We propose a time series forecasting method named Quantum Gramian Angular Field (QGAF). This approach merges the advantages of quantum computing technology with deep learning, aiming to enhance the precision of time series classification and forecasting. We successfully transformed stock return time series data into two-dimensional images suitable for Convolutional Neural Network (CNN) training by designing specific quantum circuits. Distinct from the classical Gramian Angular Field (GAF) approach, QGAF's uniqueness lies in eliminating the need for data normalization and inverse cosine calculations, simplifying the transformation process from time series data to two-dimensional images. To validate the effectiveness of this method, we conducted experiments on datasets from three major stock markets: the China A-share market, the Hong Kong stock market, and the US stock market. Experimental results revealed that compared to the classical GAF method, the QGAF approach significantly improved time series prediction accuracy, reducing prediction errors by an average of 25% for Mean Absolute Error (MAE) and 48% for Mean Squared Error (MSE). This research confirms the potential and promising prospects of integrating quantum computing with deep learning techniques in financial time series forecasting.

翻译：我们提出了一种名为量子格兰姆角场（QGAF）的时间序列预测方法。该方法融合了量子计算技术与深度学习的优势，旨在提升时间序列分类与预测的精度。通过设计特定的量子电路，我们成功将股票收益时间序列数据转化为适用于卷积神经网络（CNN）训练的二维图像。与经典格兰姆角场（GAF）方法不同，QGAF的独特性在于无需进行数据归一化与反余弦计算，从而简化了从时间序列数据到二维图像的转换过程。为验证该方法的有效性，我们在中国A股市场、香港股票市场及美国股票市场三大主要股票市场的数据集上进行了实验。实验结果表明，与经典GAF方法相比，QGAF方法显著提升了时间序列预测精度，平均绝对误差（MAE）降低了25%，均方误差（MSE）降低了48%。本研究证实了量子计算与深度学习技术在金融时间序列预测中的潜力与广阔前景。