Some theory problems on quantum computation and information

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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.