量子随机游荡（又称量子游荡）是经典随机游荡的量子类似物。作为一种新型数学结构，量子随机游荡已被应用于量子算法工程、量子模拟以及普适量子计算等量子信息理论的诸多方面。量子Bernoulli噪声是量子白噪声的离散时间类似物。本项目旨在发展和完善量子Bernoulli噪声的理论与方法，并研究它们在量子随机游荡（包括酉量子随机游荡和开放量子随机游荡）和其它数学物理问题中的应用。本项目的研究内容涉及数学、物理和量子信息等学科领域，相互交叉性强、综合程度高，其主要创新之处在于提出了将量子Bernoulli噪声应用于量子随机游荡的研究构想。

Quantum random walks (also known as quantum walks) are quantum analogues of classical random walks. As a new type of mathematical structure, quantum random walks have found applications in many fields of quantum information theory, such as quantum algorithm engineering, quantum simulation, and universal quantum computing. Quantum Bernoulli noise is a discrete-time analogue of the quantum white noise. In this project, we would like to further develop the theory of quantum Bernoulli noise, and study its application to quantum random walks (including both unitary ones and open ones) as well as some other problems in mathematical physics. The project strongly involves many research fields in mathematics, physics and quantum information theory. Its major novalty lies in that we propose a quantum Bernoulli noise approach to quantum random walks.