用量子神经网络预测金融时间序列并优化投资组合
Hybrid Quantum-Classical Ridgelet Neural Networks for Portfolio Optimization
- 将小波变换改进为岭变换，降低量子计算所需比特数
- 通过量子近似优化算法求解股票选择的均值-方差问题
- 适合对量子金融计算感兴趣的算法研究者
本研究提出一种融合岭变换与量子处理流程的量子计算方法，用于金融时间序列预测及基于量子近似优化算法（QAOA）的投资组合优化。构建了量子岭变换神经网络（QRNN）模型，结合参数化量子线路（PQC）与基于岭变换的特征提取，实现时间序列预测，并将预测结果转化为基于QUBO的均值-方差优化问题，由QAOA求解以选出最优股票组合。通过将金融时间序列分解为多分辨率成分，岭变换可有效识别局部与全局趋势，显著减少量子计算所需的比特数量，提升模型可扩展性与精度。研究从单量子比特系统理论建模出发，扩展至多量子比特系统，证明其能捕捉到重要的预测信号。
原文摘要 · Abstract (English)
In this study, we introduce a quantum computing method that incorporates Ridglet transforms into quantum processing pipelines for financial time-series forecasting with Quantum Approximate Optimization Algorithm (QAOA)-based portfolio optimization. We propose a Quantum Ridgelet Neural Network (QRNN) model for forecasting time-series data that integrates Parametrized Quantum Circuits (PQCs) with ridgelet-based feature transformations and QAOA-based portfolio optimization for asset selection. By breaking down financial time-series data into multi-resolution components, the ridgelet transform enables the identification of both local and global trends. Ridgelet-based features improve the scalability and accuracy of quantum computing by significantly reducing the number of qubits needed. However, the predicted results are turned into a QUBO-based mean-variance optimization problem and solved with QAOA to select the best stocks. Our study begins with a theoretical formulation of the single-qubit system for our proposed model. This formulation is further extended to a multi-qubit system, and we show that it captures a significant fraction of the predictive signal.
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