians possessing a spectral singularity. The correct resolutions of identity are constructed for delta like and smooth potentials. Their form and…

We give a topological classification of quantum walks on an infinite 1D lattice, which obey one of the discrete symmetry groups of the tenfold way, have a gap around some eigenvalues at symmetry protected points, and satisfy a mild locality…

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…

Non-Hermitian topological edge states have many intriguing properties, but have so far mainly been discussed in terms of bulk-boundary correspondence. Here we propose to use a bulk property of diffusion coefficients for probing the…

The quantum-mechanical counterpart of a classical random walk offers a rich dynamics that has recently been shown to include topologically protected bound states (zero-modes) at boundaries or domain walls. Here we show that a topological…

Experimental observations of quantum walks in one dimension have provided many exciting applications in quantum computing, while recent theoretical investigation of single phase defect in these system points towards interesting phenomena…

We consider a non-relativistic quantum particle interacting with a singular potential supported by two parallel straight lines in the plane. We locate the essential spectrum under the hypothesis that the interaction asymptotically…

In this paper we focus our attention on a particle that follows a unidirectional quantum walk, an alternative version of the nowadays widespread discrete-time quantum walk on a line. Here the walker at each time step can either remain in…

We investigate a space-inhomogeneous discrete-time quantum walk in one dimension. We show that the walk exhibits localization by a path counting method.

We formalize the treatment of directed (or chiral) quantum walks using Hermitian adjacency matrices, bridging two developing fields of research in quantum information and spectral graph theory. We display results and simulations which…

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…

We introduce and study a class of discrete-time quantum walks on a one-dimensional lattice. In contrast to the standard homogeneous quantum walks, coin operators are inhomogeneous and depend on their positions in this class of models. The…

The concept of lackadaisical quantum walk -- quantum walk with self loops -- was first introduced for discrete-time quantum walk on one-dimensional line. Later it was successfully applied to improve the running time of the spacial search on…

Coin and scattering are the two major formulations for discrete quantum walks models, each believed to have its own advantages in different applications. Although they are related in some cases, it was an open question their equivalence in…