Some theory problems on quantum computation and information

量子计算与信息的若干理论问题

• 批准号: 0622033
• 负责人: Yaoyun Shi
• 金额: $ 25万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-09-15 至 2009-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0622033&HistoricalAwards=false
• 关键词: Some; theory; problems; quantum; computation

Some Theory Problems in Quantum Computation and CommunicationPI: Yaoyun Shi, University of Michigan, Ann ArborIt has been demonstrated that quantum information behaves fundamentally different from classical information, and, it appears that computers based on exact quantum mechanical principles can be dramatically more powerful than those currently deployed. The goal of this project is to advanceour understanding on several fundamental questions concerningthe power and limitations of quantum information processing.There are three main directions:(A) Develop fast, systematicclassical algorithms that simulate quantum computationand the time evolution of quantum systems. Results along thisline not only will shed light on the limitations of quantum computation, but will also be valuable for the analysis and engineering of quantum information processing components.(B) Investigate properties of a special class of quantum objects called graph states. Those quantum states play an important role inquantum error-correction as well as in quantum one-way computation,a quantum computing model promising for its physical implementation.This research aims to understand the quantum properties ofgraph states in terms of the combinatorial properties of the associated graphs, and in the context of one-way quantum computing.(C) Investigate quantum entanglement using tensor norms.Tensor norms are powerful mathematical concept that are recentlyshown to be closely related to quantum entanglement. This researchaims to further explore the connection.

量子计算和通信中的一些理论问题PI：Yaoyun Shi，密歇根大学，安娜堡已经证明，量子信息的行为与经典信息有着根本的不同，而且，基于精确量子力学原理的计算机似乎比目前部署的计算机更强大。这个项目的目标是推进我们对量子信息处理能力和局限性的几个基本问题的理解，主要有三个方向：（A）开发快速、系统的经典算法，模拟量子计算和量子系统的时间演化。沿着这条线的结果不仅将揭示量子计算的局限性，而且对量子信息处理组件的分析和工程也很有价值。(B)研究一类特殊的量子对象的性质，称为图形状态。这些量子态在量子量子纠错和量子单向计算中起着重要的作用，量子单向计算是一种有望实现量子计算的量子计算模型，本研究旨在从关联图的组合性质和单向量子计算的角度来理解图态的量子性质。(C)利用张量范数研究量子纠缠，张量范数是最近被证明与量子纠缠密切相关的数学概念.本研究旨在进一步探讨两者之间的联系。