Related papers: Asymptotic evolution of quantum walks with random …
We study the light-cone and front dynamics of a single particle continuous time extended quantum walk on a one dimensional lattice with finite range hopping. We show that, in general, for an initially localized state, propagating wave…
Quantum walks are quantum counterparts of random walks and their probability distributions are different from each other. A quantum walker distributes on a Hilbert space and it is observed at a location with a probability. The finding…
Quantum walks constitute a versatile platform for simulating transport phenomena on discrete graphs including topological material properties while providing a high control over the relevant parameters at the same time. To experimentally…
A quantum walk is the quantum analogue of a random walk. While it is relatively well understood how quantum walks can speed up random walk hitting times, it is a long-standing open question to what extent quantum walks can speed up the…
The role of classical noise in quantum walks (QW) on integers is investigated in the form of discrete dichotomic random variable affecting its reshuffling matrix parametrized as a SU2)/U(1) coset element. Analysis in terms of quantum…
We consider the limit distributions of open quantum random walks on one-dimensional lattice space. We introduce a dual process to the original quantum walk process, which is quite similar to the relation of Schr\"odinger-Heisenberg…
The behaviour of random quantum walks is known to be diffusive. Here we study discrete time quantum walks in weak stochastic gauge fields. In the case of position and spin dependent gauge field, we observe a transition from ballistic to…
Random walks on the circle group $\mathbb{R}/\mathbb{Z}$ whose elementary steps are lattice variables with span $\alpha \not\in \mathbb{Q}$ or $p/q \in \mathbb{Q}$ taken mod $\mathbb{Z}$ exhibit delicate behavior. In the rational case we…
We analyze in detail the discrete--time quantum walk on the line by separating the quantum evolution equation into Markovian and interference terms. As a result of this separation, it is possible to show analytically that the quadratic…
We implement the proof of principle for the quantum walk of one ion in a linear ion trap. With a single-step fidelity exceeding 0.99, we perform three steps of an asymmetric walk on the line. We clearly reveal the differences to its…
Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…
In this article, we undertake a detailed study of the limiting behavior of a three-state discrete-time quantum walk on one dimensional lattice with generalized Grover coins. Two limit theorems are proved and consequently we show that the…
In this paper we unveil some features of a discrete-time quantum walk on the line whose coin depends on the temporal variable. After considering the most general form of the unitary coin operator, we focus on the role played by the two…
We study a 2-D disordered time-discrete quantum walk based on 1-D `generalized elephant quantum walk' where an entangling coin operator is assumed and which paves the way to a new set of properties. We show that considering a given disorder…
Exploring the quantum walk as a tool of generating various probability distributions and quantum entanglements is a topic of current interest. In the present work, we use extensive numerical simulations to investigate the influence of…
A kicking sequence of the atom optics kicked rotor at quantum resonance can be interpreted as a quantum random walk in momentum space. We show how to steer such a random walk by applying a random sequence of intensities and phases of the…
We explore a discrete-time, coined quantum walk on a quantum network where the coherent superposition of walker-moves originates from the unitary interaction of the walker-coin with the qubit degrees of freedom in the quantum network. The…
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…
We study the persistent random walk of photons on a one-dimensional lattice of random transmittances. Transmittances at different sites are assumed independent, distributed according to a given probability density $f(t)$. Depending on the…
Quantum walks have emerged as an interesting approach to quantum information processing, exhibiting many unique properties compared to the analogous classical random walk. Here we introduce a model for a discrete-time quantum walk with…