The Properties And Applications Of Quamtum Walks With Phase Defects

Quantum walks(QWs) are the quantum analogy of the classical random walks(RWs) in quantum world and show different properties compared to RWs. The walker’s diffusion rate of QWs is faster than that of RWs. This paper focus on discussing the properties of one-dimensional QWs with phase defects firstly, and then it reports the properties of the two-dimensional QWs with point, line, and circle disorders in phase. Numerical calculations show that the walker’s spread velocity is largely decreased because of the phase defect and there exists localization phenomenon with special initial states. This dissertation shows that the localization phenomenon in quantum walk depends on three factors: the value of the phase defect, the position of the phase defect and the initial state of walker + coin system. It also gives an explanation on the localization via the fidelity between the initial state of the whole system and the localized stationary states of unitary operator.