具有时间相关噪声的离散时间量子行走

Y. Peng, W. Wang, X. Yi
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引用次数: 3

摘要

研究了受时间相关噪声影响的离散时间量子行走动力学。在每一步之前,噪声被描述为一个统一的硬币型算子,并且注意力集中在高斯Ornstein Uhlenbeck过程产生的噪声上,超越了通常的电报噪声,其中随机变量仅由-1和1组成。在BCH公式的一阶近似下,导出了噪声离散时间量子行走的主方程。在受噪声参数控制的一定步长范围内,主方程给出的动力学特性与数值模拟结果吻合较好。在数值模拟中观察到长时间噪声动力学的两种重新标记行为,对应于两种相反的噪声状态:在慢噪声状态下,随着噪声幅值的增加,量子相干性被抑制,噪声离散时间量子游动的动力学逐渐过渡到经典随机游动的动力学。在快速噪声条件下,步行者被限制在几个点阵中,波包宽度比慢噪声条件下要窄得多。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Discrete-time quantum walk with time-correlated noise
We investigate the dynamics of discrete-time quantum walk subject to time correlated noise. Noise is described as an unitary coin-type operator before each step, and attention is focused on the noise generated by a Gaussian Ornstein Uhlenbeck process, going beyond the usual telegraph noise, where the random variables are consist of only -1 and 1. Under the first-order approximation of BCH formula, the master equation of noisy discrete-time quantum walk is derived. The dynamics given by the master equation are in good agreement with those given by numerical simulations within a certain period of steps, which is controlled by noise parameters. Two remarker behaviors of long time noisy dynamics are observed in numerical simulations, corresponding to two opposite noise regimes: in slow noise regime, with the increase of the noise amplitude, the quantum coherence is suppressed, and the dynamics of noisy discrete-time quantum walk gradually transits to that of classical random walk. In fast noise regime, the walker is confined into few lattice sites, and the width of wave packet is much narrower compared with that in slow noise regime.
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