# Quantum-Enhanced Forecasting: Leveraging Quantum Gramian Angular Field and CNNs for Stock Return Predictions

arXiv: https://arxiv.org/abs/2310.07427 · HTML: https://mlsanity.com/paper/2310.07427/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 52 references that are in the map.
- First posted on arXiv 11 Oct 2023.

## Builds on (most cited first, 7 of 7)

- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)
- [Financial Time Series Forecasting with Deep Learning : A Systematic Literature Review: 2005-2019](https://mlsanity.com/paper/1911.13288/) (2019)
- [Challenges and Opportunities in Quantum Machine Learning](https://mlsanity.com/paper/2303.09491/) (2023)
- [Imaging Time-Series to Improve Classification and Imputation](https://mlsanity.com/paper/1506.00327/) (2015)
- [Layer VQE: A Variational Approach for Combinatorial Optimization on Noisy Quantum Computers](https://mlsanity.com/paper/2102.05566/) (2021)
- [Deep Neural Network Ensembles for Time Series Classification](https://mlsanity.com/paper/1903.06602/) (2019)
- [Quantum Speedups for Exponential-Time Dynamic Programming Algorithms](https://mlsanity.com/paper/1807.05209/) (2018)

## Built on by (most cited first, 1 of 1)

- [How Can Time Series Analysis Benefit From Multiple Modalities? A Survey and Outlook](https://mlsanity.com/paper/2503.11835/) (2025)

## Abstract (arXiv)

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.