Continuous deformations of the Grover walk preserving localization
arXiv:1206.0881 · doi:10.1140/epjd/e2012-30146-9
Abstract
The three-state Grover walk on a line exhibits the localization effect characterized by a non-vanishing probability of the particle to stay at the origin. We present two continuous deformations of the Grover walk which preserve its localization nature. The resulting quantum walks differ in the rate at which they spread through the lattice. The velocities of the left and right-traveling probability peaks are given by the maximum of the group velocity. We find the explicit form of peak velocities in dependence on the coin parameter. Our results show that localization of the quantum walk is not a singular property of an isolated coin operator but can be found for entire families of coins.
References in corpus (15)
- A Quantum Random Walk Search Algorithm
- Decoherence and disorder in quantum walks: From ballistic spread to localization
- Controlling discrete quantum walks: coins and intitial states
- Weak limits for quantum random walks
- One-Dimensional Three-State Quantum Walk
- Quantum walk on the line as an interference phenomenon
- Localization of Two-Dimensional Quantum Walks
- Asymptotic evolution of quantum walks with random coin
- Quantum Walks on a Random Environment
- Recurrence and Pólya number of quantum walks
- Limit distributions of two-dimensional quantum walks
- Localization of Multi-State Quantum Walk in One Dimension
- Recurrence of biased quantum walks on a line
- Recurrences in three-state quantum walks on a plane
- Group Velocity of Discrete-Time Quantum Walks
Cited by in corpus (22)
- Staggered Quantum Walks on Graphs
- Limit distributions of three-state quantum walks: the role of coin eigenstates
- Coined Quantum Walks on Weighted Graphs
- Photonic quantum walks with four-dimensional coins
- Search by Lackadaisical Quantum Walk with Nonhomogeneous Weights
- One dimensional lazy quantum walks and occupancy rate
- Strongly trapped two-dimensional quantum walks
- The Lackadaisical Quantum Walker is NOT Lazy at all
- Understanding and controlling N-dimensional quantum walks via dispersion relations. Application to the 2D and 3D Grover walks: Diabolical points and more
- Percolation assisted excitation transport in discrete-time quantum walks
- Complete classification of trapping coins for quantum walks on the 2D square lattice
- Coin dimensionality as a resource in quantum metrology involving discrete-time quantum walks
- Grover Walks on a Line with Absorbing Boundaries
- Limit theorems and localization of three state quantum walks on a line defined by generalized Grover coins
- Quantum walks on two kinds of two-dimensional models
- Suitable bases for quantum walks with Wigner coins
- Universal dynamical scaling laws in three-state quantum walks
- Monitored Recurrence of a One-parameter Family of Three-state Quantum Walks
- A characterization of orthogonal permutative matrices of order 4
- Stability of point spectrum for three-state quantum walks on a line
- Persistence of unvisited sites in quantum walks on a line
- Bifurcation Curves of Two-Dimensional Quantum Walks