The Effect of Quantum Coins on the Spreading of Binary Disordered Quantum Walk

Tushar Kanti Bose

Jing Zhao, Yayun Hu, Peiqing Tong

The dynamical and static disordered quantum walks were extensively studied recently. It is found that, for the dynamical disorder case, the transport behavior of particles is diffusive, and for the static disorder case the transport behavior is localized. In this work, we study the effect of quantum coins on the transport behaviors of the binary disordered quantum walks. We find that once the coins satisfy certain conditions, the sub-ballistic spreading could be found in binary dynamical disorder quantum walks, and the sub-ballistic, diffusive and sub-diffusive spreadings could be found in binary static disorder quantum walks. We obtain the necessary conditions for those abnormal diffusive behaviors.

Meng Zeng, Ee Hou Yong

Quantum Walk (QW) has very different transport properties to its classical counterpart due to interference effects. Here we study the discrete-time quantum walk (DTQW) with on-site static/dynamic phase disorder following either binary or uniform distribution in both one and two dimensions. For one dimension, we consider the Hadamard coin; for two dimensions, we consider either a 2-level Hadamard coin (Hadamard walk) or a 4-level Grover coin (Grover walk) for the rotation in coin-space. We study the transport properties e.g. inverse participation ratio (IPR) and the standard deviation of the density function (σ) as well as the coin-position entanglement entropy (EE), due to the two types of phase disorders and the two types of coins. Our numerical simulations show that the dimensionality, the type of coins, and whether the disorder is static or dynamic play a pivotal role and lead to interesting behaviors of the DTQW. The distribution of the phase disorder has very minor effects on the quantum walk.

甘姝, 何兴道, 刘彬 +1 more

张融 Zhang Rong, 张马龙 Zhang Malong, 薛鹏 Xue Peng

Caio B. Naves, Marcelo A. Pires, Diogo O. Soares-Pinto +1 more

Abstract We study a 2D disordered discrete-time quantum walk (QW) based on 1D generalized elephant QW where an entangling coin operator is assumed. We show that considering a given disorder in one direction, it is possible to control the degree of spreading and entanglement in the other direction. This observation helps assert that the random QWs of this ilk serve as a controllable decoherence channel with the degree of randomness being the tunable parameter and highlight the role of dimensionality in quantum systems regarding information and transport.