In a paper published in Entropy, researchers explored a hybrid quantum-classical approach for stock price prediction using a quantum long short-term memory (QLSTM) model, which integrated classical LSTM with quantum computing.
Study: A Hybrid Quantum-Classical Model for Stock Price Prediction Using Quantum-Enhanced Long Short-Term Memory. Image Credit: Travis Wolfe/Shutterstock.com
They validated QLSTM on an International Business Machines (IBM) quantum simulator and a real quantum computer, comparing its performance to classical models. The QLSTM model achieved superior results, with lower RMSE and higher prediction accuracy, outperforming the classical LSTM and other models. Hyperparameter impacts were also analyzed to optimize performance.
Quantum-Enhanced Stock Prediction Model
The QLSTM architecture for stock price prediction merges classical long short-term memory (LSTM) networks with variational quantum circuits (VQCs), capitalizing on quantum-enhanced learning.
Designed to operate on noisy intermediate-scale quantum (NISQ) devices, this model utilized quantum processes such as data initialization, quantum state encoding, and quantum state manipulation through gates.
To prepare stock-price data for this hybrid model, normalization was applied to ensure compatibility with both classical and quantum layers. Quantum gates were employed to perform rotations and entanglements of qubits. Outputs from the VQCs were measured and iteratively refined to minimize prediction errors, enhancing the model’s overall accuracy.
The QLSTM retained the foundational structure of classical LSTMs but replaced classical gates with VQCs. In this framework, the forget, input, update, and output gates were redefined as VQCs1 through VQCs4, respectively. Additional VQCs5 and VQCs6 transformed the cell state into the hidden and final output states.
By operating on quantum principles, these gates generated outputs through linear combinations, which offered enhanced capabilities for learning complex temporal dependencies in stock price data, surpassing the limitations of discrete operations used in classical LSTMs.
The VQCs themselves were integral to the model, consisting of encoding, variational, and measurement layers. The encoding layer used quantum gates such as Hadamard and rotation gates to transform classical inputs into quantum states, ensuring proper normalization of input values. The variational layer contained tunable parameters, which were iteratively optimized using gradient-based methods to capture nonlinear and intricate relationships in the data. Entanglement and rotation operations, facilitated by controlled-NOT (CNOT) and single-qubit rotation gates, were essential for representing multiqubit interactions and enriching the model's predictive potential.
Key to the model’s performance was the ability of the VQCs to optimize rotation angles dynamically during training rather than relying on predefined values. The integration of repeated VQC layers within the QLSTM architecture allowed for increased expressiveness and the ability to detect intricate stock price patterns.
While this innovation offered significant advantages in predictive accuracy, it came with trade-offs in computational time, reflecting the challenges of working with quantum systems in real-world applications. This study demonstrated the potential of hybrid quantum-classical models to revolutionize stock price prediction by leveraging the unique strengths of quantum computing.
Experimental Setup Overview
The study utilized stock price data for Apple Inc., spanning from January 1, 2022, to January 1, 2023, comprising 251 observations with five columns: date, open, high, low, and close.
Data pre-processing ensured numerical stability, and the dataset was divided into 70 % training and 30 % testing splits. Performance was evaluated using root mean square error (RMSE) and prediction accuracy as metrics. Both classical LSTM and QLSTM models were trained using a learning rate of 0.01, with mean squared error (MSE) as the loss function and the Adam optimizer.
The QLSTM model demonstrated superior performance compared to classical LSTM and other benchmark models. Its training losses (MSE) were consistently lower and exhibited less fluctuation, reflecting improved data representation facilitated by quantum encoding. The Noiseless QLSTM achieved an accuracy of 1 and an RMSE of 0.0371, while the Noisy QLSTM achieved an accuracy of 0.9714 and an RMSE of 0.0511.
These results underscored QLSTM's robustness, even under the limitations posed by actual quantum devices, as it outperformed classical models with a 10 % improvement in accuracy and a 50 % reduction in RMSE.
In prediction tasks, QLSTM maintained superior performance in both Noiseless and Noisy scenarios. However, its effectiveness diminished in Actual environments due to quantum noise, reflecting the current challenges of working with real-world quantum devices.
Experiments examining the impact of qubit count revealed no significant performance improvements with additional qubits. Notably, performance degradation was observed when scaling from 8 to 11 qubits, attributed to the barren plateau problem, which hampers the optimization of variational quantum circuits (VQCs) as the qubit count increases.
Conclusion
In conclusion, this study presented the QLSTM framework, a hybrid quantum-classical approach that integrated classical LSTM networks with VQCs for stock price prediction. The QLSTM model demonstrated significant improvements over classical LSTM, achieving a 50 % reduction in RMSE and a 10 % increase in accuracy, highlighting the potential of quantum-enhanced learning for complex time-series analysis.
Despite its advantages, QLSTM faced limitations when implemented on actual quantum hardware, where performance lagged behind classical models due to quantum noise and hardware constraints. These findings underscore the challenges of deploying quantum models in practical scenarios. Future research will focus on enhancing scalability, implementing quantum error mitigation strategies, and broadening QLSTM's applicability to other time-series prediction tasks, such as energy forecasting and healthcare analytics, paving the way for advancements in quantum computing applications.
Journal Reference
Kea, K., et al. (2024). A Hybrid Quantum-Classical Model for Stock Price Prediction Using Quantum-Enhanced Long Short-Term Memory. Entropy, 26:11, 954. DOI: 10.3390/e26110954, https://www.mdpi.com/1099-4300/26/11/954
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