Related papers: Probing the topological Anderson transition with q…
Topological phases exhibit a plethora of striking phenomena including disorder-robust localization and propagation of waves of various nature. Of special interest are the transitions between the different topological phases which are…
We offer theoretical explanations for some recent observations in numerical simulations of quantum random walks (QRW). Specifically, in the case of a QRW on the line with one particle (walker) and two entangled coins, we explain the…
Focusing on a continuous-time quantum walk on $\mathbb{Z}=\left\{0,\pm 1,\pm 2,\ldots\right\}$, we analyze a probability distribution with which the quantum walker is observed at a position. The walker launches off at a localized state and…
The dimensionality of the internal coin space of discrete-time quantum walks has a strong impact on the complexity and richness of the dynamics of quantum walkers. While two-dimensional coin operators are sufficient to define a certain…
We examine the physical implementation of a discrete time quantum walk with a four-dimensional coin. Our quantum walker is a photon moving repeatedly through a time delay loop, with time being our position space. The quantum coin is…
The atom-optics kicked rotor can be used to prepare specific momentum distributions on a discrete basis set. We implement a continuous-time quantum walk and a quantum search protocol in this momentum basis. In particular we propose ways to…
Quantum walk represents one of the most promising resources for the simulation of physical quantum systems, and has also emerged as an alternative to the standard circuit model for quantum computing. Up to now the experimental…
A new model that maps a quantum random walk described by a Hadamard operator to a particular case of a random walk is presented. The model is represented by a Markov chain with a stochastic matrix, i.e., all the transition rates are…
We discuss a particular kind of quantum walk on a general graph. We affix two semi-infinite lines to a general finite graph, which we call tails. On the tails, the particle making the walk simply advances one unit at each time step, so that…
Quantum walk serves as a versatile tool for universal quantum computing and algorithmic research. However, the implementation of discrete-time quantum walks (DTQWs) with superconducting circuits is still constrained by some limitations such…
We introduce the driven discrete time quantum walk, where walkers are added during the walk instead of only at the beginning. This leads to interference in walker number and very different dynamics when compared to the original quantum…
Recently, several groups have investigated quantum analogues of random walk algorithms, both on a line and on a circle. It has been found that the quantum versions have markedly different features to the classical versions. Namely, the…
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 present a mathematical formalism for the description of unrestricted quantum walks with entangled coins and one walker. The numerical behaviour of such walks is examined when using a Bell state as the initial coin state, two different…
The quantum random walk is a possible approach to construct new quantum algorithms. Several groups have investigated the quantum random walk and experimental schemes were proposed. In this paper we present the experimental implementation of…
Quantum walks in atomic systems, owing to their continuous nature, are especially well-suited for the simulation of many-body physics and can potentially offer an exponential speedup in solving certain black box problems. Photonics offers…
The dynamics of the survival probability of quantum walkers on a one-dimensional lattice with random distribution of absorbing immobile traps are investigated. The survival probability of quantum walkers is compared with that of classical…
In this paper we present a model exhibiting a new type of continuous-time quantum walk (as a quantum mechanical transport process) on networks, which is described by a non-Hermitian Hamiltonian possessing a real spectrum. We call it…
We study a spin-1/2-particle moving on a one dimensional lattice subject to disorder induced by a random, space-dependent quantum coin. The discrete time evolution is given by a family of random unitary quantum walk operators, where the…
We propose a quantum algorithm for simulation of the Anderson transition in disordered lattices and study numerically its sensitivity to static imperfections in a quantum computer. In the vicinity of the critical point the algorithm gives a…