Research On Quantum States Preparation And Clique Problem Based On NMR System

Quantum computing and information is a new subject based on quantum mechan-ics,and combined with mathematics,computer science,communications and other sub-jects.Compared to classical computing,quantum computing has a significant advan-tage in solving specific problems.For example,to factor a 29 bit integer,the classical computer with the speed of MIPS(Million Instructions Per Second)needs 8400 years.However,by utilizing quantum computer we only need 3.5 hours! The advantage of quantum computing is very attractive,so it is one of the hottest topics in the scientific research.In all potential physical systems which might be used to build quantum computer-s,NMR(Nuclear Magnetic Resonance)system is supposed to be the most rapid on in progress.This thesis implement the following three experiments based on NMR sys-tem:(3)Preparation of 7-qubit labelled pseudo-pure state.(1)Preparation of arbitrary dimension equal superposition state.(2)The quantum algorithm for solving the clique problem.(3)Preparation of 7-qubit labelled pseudo-pure state.Now we introduce the specific content of the thesis.In Chapter 1,taking the classical computing as an example,we introduce basic concepts in quantum information processing,such as quantum bits,quantum logic gates and quantum measurements.Also,we introduce DiVincenzo criterion.In Chapter 2,we specifically introduce the nuclear magnetic resonance technology,which explains how to construct quantum bits,logic gates and other basic concepts in the nuclear magnetic resonance system.Chapter 3 describes my first work,which is an equal superposition state(ESS)of arbitrary dimension.We give a method to construct ESS of arbitrary dimensions.The purpose of this work is to broaden the application of some quantum algorithms.More-over,we also discuss the entanglement detection of ESS by creating the corresponding observation operator to detect the entanglement properties of ESS.Chapter 4 describes my second work,which is the quantum algorithm to solve the clique problem.This thesis prove the complexity of clique problem can be reduced to O((?)2n)by quantum search algorithm.We finish the clique problem of the simplest graph by using the nuclear magnetic resonance system.As the clique problem is ap-plied in sociology,biology and chemistry frequently,the quantum algorithm we have developed provides a new way to solve the corresponding problems in these fields.Chapter 5 describes my third work,which is the preparation of 7 qubit labelled pseudo-pure state.We use the cat state method and the pulse compilation technique to construct the pulse sequence.Finally,we implement the labelled pseudo-pure with the crotonic sample.Above all,we demonstrated the advantages of quantum computing and quantum algorithms in theory.Although quantum computing has not yet reflected the great po-tential in the experiment.But with the further study of these physical systems,large-bit quantum computers can be born in anticipation of people one day.