前沿方法：多分步量子漫步在量子態準備與金融市場模擬中的應用

Abstract

本博士論文探討量子計算在金融領域的創新應用，專注於為應用及開發量子演算法於複雜金融模擬。透過運用量子力學的原理—疊加、纏結及干涉—本研究將量子物理與計算金融結合，創造了一個開創性的量子演算法。本研究的核心，多分步量子漫步（multi-SSQW），在傳統量子漫步的框架上進行擴展，融入多代理決策過程。此整合使得能夠精細模擬反映真實世界金融市場複雜性的複雜金融分佈和場景。該演算法的顯著靈活性、可靠的收斂特性和快速計算能力，將其定位為金融分析和戰略決策的變革工具。本研究展示了實際應用，為未來的金融模型和風險評估設定了新的先例。

This dissertation delves into the innovative application of quantum computing within the finance sector, focusing on developing and implementing specialized quantum algorithms designed for complex financial simulations. By harnessing the principles of quantum mechanics—superposition, entanglement, and interference—this research synergizes quantum physics with computational finance to create a pioneering quantum algorithm. The centerpiece of our research, the multi-split-steps quantum walk (multi-SSQW), expands on traditional quantum walk frameworks by integrating multi-investors decision-making processes. This integration allows for the sophisticated modeling of complex financial distributions and scenarios, reflecting real-world financial market complexities. The algorithm's remarkable adaptability, consistent convergence, and capacity for swift calculations establish it as a revolutionary resource for financial analysis and strategic decision-making. Beyond theoretical implications, this research demonstrates practical applications, providing a significant computational edge over traditional methods and setting a new precedent for the future of financial modeling and risk assessment.