  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.
