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標題: | 以可視化模型協助之量子計算解決最佳化問題 Visualization Model Assisted Quantum Computing in Solving Optimization Problems |
作者: | 江育綺 Yu-Chi Jiang |
指導教授: | 郭斯彥 Sy-Yen Kuo |
關鍵字: | 量子計算,視覺化呈現,量子布林電路合成,加權投資組合最佳化,量子啟發式最佳化, quantum computing,visualization,quantum Boolean circuit synthesis,weighted portfolio optimization,quantum-inspired optimization, |
出版年 : | 2023 |
學位: | 博士 |
摘要: | 量子計算是能在現實應用中實現強大量子優勢的關鍵。目前的量子電腦還處在具中尺度雜訊的裝置階段,量子電腦的運算都還處在較低的保持特性相干時間以及較高的雜訊,使運算不穩定,無法獲得精確的結果。因此,這篇論文主要是希望能推進量子計算進展以利用量子優勢協助解決實際應用問題,並且從兩方面問題著手:(a)量子電路最小化以實現量子實際應用的功能、(b)量子啟發式最佳化以展示如何透過量子特性設計一個演算法以解決實際應用問題。在第一個問題中,這篇論文提出了以超立方體為基礎的量子布林電路合成方法,可以達到高位元量子函式並表現比其他現有的方法更好。超立方體和可逆函式有相似特性,因此將可逆函式轉換至超立方體上可以透過視覺化觀察整體電路特性,並幫助實現合成更簡短的量子布林電路。因此,新穎的兩個指標,相鄰漢明距離及整體循環距離被提出,幫助有效進行決策及產生較短電路。當實現較小的量子電路穩定量子電腦效能後,就能考慮現實應用,其中金融應用是常見的重要研究議題。然而,目前經典電腦依然具有許多比量子電腦更具優勢的特點。量子啟發式最佳化是在目前量子電腦成熟之前的過渡期期間,以實現量子計算的一種混合式方法,能處理實際應用問題並且在經典電腦上發展量子計算理論。除此之外,本研究也透過量子啟發式最佳化技術應用在具加權的投資組合最佳化問題上,使搜尋最佳化並擴展量子計算的適用性。這篇論文考慮多變市場情況並且利用量子啟發式最佳化搭配趨勢值模型找到穩定的加權投資組合,並且提出心情值以計算投資期間的投資者情緒波動。在這兩項最佳化問題中,視覺化呈現能幫助理解複雜問題及促使這篇論文提出有效解法以解決量子布林電路合成及金融應用問題的重要部分。 Quantum computing is the key to realizing the decisive quantum advantage in real-world applications. The current quantum computer is in a noisy intermediate-scale quantum (NISQ) device stage. The operation in a quantum computer has a low coherence time and high noise, making the result unstable to realize the precise result. This study aims to progress the development of quantum computing, addressing real-world applications through quantum advantage. This study addresses two aspects of quantum computing: (a) Quantum circuit minimization to realize the functionality of quantum applications. (b) Quantum-inspired optimization (QIO) to demonstrate how to design an algorithm by utilizing quantum property in solving applications. In the first topic, this study proposes a hypercube-based quantum Boolean circuit synthesis method that can achieve a higher-bit function and outperform other present works. The hypercube has a similar property to the reversible function. Transforming the reversible function into the hypercube can visually observe the overall circuit properties to help realize a compact quantum Boolean circuit. As a result, novel indicators, the adjacent Hamming distance (AHD) and total cycle distance (TCD), are proposed to aid in effective decision-making and generate shorter circuits. Real applications can be considered after a smaller quantum circuit stabilizes the quantum computer performance. Financial applications are a critical issue. However, classical computer still has many advantages over quantum computer currently. QIO is a hybrid method in the transitional period to realize quantum computing, address real-world applications, and develop theory in classical computers. This study utilizes the QIO technique to optimize the search and expand the applicability of quantum computing in the weighted portfolio optimization problem. This study considers the dynamic market situation and utilizes QIO to search for a stable weighted portfolio through the trend ratio model. The emotion index is proposed to evaluate the investor's fluctuating emotions in the investment period. In these two topics, visualization presentation is a critical issue in comprehending the complicated problem and urges this study to propose a practical solution to solve quantum Boolean circuit synthesis and financial application. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/90161 |
DOI: | 10.6342/NTU202303207 |
全文授權: | 同意授權(限校園內公開) |
顯示於系所單位: | 電機工程學系 |
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ntu-111-2.pdf 目前未授權公開取用 | 2.66 MB | Adobe PDF | 檢視/開啟 |
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