Quantum Walk with Jumps

Abstract

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 neighbor but to another multi-port at a fixed distance - we call this a jump. We study two cases of QW with jumps where multiple displacements can emerge at one timestep. The first case assumes time-correlated jumps (static disorder). In the second case, we choose the positions of jumps randomly in time (dynamic disorder). The probability distributions of position of the QW walker in both instances differ significantly: dynamic disorder leads to a Gaussian-like distribution, while for static disorder we find two distinct behaviors depending on the parity of jump size. In the case of even-sized jumps, the distribution exhibits a three-peak profile around the position of the initial excitation, whereas the probability distribution in the odd case follows a Laplace-like discrete distribution modulated by additional (exponential) peaks for long times. Finally, our numerical results indicate that by an appropriate mapping an universal functional behavior of the variance of the long-time probability distribution can be revealed with respect to the scaled average of jump size.

arXiv comment11 pages, 13 figures

References in corpus (23)

• Quantum random walks - an introductory overview
• Emergence of Cooperation and Organization in an Evolutionary Game
• Quantum Walk in Position Space with Single Optically Trapped Atoms
• Photons Walking the Line: A quantum walk with adjustable coin operations
• From quantum cellular automata to quantum lattice gases
• Realization of a quantum walk with one and two trapped ions
• Quantum walk of a trapped ion in phase space
• Implementing the quantum random walk
• Quantum random walks in optical lattices
• Quantum quincunx in cavity quantum electrodynamics
• Nonadditive entropy: the concept and its use
• Nonextensive statistical mechanics: A brief introduction
• Limit Theorem for Continuous-Time Quantum Walk on the Line
• Aperiodic Quantum Random Walks
• Quantum Walks on a Random Environment
• Recurrence and Pólya number of quantum walks
• Recurrence properties of unbiased coined quantum walks on infinite $d$-dimensional lattices
• Coined quantum walks on percolation graphs
• Dynamical Localization in the Paul Trap
• Recurrence of biased quantum walks on a line
• Sub-ballistic behavior in quantum systems with Lévy noise
• The meeting problem in the quantum random walk
• Measurements in the Lévy quantum walk

Cited by in corpus (11)

• Asymptotic dynamics of coined quantum walks on percolation graphs
• Quantum walks with sequential aperiodic jumps
• Aperiodic space-inhomogeneous quantum walks: localization properties, energy spectra and enhancement of entanglement
• Multiple transitions between normal and hyperballistic diffusion in quantum walks with time-dependent jumps
• Enhancing entanglement with the generalized elephant quantum walk from localized and delocalized states
• Scaling and crossover behaviour in a truncated long range quantum walk
• Discrete dynamics and non-Markovianity
• Inhibition of spreading in quantum random walks due to quenched Poisson-distributed disorder
• Quantum walks in two dimensions: controlling directional spreading with entangling coins and tunable disordered step operator
• Quantum walks with spatiotemporal fractal disorder
• Response to glassy disorder in coin on spread of quantum walker