顏嗣鈞臺灣大學：電機工程學研究所張子璿Chang, Tzu-HsuanTzu-HsuanChang2007-11-262018-07-062007-11-262018-07-062006http://ntur.lib.ntu.edu.tw//handle/246246/53497In this thesis, we discover a new way to analyze quantum random walks over general graphs. We first define distance of the graph to compare classical random walks and quantum random walks. Then we run unitary quantum random walk algorithm over general graphs and do discover the existence of the advantages of the quantum walks. Next we perform the algorithm to solve a tiny problem “Tile Puzzle”. During the simulation, we find out the rules in how to choose the solution of edge-coloring problems. Finally, we define the general form of unitary quantum random walk and discuss the characteristic of the formula.Contents 0. Abstract 0 1 Introduction 1 2 Preliminaries 4 2.1 Quantum Computation 4 2.1.1 Quantum Bit 5 2.1.2 Quantum Gates 6 2.1.3 Quantum Algorithms 8 2.2 Random Walks 10 3 Quantum Random Walk 12 3.1 Quantum Random Walk on a Line 12 3.2 Quantum Random Walk on higher Dimension 14 3.3 Quantum Random Walk on general Graph 16 4 Quantum Random Walk on General Graph 19 4.1 Syntax and Constraints of Quantum Random Walk19 4.1.1 Self-Loop and the Definition of Regular Graph19 4.1.2 Constraints of Unitary labeling 20 4.1.3 Edge Coloring 21 4.2 Unitary Quantum Random Walk Algorithm 24 4.3 Simulation of Quantum random Walk on the General Graph 27 4.4 Tile-Puzzle Problems 32 5 General Formula of Quantum Random Walk 36 5.1 Quantum walk with Unitary Labeling (QWUL) 36 5.2 Characteristic observing of Quantum Random Walk39 6 Conclusions 43 7 References 44578137 bytesapplication/pdfen-US隨機漫步單位量子隨機漫步測量的量子隨機漫步quantum random walkQWULQWIMquantum random walk with measurementthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/53497/1/ntu-95-R93921034-1.pdf