Asymptotic dynamics of coined quantum walks on percolation graphs
arXiv:1204.6149 · doi:10.1103/PhysRevLett.108.230505
Abstract
Quantum walks obey unitary dynamics: they form closed quantum systems. The system becomes open if the walk suffers from imperfections represented as missing links on the underlying basic graph structure, described by dynamical percolation. Openness of the system's dynamics creates decoherence, leading to strong mixing. We present a method to analytically solve the asymptotic dynamics of coined, percolated quantum walks for a general graph structure. For the case of a circle and a linear graph we derive the explicit form of the asymptotic states. We find that a rich variety of asymptotic evolutions occur: not only the fully mixed state, but other stationary states; stable periodic and quasiperiodic oscillations can emerge, depending on the coin operator, the initial state, and the topology of the underlying graph.
5 pages, 2 figures. Accepted for publication in Physical Review Letters
References in corpus (23)
- Quantum random walks - an introductory overview
- Quantum walks of correlated particles
- Quantum Walk in Position Space with Single Optically Trapped Atoms
- Photons Walking the Line: A quantum walk with adjustable coin operations
- Realization of a quantum walk with one and two trapped ions
- Topological Transition in a Non-Hermitian Quantum Walk
- Quantum walk of a trapped ion in phase space
- A 2D Quantum Walk Simulation of Two-Particle Dynamics
- Discrete single-photon quantum walks with tunable decoherence
- Decoherence and disorder in quantum walks: From ballistic spread to localization
- Continuous-Time Quantum Walks: Models for Coherent Transport on Complex Networks
- Search via Quantum Walk
- Decoherence in quantum walks - a review
- Decoherence in the quantum walk on the line
- Asymptotic evolution of quantum walks with random coin
- Disordered Quantum Walks in one lattice dimension
- Decoherence in Quantum Walks on the Hypercube
- Coined quantum walks on percolation graphs
- Decoherence in one-dimensional Quantum Walk
- Asymptotic Evolution of Random Unitary Operations
- Quantum Walk with Jumps
- Quantum Persistence: A Random Walk Scenario
- Bounds for mixing time of quantum walks on finite graphs
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- How fast do quantum walks mix?
- Bounds on the dynamics of periodic quantum walks and emergence of the gapless and gapped Dirac equation
- Central limit theorem for reducible and irreducible open quantum walks
- Asymptotic properties of quantum Markov chains
- Two-walker discrete-time quantum walks on the line with percolation
- Time evolution of continuous-time quantum walks on dynamical percolation graphs
- Discrete time quantum walks on percolation graphs
- Quantum walk transport on carbon nanotube structures
- Percolation induced effects in 2D coined quantum walks: analytic asymptotic solutions
- Entropy rate of message sources driven by quantum walks
- Percolated quantum walks with a general shift operator: From trapping to transport
- Strongly trapped two-dimensional quantum walks
- A counterintuitive role of geometry in transport by quantum walks
- Quantum walks on random lattices: Diffusion, localization and the absence of parametric quantum speed-up
- Single-point position and transition defects in continuous time quantum walks
- Percolation assisted excitation transport in discrete-time quantum walks
- Geometrical aspects of quantum walks on random two-dimensional structures
- Quantum walker as a probe for its coin parameter
- A Simple Method for Finding the Scattering Coefficients of Quantum Graphs
- Quantum random walks on congested lattices
- Complete classification of trapping coins for quantum walks on the 2D square lattice
- Study of Quantum Walk over a Square Lattice
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- Decoherence on Staggered Quantum Walks
- The switching effect of the side chain on quantum walks on triple graphs
- Attractors and asymptotic dynamics of open discrete-time quantum walks on cycles
- Monitored Recurrence of a One-parameter Family of Three-state Quantum Walks
- Coherent transport over an explosive percolation lattice
- Exact simulation of coined quantum walks with the continuous-time model
- Quantum walks under superposition of causal order
- Two-particle Hadamard walk on dynamically percolated line and circle
- Key graph properties affecting transport efficiency of flip-flop Grover percolated quantum walks