STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
An Example of the Difference Between Quantum and Classical Random Walks
Quantum Information Processing
Quantum Random Walks in One Dimension
Quantum Information Processing
Quantum Walks for Computer Scientists
Quantum Walks for Computer Scientists
One dimensional quantum walks with memory
Quantum Information & Computation
Localization of discrete-time quantum walks on a half line via the CGMV method
Quantum Information & Computation
Limit theorems for quantum walks with memory
Quantum Information & Computation
Quantum walks: a comprehensive review
Quantum Information Processing
| Hi-index | 0.00 |
We advance the previous studies of quantum walks on the line with two coins. Such four-state quantum walks driven by a three-direction shift operator may have nonzero limiting probabilities (localization), thereby distinguishing them from the quantum walks on the line in the basic scenario (i.e., driven by a single coin). In this work, asymptotic position distributions of the quantum walks are examined. We derive a weak limit for the quantum walks and explicit formulas for the limiting probability distribution, whose dependencies on the coin parameter and the initial state of quantum walks are presented. In particular, it is shown that the weak limit for the present quantum walks can be of the form in the basic scenario of quantum walks on the line, for certain initial states of the walk and certain values of the coin parameter. In the case where localization occurs, we show that the limiting probability decays exponentially in the absolute value of a walker's position, independent of the parity of time.