顏嗣鈞臺灣大學：電機工程學研究所楊育翰Yang, Yu-HanYu-HanYang2007-11-262018-07-062007-11-262018-07-062007http://ntur.lib.ntu.edu.tw//handle/246246/53211在文獻中，有幾個量子演算法已被證明具有優越性超過其相對應之傳統演算法。最近的一個是量子隨機漫步。我們提出一個量子隨機漫步於一般圖形的統一架構。引進單一標籤的概念進入量子隨機漫步演算法。如果單一約束都無法滿足，我們還提供另一種中間量測的方法。我們並以幾個例子說明了所設計的演算法能保持量子干涉性質。In the literature, several quantum computation algorithms have been shown to have superiority over their classical counterparts. The most recent one is quantum random walks. We propose a unified framework for quantum walk algorithms on general graphs. We introduce the concept of unitary labeling into the quantum walk algorithm, and also provide another solution with intermediate measurement if the unitary constraint is not satisfied. We also demonstrate that the designed algorithms maintain the quantum interfering property with a few examples.Chapter 1 Introduction 1 Chapter 2 Preliminaries 4 2.1 Quantum Computation 4 2.1.1 Quantum Bit 5 2.1.2 Quantum Gates 7 2.1.3 Quantum Algorithms 8 2.2 Random Walk 10 Chapter 3 Quantum Random Walk 12 3.1 Quantum Random Walk on a Line 12 3.2 Quantum Random Walk on Higher Dimensions 14 3.3 Quantum Random Walk on General Graph 16 Chapter 4 Quantum Random Walk on General Graphs 19 4.1 Regular Graph 19 4.2 Unitary Labeling 20 4.3 Quantum Walk with Unitary Labeling (QWUL) Algorithm 21 4.4 Edge-coloring 25 4.5 Quantum Walk with Intermediate Measurement (QWIM) Algorithm 28 Chapter 5 Simulation Results 32 5.1 QWUL on a Finite Line 32 5.2 QWIM on a Grid 34 Chapter 6 Conclusion and Future Work 39 References 40en-US量子演算法隨機漫步quantum algorithmrandom walkthesis