Abstract
Modern financial problems are essentially complex mathematical problems. The most important and common problems are combinatorial optimization problems in finance, such as common stock investment, financial management, etc. Among such problems, linear system solving problems are of this type. The core of the problem. Now with the development of machine learning and artificial intelligence technology, it has been well applied in the financial industry, but with the advent of the era of big data, massive amounts of data have brought huge challenges to the solution of classic solving methods and computing resources. Lloyd et al. proposed an HHL algorithm for solving linear systems. Under some assumptions, this algorithm can solve linear equations with exponential acceleration compared to classical algorithms. It is a key step in current quantum machine learning algorithms. More classic algorithms can achieve exponential acceleration. In this paper, the use of HHL algorithm to solve combinatorial optimization problems in finance has been researched and tested. The problem is described as a quadratic programming problem with equality constraints and the corresponding program design is carried out, verified and the final system state is carried out. The results are measured, and the results are analyzed. It is found that compared with the classical solution method, the HHL algorithm can be used to solve such combinatorial optimization problems, and the approximate solution obtained is in good agreement with the exact solution, which can be applied well. The solution process of such combinatorial optimization problems can be accelerated, and quantum computing can be better applied to such problems.
H. Wu—Contribute equally to the paper.
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Li, Q., Wu, H., Qian, W., Li, X., Zhu, Q., Yang, S. (2022). Portfolio Optimization Based on Quantum HHL Algorithm. In: Sun, X., Zhang, X., Xia, Z., Bertino, E. (eds) Artificial Intelligence and Security. ICAIS 2022. Lecture Notes in Computer Science, vol 13339. Springer, Cham. https://doi.org/10.1007/978-3-031-06788-4_8
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