Quantum Walks and Weak Measurements

量子行走和弱测量

• 批准号: 0829870
• 负责人: Todd Brun
• 金额: $ 30万
• 依托单位: University of Southern California
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-09-01 至 2013-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0829870&HistoricalAwards=false
• 关键词: Quantum; Walks; Weak; Measurements

Quantum information processing (QIP) uses quantum phenomena such as superposition, interference, and entanglement to perform information-processing tasks that are difficult or impossible with classical resources. This research project studies two important tools in QIP, and their relationship to each other: quantum walks and weak measurements.Quantum walks are analogous to classical random walks. A "walker" at one of the vertices of a graph repeatedly moves randomly along the edges to neighboring vertices. In the quantum version the walker simultaneously moves in a superposition along every possible edge, producing novel interference effects. These effects are strongly influenced by the global symmetry of the graph, opening up the possibility of new quantum algorithms. However, in quantum mechanics measuring the location of the walker disturbs the state of the system and destroys the interference effects. To avoid this problem we use weak measurements that give less information but also disturb the state less. Choosing the optimal measurement strength maximizes the likelihood of finding the system in the desired state while minimizing the expected hitting time.The researchers address several important problems involving quantum walks and weak measurements. They study the effect of symmetry on hitting time for continuous-time quantum walks, the existence of infinite hitting-time walks, and how these allow a new class of quantum algorithms. They are developing path-integral techniques for quantum walks on graphs. They also study how to decompose strong generalized measurements into a sequence of weak (or continuous) measurements. It is an open problem, given a family of possible weak measurements, to determine which generalized measurements can be produced.

量子信息处理（QIP）利用叠加、干涉和纠缠等量子现象来执行经典资源难以或不可能完成的信息处理任务。 本研究计划主要研究QIP中的两个重要工具：量子游动和弱测量，以及它们之间的关系。 在图的一个顶点处的“步行者”重复地沿着边随机地沿着移动到相邻的顶点。 在量子版本中，步行者同时沿着每一个可能的边缘以叠加的方式移动，产生新颖的干涉效应。 这些效应受到图的全局对称性的强烈影响，开辟了新量子算法的可能性。 然而，在量子力学中，测量步行者的位置会干扰系统的状态并破坏干涉效应。 为了避免这个问题，我们使用弱测量，它提供的信息较少，但对状态的干扰也较少。选择最佳测量强度可以最大限度地提高在期望状态下找到系统的可能性，同时最小化预期的命中时间。研究人员解决了涉及量子漫步和弱测量的几个重要问题。 他们研究对称性对连续时间量子行走的命中时间的影响，无限命中时间行走的存在，以及这些如何允许一类新的量子算法。 他们正在开发图上量子行走的路径积分技术。 他们还研究如何将强广义测量分解为弱（或连续）测量序列。 这是一个开放的问题，给定一个家庭的可能的弱测量，以确定哪些广义测量可以产生。