The Elephant Quantum Walk

Abstract

We explore the impact of long-range memory on the properties of a family of quantum walks in a one-dimensional lattice and discrete time, which can be understood as the quantum version of the classical "Elephant Random Walk" non-Markovian process. This Elephant Quantum Walk is robustly superballistic with the standard deviation showing a constant exponent, $\sigma \propto t^{3/2}$ , whatever the quantum coin operator, on which the diffusion coefficient is dependent. On the one hand, this result indicates that contrarily to the classical case, the degree of superdiffusivity in quantum non- Markovian processes of this kind is mainly ruled by the extension of memory rather than other microscopic parameters that explicitly define the process. On the other hand, these parameters reflect on the diffusion coefficient.

4 figures, any comments is welcome. Accepted in PRA

References in corpus (12)

• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Environment-Assisted Quantum Walks in Photosynthetic Energy Transfer
• Universal computation by quantum walk
• Quantum Non-Markovianity: Characterization, Quantification and Detection
• Exploring Topological Phases With Quantum Walks
• Foundations and Measures of Quantum Non-Markovianity
• Spatial search and the Dirac equation
• Diffusion of individual birds in starling flocks
• Dynamical Anderson transition in one-dimensional periodically kicked incommensurate lattices
• Fermion confinement via Quantum Walks in 2D+1 and 3D+1 spacetime
• On a generalised model for time-dependent variance with long-term memory
• Noise, delocalization, and quantum diffusion in one-dimensional tight-binding models

Cited by in corpus (18)

• Quantum walks with sequential aperiodic jumps
• Aperiodic space-inhomogeneous quantum walks: localization properties, energy spectra and enhancement of entanglement
• Enhanced non-Markovian behavior in quantum walks with Markovian disorder
• Genuine Parrondo's paradox in quantum walks with time-dependent coin operators
• 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
• Parrondo's effect in continuous-time quantum walks
• Negative correlations can play a positive role in disordered quantum walks
• Multi-Dimensional Elephant Random Walk with Coupled Memory
• Quantum walks in two dimensions: controlling directional spreading with entangling coins and tunable disordered step operator
• Persistent quantum walks: dynamic phases and diverging timescales
• Steered discrete-time quantum walks for engineering of quantum states
• Quantum walks with spatiotemporal fractal disorder
• Random walk with multiple memory channels: a new paradigm
• Limit theorems for a random walk with memory perturbed by a dynamical system
• Phase vs coin vs position disorder as a probe for the resilience and revival of single particle entanglement in cyclic quantum walks
• Response to glassy disorder in coin on spread of quantum walker