Implementation of two-dimensional quantum walks

Kia Manouchehri, Jingbo B. Wang

Hao Qin, Peng Xue

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).

Yu‐Guang Yang, Xixi Wang, Jian Li +3 more

Two-dimensional quantum walks using a two-state coin have simpler experimental implementation than two-dimensional quantum walks using a four-state coin. However, decoherence occurs inevitably during the evolution of quantum walks due to the coupling between the quantum systems and their environment. Thus, it is interesting to investigate the robustness against decoherence for two- and four-state two-dimensional quantum walks. Here, we investigate the effects of the decoherence on two- and four-state two-dimensional quantum walks produced by the broken-link-type noise and compare their robustness against the broken-link-type noise. Specifically, we analyze the quantum correlation between the two spatial dimensions x and y by using measurement-induced disturbance for the two-state quantum walks, i.e. the alternate walk and the Pauli walk, and the four-state quantum walks, i.e. the Grover, Hadamard and Fourier walks, respectively. Our analysis shows that the two-state walks are more robust against the broken-link-type noise than the four-state walks.

Kendon

Peng Xue

Quantum random walks have been much studied recently,largely due to their highly non-classical behaviors.In this paper,we review the classical and quantum random walks of one-dimensional,and analyze two classical two-dimensional models and compare them.Furthermore we propose a two-dimensional quantum random walk algorithm.We compute the standard deviation,thereby proving our two-dimensional algorithm is superior to that of one-dimension.We propose a scheme,which is based on single photon with pairs of qubits,to implement it.

Kyohei Watanabe