Title: Quantum Machine Learning methods for Fourier-based distribution estimation with application in option pricing Show Chinese title

Title: 基于傅里叶的分布估计的量子机器学习方法及其在期权定价中的应用

Abstract: The ongoing progress in quantum technologies has fueled a sustained exploration of their potential applications across various domains. One particularly promising field is quantitative finance, where a central challenge is the pricing of financial derivatives-traditionally addressed through Monte Carlo integration techniques. In this work, we introduce two hybrid classical-quantum methods to address the option pricing problem. These approaches rely on reconstructing Fourier series representations of statistical distributions from the outputs of Quantum Machine Learning (QML) models based on Parametrized Quantum Circuits (PQCs). We analyze the impact of data size and PQC dimensionality on performance. Quantum Accelerated Monte Carlo (QAMC) is employed as a benchmark to quantitatively assess the proposed models in terms of computational cost and accuracy in the extraction of Fourier coefficients. Through the numerical experiments, we show that the proposed methods achieve remarkable accuracy, becoming a competitive quantum alternative for derivatives valuation. Show Chinese abstract

Abstract: 量子技术的持续进步推动了其在各个领域潜在应用的持续探索。 一个特别有前景的领域是量化金融，其中核心挑战是金融衍生品的定价——传统上通过蒙特卡洛积分技术解决。 在本工作中，我们引入两种混合经典-量子方法来解决期权定价问题。 这些方法依赖于从基于参数化量子电路（PQCs）的量子机器学习（QML）模型的输出中重建统计分布的傅里叶级数表示。 我们分析了数据规模和PQC维度对性能的影响。 量子加速蒙特卡洛（QAMC）被用作基准，以计算成本和傅里叶系数提取的准确性为指标，对所提出的模型进行定量评估。 通过数值实验，我们表明所提出的方法实现了显著的准确性，成为衍生品估值的有竞争力的量子替代方案。