Some theory problems on quantum computation and information

Regents Of The University Of Michigan - Ann Arbor, Ann Arbor MI

Investigators

Abstract

Some Theory Problems in Quantum Computation and Communication PI: Yaoyun Shi, University of Michigan, Ann Arbor It 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 advance our understanding on several fundamental questions concerning the power and limitations of quantum information processing. There are three main directions: (A) Develop fast, systematic classical algorithms that simulate quantum computation and the time evolution of quantum systems. Results along this line 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 in quantum 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 of graph 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 recently shown to be closely related to quantum entanglement. This research aims to further explore the connection.