Percolation induced effects in 2D coined quantum walks: analytic asymptotic solutions

Abstract

Quantum walks on graphs can model physical processes and serve as efficient tools in quantum information theory. Once we admit random variations in the connectivity of the underlying graph, we arrive at the problem of percolation, where the long-time behaviour appears untreatable with direct numerical methods. We develop novel analytic methods based on the theory of random unitary operations which help us to determine explicitly the asymptotic dynamics of quantum walks on 2D finite integer lattices with percolation. Based on this theory we find new unexpected features of percolated walks like asymptotic position inhomogeneity or special directional symmetry breaking.

21 pages, 3 figures

References in corpus (13)

• Universal computation by quantum walk
• Quantum walks of correlated particles
• Exponential algorithmic speedup by quantum walk
• Quantum Walk in Position Space with Single Optically Trapped Atoms
• A 2D Quantum Walk Simulation of Two-Particle Dynamics
• Discrete single-photon quantum walks with tunable decoherence
• Decoherence in quantum walks - a review
• Quantum transport on small-world networks: A continuous-time quantum walk approach
• Recurrence properties of unbiased coined quantum walks on infinite $d$-dimensional lattices
• Asymptotic dynamics of coined quantum walks on percolation graphs
• Coined quantum walks on percolation graphs
• Implementation of a spatial two-dimensional quantum random walk with tunable decoherence
• Localization and Fractality in Inhomogeneous Quantum Walks with Self-Duality

Cited by in corpus (11)

• Quantum Walks with Dynamical Control: Graph Engineering, Initial State Preparation and State Transfer
• Discrete time quantum walks on percolation graphs
• Quantum walk transport on carbon nanotube structures
• Strongly trapped two-dimensional quantum walks
• Percolated quantum walks with a general shift operator: From trapping to transport
• Complete classification of trapping coins for quantum walks on the 2D square lattice
• The switching effect of the side chain on quantum walks on triple graphs
• Monitored Recurrence of a One-parameter Family of Three-state Quantum Walks
• Attractors and asymptotic dynamics of open discrete-time quantum walks on cycles
• Two-particle Hadamard walk on dynamically percolated line and circle
• Key graph properties affecting transport efficiency of flip-flop Grover percolated quantum walks