Exponentially decaying velocity bounds of quantum walks in periodic fields
Quantum walks are quantum analogues of classical random walks. They provide important tools in quantum computing, information, simulation, and communications. In this talk, we introduce a class of discrete-time one-dimensional quantum walks, associated with CMV unitary matrices, in the presence of a local (electric) field. This class is parametrized by a transmission parameter t∈[0,1]. We show that the asymptotic velocity can be made arbitrarily small by introducing a periodic local field with a sufficiently large period. In particular, we prove an upper bound for the velocity of the n-periodic quantum walk that is decaying exponentially in the period length n. Hence, localization-like effects are observed even after a long number of quantum walk steps when n is large.
The talk will take place via zoom. For login data contact Benjamin Hinrichs.