A Study and Design on the Architecture of Quantum Computers

自從量子電腦的概念於1980 年代初 期被提出後[1-3]，量子資訊科學便成為一 門相當新而發展快速的研究領域。本計劃 由量子電路的觀點研究量子計算系統之架 構， 同時以核磁共振(Nuclear Magnetic Resonance, NMR)之技術實作一個量子計 算系統。 要實作完成一部量子電腦，發展一套 有效的量子電路合成方法是有必要的。量 子電路的基本元件是量子位元，因為量子 位元製作不易，所以合成出來之量子電路 需要具有較低成本和較容易實作的特性。 本計劃中，我們使用表格式演算法發展出 一個量子布林電路化簡方法，這個方法可 以同時地執行AND 和XOR 函數化簡，當 一個量子布林電路被化簡後，我們還必須 驗證化簡後的電路與原來電路有相同的功 能。 在有了量子電路合成的工具之後，本 計劃選擇使用核磁共振的方式來實作一個 量子計算系統。我們利用基於碳的同位素 碳13 之三氯甲烷(chloroform)中的1H和13C (13CHC13)做為資訊的承載單位，NMR RF 脈衝用來操控其中之量子狀態，以實現一 個2 位元的NMR 量子計算系統雛形。值 得注意的是，只要承載資訊的單位(量子位 元)可以根據量子力學的方式進行操作，一 個量子計算系統獨立於底層The study of quantum information science has expanded rapidly since the theoretical model of quantum computers were introduced in the early 1980's [1-3]. In this project, we study the architecture of quantum computing systems from the circuit point of view and demonstrate physical implementations using nuclear magnetic resonance (NMR) technology. To implement a quantum computer, it is necessary to develop an efficient quantum circuit synthesis method. Since the quantum bit (which is the basic component of a quantum circuit) is very expensive, a good quantum circuit has to be designed in a cost-effective way and, at the same time, it must be easy for implementation. In this project we describe a simplification method of quantum Boolean circuits using a tabulation algorithm. This method performs AND and XOR function simplification simultaneously. After a quantum Boolean circuit is simplified, we verify the circuits to confirm its function is correct. With the capability of performing quantum circuit synthesis, we report an experimental realization of quantum switch using nuclear spins and magnetic resonant pulses in this project. The nuclear spins of 1H and 13C in carbon-13 labeled chloroform are used to carry the information. Then nuclear magnetic resonance pulses are applied to perform quantum operations on a two-qubit quantum computer prototype. Note that, an ideal quantum computation system is independent of the underlying physical implementation, as long as the information carrier (qubit) can be manipulated according to quantum mechanics