Limit Distribution for a Time-Inhomogeneous 2-State Quantum Walk

Caishi Wang, Wen-Ling Wang, d Xiangying Lu

Norio Konno, Tomasz Łuczak, Etsuo Segawa

Takuya Machida

Chia-Han Chou, Wei-Shih Yang

In quantum computation theory, quantum random walks have been utilized by many quantum search algorithms which provide improved performance over their classical counterparts. However, due to the importance of the quantum decoherence phenomenon, decoherent quantum walks and their applications have been studied on a wide variety of structures. Recently, a unified time-inhomogeneous coin-turning random walk with rescaled limiting distributions, Bernoulli, uniform, arcsine and semi-circle laws as parameter varies have been obtained. In this paper we study the quantum analogue of these models. We obtained a representation theorem for time-inhomogeneous quantum walk on discrete infinite state space. Additionally, the convergence of the distributions of the decoherent quantum walks are numerically estimated as an application of the representation theorem, and the convergence in distribution of the quantum analogues of Bernoulli, uniform, arcsine and semicircle laws are statistically analyzed.

拓也 町田

Meng Li, Caishi Wang, Rui Fu

The evolution equation of the Space-time inhomogeneous quantum random walk in terms of quantum Bernoulli noise not only depends on the change of time, but also on the spatial position of the walker.The model is defined on the space of square summable functions.The canonical isomorphism relationship also can deduce the representation of the model in the tensor space.Mathematical induction gives the probability distribution of the quantum random walk in the general initial state and find that it has the same limit distribution as the classical random walk.