Related papers: Localisation, delocalisation, and topological tran…
Discrete quantum walks are dynamical protocols for controlling a single quantum particle. Despite of its simplicity, quantum walks display rich topological phenomena and provide one of the simplest systems to study and understand…
Transport phenomena play a crucial role in modern physics and applied sciences. Examples include the dissipation of energy across a large system, the distribution of quantum information in optical networks, and the timely modeling of…
We investigate a generalized Hadamard walk in two dimensions with five inner states. The particle governed by a five-state quantum walk (5QW) moves, in superposition, either leftward, rightward, upward, or downward according to the inner…
The quantum walk was originally proposed as a quantum mechanical analogue of the classical random walk, and has since become a powerful tool in quantum information science. In this paper, we show that discrete time quantum walks provide a…
We propose a variation of the quantum walk on a circle in phase space by conjoining the Hadamard coin flip with simultaneous displacement of the walker's location in phase space and show that this generalization is a proper quantum walk…
We find out a few ways to improve the realization of entanglement between the internal (spin) and external (position) degrees of freedom of a quantum particle, through the insertion of disordered time steps along a one-dimensional discrete…
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,…
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 on translation invariant regular graphs spread quadratically faster than their classical counterparts. The same coherence that gives them this quantum speedup inhibits, or even stops their spread in the presence of disorder.…
We analyze the quantum walk in higher spatial dimensions and compare classical and quantum spreading as a function of time. Tensor products of Hadamard transformations and the discrete Fourier transform arise as natural extensions of the…
We extend the non-Hermitian one-dimensional quantum walk model [Phys. Rev. Lett. 102, 065703 (2009)] by taking the dephasing effect into account. We prove that the feature of topological transition does not change even when dephasing…
Discrete-time quantum walks, quantum generalizations of classical random walks, provide a framework for quantum information processing, quantum algorithms and quantum simulation of condensed matter systems. The key property of quantum…
We study the effects of interparticle interactions and power-law tunneling couplings on quantum walks executed by both a single one and a pair of hard-core bosons moving in clean and disordered one-dimensional lattices. For this purpose, we…
One-dimensional discrete-time quantum walks show a rich spectrum of topological phases that have so far been exclusively analysed in momentum space. In this work we introduce an alternative approach to topology which is based on the…
The staggered quantum walk is a type of discrete-time quantum walk model without a coin which can be generated on a graph using particular partitions of the graph nodes. We design Hamiltonians for potential realization of the staggered…
It has been discovered that open quantum walks diffusively distribute in space, since they were introduced in 2012. Indeed, some limit distributions have been demonstrated and most of them are described by Gaussian distributions. We operate…
We derive analytical results for continuous-time quantum walks from a new class of initial states with tunable delocalization. The dynamics are governed by a Hamiltonian with complex hopping amplitudes. We provide closed-form equations for…
Entanglement generation in discrete time quantum walks is deemed to be another key property beyond the transport behaviors. The latter has been widely used in investigating the localization or topology in quantum walks. However, there are…
We show how a quantum walk can be implemented for the first time in a quantum quincunx created via superconducting circuit quantum electrodynamics (QED), and how interpolation from quantum to random walk is implemented by controllable…
We analyze a special class of 1-D quantum walks (QWs) realized using optical multi-ports. We assume non-perfect multi-ports showing errors in the connectivity, i.e. with a small probability the multi- ports can connect not to their nearest…