Some theory problems on quantum computation and information

量子计算和通信中的一些理论问题：史耀云，密歇根大学安娜堡分校已经证明，量子信息的行为与经典信息有着根本的不同，而且，似乎基于精确量子力学原理的计算机可以比目前部署的计算机强大得多。该项目的目标是促进我们对量子信息处理的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有价值。(B)研究称为图态的一类特殊量子物体的性质。这些量子态在量子纠错和量子单向计算中发挥着重要作用，这是一种有望实现的量子计算模型。本研究的目的是在单向量子计算的背景下，根据相关图的组合特性来理解图状态的量子特性。(C)利用张量范数研究量子纠缠。张量范数是一个强大的数学概念，最近被证明与量子纠缠密切相关。本研究旨在进一步探讨两者之间的联系。

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.