This dissertation explores the groundbreaking application of quantum computing in the finance sector, concentrating on the development and implementation of specialized quantum algorithms for complex financial simulations. Leveraging the principles of quantum mechanics—superposition, entanglement, and interference—this research integrates quantum physics with computational finance to formulate an innovative quantum algorithm. Central to our study is the multi-Split-Step Quantum Walk (multi-SSQW), which extends traditional quantum walk frameworks by incorporating multi-agent decision-making processes. This enhancement enables the sophisticated modeling of complex financial distributions and scenarios, accurately reflecting real-world market intricacies. The algorithm's notable adaptability, reliable convergence, and rapid computational capabilities make it a transformative tool for financial analysis and strategic decision-making. Beyond theoretical contributions, this research showcases practical applications, offering a significant computational advantage over traditional methods and setting a new standard for the future of financial modeling and risk assessment.

     Quantum-inspired optimization has demonstrated superior performance compared to traditional algorithms but still faces challenges in solving complex problems. Our new technology addresses these issues by utilizing superposition encoding to prevent premature convergence, incorporating effective guidance for rapid search, combining quantum NOT gates to escape local optima, and adaptively adjusting parameters and convergence speed. It also considers variable relationships using entanglement local search, effectively searches for the optimal solution, and extends to multi-objective models, offering diverse strategies and developing a visual application interface. When applied to quantum circuit synthesis, this technology significantly reduces the number of logic gates, accelerating the development of IBM quantum computers. Additionally, we have developed an innovative trend-based financial investment model that precisely defines stable upward trends, proving its applicability in global stock markets. This model, encoded on D-Wave quantum computers, significantly reduces computation time and improves investment returns and risk management performance.

     To solve the NP-complete problem of natural product structure elucidation, we transformed the combination of structures and molecular weights into Quadratic Unconstrained Binary Optimization (QUBO) formulation according to the database and target peaks. Quantum-inspired computing identified the validating structures with linear running time complexity. This study can help scientists elucidate the structures of effective compounds from natural product mixure and accelerate the progress of drug discovery.

• Problem to be addressed:
  This technology aims to develop an automated toolchain for quadratic unconstrained binary optimization (QUBO)-based quantum-inspired annealing optimization to solve combinatorial optimization problems (COP).
• Importance/Breakthrough:
  It helps general users who are not familiar with QUBO to utilize quantum-inspired annealers to solve common COP problems.
• Relevance to the future research directions of the project:
  The objective of Subproject 3 of this project is to implement a QUBO-based software development platform (QSDP) for quantum optimization. This system is crucial for achieving the goals of this project.