Quantum Walk with a time-dependent coin
arXiv:quant-ph/0510046 · doi:10.1103/PhysRevA.73.062304
Abstract
We introduce quantum walks with a time-dependent coin, and show how they include, as a particular case, the generalized quantum walk recently studied by Wojcik et al. {[}Phys. Rev. Lett. \textbf{93}, 180601(2004){]} which exhibits interesting dynamical localization and quasiperiodic dynamics. Our proposal allows for a much easier implementation of this particular rich dynamics than the original one. Moreover, it allows for an additional control on the walk, which can be used to compensate for phases appearing due to external interactions. To illustrate its feasibility, we discuss an example using an optical cavity. We also derive an approximated solution in the continuous limit (long--wavelength approximation) which provides physical insight about the process.
18 pages, 6 figures Revised version
References in corpus (20)
- Quantum random walks - an introductory overview
- Quantum Computation and Decision Trees
- From quantum cellular automata to quantum lattice gases
- Implementing the quantum random walk
- Quantum random walks in optical lattices
- One-Dimensional Three-State Quantum Walk
- Quantum walk on the line as an interference phenomenon
- Quantum quincunx in cavity quantum electrodynamics
- Classical wave-optics analogy of quantum information processing
- Aperiodic Quantum Random Walks
- Quantum walks based on an interferometric analogy
- Simulation of quantum random walks using interference of classical field
- Localization of Multi-State Quantum Walk in One Dimension
- One- and two-dimensional quantum walks in arrays of optical traps
- Optical Cavity Implementations of the Quantum Walk
- Quantum Walks with Entangled Coins
- Propagating Quantum Walks: the origin of interference structures
- Generalized Quantum Walk in Momentum Space
- Quantum random walk of the field in an externally driven cavity
- Optical implementability of the two-dimensional Quantum Walk
Cited by in corpus (48)
- Quantum walks: a comprehensive review
- Electric quantum walks with individual atoms
- Observing Topological Invariants Using Quantum Walk in Superconducting Circuits
- Experimental quantum-walk revival with a time-dependent coin
- Direct Probe of Topological Invariants Using Bloch Oscillating Quantum Walks
- Propagation and spectral properties of quantum walks in electric fields
- Dynamically Disordered Quantum Walk as a Maximal Entanglement Generator
- Nonlinear optical Galton board
- Entangling Power of Disordered Quantum Walks
- Asymptotic behavior of quantum walks with spatio-temporal coin fluctuations
- Quantum state engineering using one-dimensional discrete-time quantum walks
- Observation of quasiperiodic dynamics in a one-dimensional quantum walk of single photons in space
- Weak Limit of the 3-State Quantum Walk on the Line
- Distribution of chirality in the quantum walk: Markov process and entanglement
- Driving quantum walk spreading with the coin operator
- Tailoring discrete quantum walk dynamics via extended initial conditions: Towards homogeneous probability distributions
- Trapping photons on the line: controllable dynamics of a quantum walk
- Controlling quantum random walk with a step-dependent coin
- Localized State in a Two-Dimensional Quantum Walk on a Disordered Lattice
- Aperiodic space-inhomogeneous quantum walks: localization properties, energy spectra and enhancement of entanglement
- Genuine Parrondo's paradox in quantum walks with time-dependent coin operators
- Electric quantum walks in two dimensions
- Quantum walks: decoherence and coin-flipping games
- Limit theorem for a time-dependent coined quantum walk on the line
- Quantum walks in weak electric fields and Bloch oscillations
- Bloch-Landau-Zener dynamics induced by a synthetic field in a photonic quantum walk
- Quantum and random walks as universal generators of probability distributions
- Unitary Equivalence of Quantum Walks
- Classical-like behavior in quantum walks with inhomogeneous, time-dependent coin operators
- Bloch-like super-oscillations and unidirectional motion of phase driven quantum walkers
- Localization-like effect in two-dimensional alternate quantum walks with periodic coin operations
- Understanding and controlling N-dimensional quantum walks via dispersion relations. Application to the 2D and 3D Grover walks: Diabolical points and more
- Invariance in quantum walks with time-dependent coin operators
- Negative correlations can play a positive role in disordered quantum walks
- Green function approach for scattering quantum walks
- Parrondo's paradox in quantum walks with inhomogeneous coins
- Limit theorems for a localization model of 2-state quantum walks
- Anomalous diffusion in the resonant quantum kicked rotor
- Discrete-time quantum walks generated by aperiodic fractal sequence of space coin operators
- Quantum walks with spatiotemporal fractal disorder
- Revivals in One-dimensional Quantum Walks with a Time and Spin-dependent Phase Shift
- Investigating the quench dynamics of the bound states in a spin-orbital coupling system using a trapped ion
- Invariance in Quantum Walks
- Theoretical Studies on Quantum Walks with a Time-varying Coin
- Limit distribution of a time-dependent quantum walk on the half line
- A limit theorem for a 3-period time-dependent quantum walk
- Characterization of anomalous diffusion in one-dimensional quantum walks
- Three-state quantum walk on the Cayley Graph of the Dihedral Group