Tailoring discrete quantum walk dynamics via extended initial conditions: Towards homogeneous probability distributions
arXiv:1004.0976 · doi:10.1088/1367-2630/12/12/123022
Abstract
We study the evolution of initially extended distributions in the coined quantum walk on the line by analyzing the dispersion relation of the process and its associated wave equations. This allows us, in particular, to devise an initially extended condition leading to a uniform probability distribution whose width increases linearly with time, with increasing homogeneity.
4 pages, 2 figures
References in corpus (25)
- Quantum random walks - an introductory overview
- Quantum Computation and Decision Trees
- 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 quantum walks with negligible decoherence in waveguide lattices
- Realization of a quantum walk with one and two trapped ions
- Quantum walk of a trapped ion in phase space
- Decoherence in quantum walks - a review
- Decoherence can be useful in quantum walks
- Connecting the discrete and continuous-time quantum walks
- Quantum walk on the line as an interference phenomenon
- Spatial search and the Dirac equation
- A random walk approach to quantum algorithms
- Relativistic quantum walks
- Quantum Walk with a time-dependent coin
- Optical Cavity Implementations of the Quantum Walk
- Implementing the one-dimensional quantum (Hadamard) walk using a Bose-Einstein Condensate
- Quantum phase transition using quantum walks in an optical lattice
- Distribution of chirality in the quantum walk: Markov process and entanglement
- Driving quantum walk spreading with the coin operator
- Generalized Quantum Walk in Momentum Space
- Unravelling quantum carpets: a travelling wave approach
- Group Velocity of Discrete-Time Quantum Walks
- Optical implementability of the two-dimensional Quantum Walk
Cited by in corpus (25)
- Quantum walks: a comprehensive review
- Quantum Field as a quantum cellular automaton: the Dirac free evolution in one dimension
- Discrete-time quantum walk with feed-forward quantum coin
- Experimental demonstration of quantum walks with initial superposition states
- Driven Quantum Walks
- The Dirac Quantum Cellular Automaton in one dimension: Zitterbewegung and scattering from potential
- Nonlocality, quantum correlations, and violations of classical realism in the dynamics of two noninteracting quantum walkers
- Electric quantum walks in two dimensions
- Asymptotic entanglement in quantum walks from delocalized initial states
- Connecting velocity and entanglement in quantum walks
- Weak disorder enhancing the production of entanglement in quantum walks
- Asymptotic properties of the Dirac quantum cellular automaton
- N-dimensional alternate coined quantum walks from a dispersion relation perspective
- Dirac quantum walks on triangular and honeycomb lattices
- Quantum walk on a cylinder
- Understanding and controlling N-dimensional quantum walks via dispersion relations. Application to the 2D and 3D Grover walks: Diabolical points and more
- A quantum walk with a delocalized initial state: contribution from a coin-flip operator
- Quantum Walks with Non-Orthogonal Position States
- High-fidelity state transfer via quantum walks from delocalized states
- Driving the resonant quantum kicked rotor via extended initial conditions
- Limit theorems of a 3-state quantum walk and its application for discrete uniform measures
- Enhanced spreading in continuous-time quantum walks using aperiodic temporal modulation of defects
- Directionality and quantum backfire in continuous-time quantum walks from delocalized states: Exact results
- Continuous-time quantum walks on a defective lattice: Boosting the spreading of delocalized states through Parrondo's strategy
- Realization of the probability laws in the quantum central limit theorems by a quantum walk