The properties of the two-dimensional quantum walk with point, line, and circle disorders in phase are reported.Localization is observed in the two-dimensional quantum walk with certain phase disorder and specific initial coin states.We give an explanation of the localization behavior via the localized stationary states of the unitary operator of the walker＋ coin system and the overlap between the initial state of the whole system and the localized stationary states.
We present a scheme of quantum computing with charge qubits corresponding to one excess electron shared between dangling-bond pairs of surface silicon atoms that couple to a microwave stripline resonator on a chip. By choosing a certain evolution time, we propose the realization of a set of universal single-and two-qubit logical gates. Due to its intrinsic stability and scalability, the silicon dangling-bond charge qubit can be regarded as one of the most promising candidates for quantum computation. Compared to the previous schemes on quantum computing with silicon bulk systems, our scheme shows such advantages as a long coherent time and direct control and readout.
Quantum walks have been investigated as they have remarkably different features in contrast to classical random walks. We present a quantum walk in a one-dimensional architecture, consisting of two coins and a walker whose evolution is in both position and phase spaces alternately controlled by the two coins respectively. By analyzing the dynamics evolution of the walker in both the position and phase spaces, we observe an influence on the quantum walk in one space from that in the other space, which behaves like decoherence. We propose an implementation of the two-coin quantum walk in both position and phase spaces via cavity quantum electrodynamics （QED）.
This article aims to provide a review on quantum walks. Starting form a basic idea of discrete-time quantum walks, we will review the impact of disorder and decoherence on the properties of quantum walks. The evolution of the standard quantum walks is deterministic and disorder introduces randomness to the whole system and change interference pattern leading to the localization effect. Whereas, decoherence plays the role of transmitting quantum walks to classical random walks.
Quantum walks act in obviously different ways from their classical counterparts, but decoherence will lessen and close this gap between them. To understand this process, it is necessary to investigate the evolution of quantum walks under different decoherence situations. In this article, we study a non-Markovian decoherent quantum walk on a line. In a short time regime, the behavior of the walk deviates from both ideal quantum walks and classical random walks. The position variance as a measure of the quantum walk collapses and revives for a short time, and tends to have a linear relation with time. That is, the walker’s behavior shows a diffusive spread over a long time limit, which is caused by non-Markovian dephasing affecting the quantum correlations between the quantum walker and his coin. We also study both quantum discord and measurement-induced disturbance as measures of the quantum correlations, and observe both collapse and revival in the short time regime, and the tendency to be zero in the long time limit. Therefore, quantum walks with non-Markovian decoherence tend to have diffusive spreading behavior over long time limits, while in the short time regime they oscillate between ballistic and diffusive spreading behavior, and the quantum correlation collapses and revives due to the memory effect.
