Hybrid Quantum Recurrent Neural Network For Remaining Useful Life Prediction

TL;DR

The paper tackles remaining useful life forecasting for jet engines under limited data by proposing a Hybrid Quantum Recurrent Neural Network (HQRNN) that replaces LSTM gate transformations with Quantum Depth-Infused (QDI) circuits in a QLSTM stack and fuses them with classical dense layers. It demonstrates that the quantum-enhanced model achieves up to about a 5% improvement in RMSE and MAE over a parameter-matched classical RNN on the NASA C-MAPSS FD001 dataset, reporting an RMSE of $15.46$ in one configuration. The authors analyze the quantum circuit with ZX calculus, Fisher Information, and Fourier analysis, showing the circuit is irreducible, trainable, and capable of accessing a rich Fourier space, which supports learning high-frequency temporal patterns under data scarcity. Overall, the work provides evidence that hybrid quantum-classical architectures can yield practical benefits for time-series forecasting in predictive maintenance and points to directions for integrating quantum components with ensembles and transformer-based models.

Abstract

Predictive maintenance in aerospace heavily relies on accurate estimation of the remaining useful life of jet engines. In this paper, we introduce a Hybrid Quantum Recurrent Neural Network framework, combining Quantum Long Short-Term Memory layers with classical dense layers for Remaining Useful Life forecasting on NASA's Commercial Modular Aero-Propulsion System Simulation dataset. Each Quantum Long Short-Term Memory gate replaces conventional linear transformations with Quantum Depth-Infused circuits, allowing the network to learn high-frequency components more effectively. Experimental results demonstrate that, despite having fewer trainable parameters, the Hybrid Quantum Recurrent Neural Network achieves up to a 5% improvement over a Recurrent Neural Network based on stacked Long Short-Term Memory layers in terms of mean root mean squared error and mean absolute error. Moreover, a thorough comparison of our method with established techniques, including Random Forest, Convolutional Neural Network, and Multilayer Perceptron, demonstrates that our approach, which achieves a Root Mean Squared Error of 15.46, surpasses these baselines by approximately 13.68%, 16.21%, and 7.87%, respectively. Nevertheless, it remains outperformed by certain advanced joint architectures. Our findings highlight the potential of hybrid quantum-classical approaches for robust time-series forecasting under limited data conditions, offering new avenues for enhancing reliability in predictive maintenance tasks.

Figures (5)

• Figure 1: Remaining useful life of engine 2 according to linear degradation and piecewise linear degradation models. This work adopts the piecewise linear model with an early RUL threshold of 125.
• Figure 2: (a) HQRNN model pipeline. A data window of size $W \times 14$ (where $W$ is the window size and 14 is the number of sensor features) is processed through three stacked QLSTM layers followed by classical Dense layers, yielding a single RUL value. The dimensions of the QLSTM layers are 32, 16, and 8, while the Dense layers transition from $8 \times W$ to 16, 16 to 32, and finally 32 to 1. (b) Structure of the QLSTM layer. Conventional linear transformations are replaced by QDI layers for each of the four LSTM gates (forget, input, update, output). (c) A schematic of the QDI layer used in the QLSTM. Each input feature is encoded via parameterized $R_z$ gates on a 4-qubit quantum circuit. The variation part consists of parameterized rotations of $R_z$ and CNOT gates. The blue block repeats $n=1$ time. The observable is the Pauli $Y$ matrix.
• Figure 3: (a) A QDI layer before applying ZX-based parameter reduction. (b) The ZX-reduced QDI layer structure with rearranged weights. Despite these simplifications, no parameters can be removed without affecting the layer’s functionality.
• Figure 4: (a) The normalized histogram of the Fisher eigenvalue spectrum. There are several eigenvalue groups with slightly higher contribution; thus, the circuit doesn't fully rely on just few significant parameters, especially as all the others follow them closely in terms of eigenvalue percentage. Furthermore, according to abbas2021power, small number of close to zero eigenvalues indicates the resilience to the barren plateau problem. Additionally, none of those groups come close to the $95\%$ majority threshold, thus showing equal contributive distribution. (b) This is an averaged normalized Fisher Information Matrix. The diagonal of this matrix shows that the quantum circuit equally distributes the gradients to all trainable parameters, and there is no evident single-parameter dominance. Anti-diagonal elements aren't pronounced which means parameters aren't interconnected resulting in easier optimisation for circuit's weights.
• Figure 5: Real and imaginary parts of the Fourier coefficients for a QDI layer with four input features. The prevalence of non-zero coefficients ($\sim67\%$) indicates substantial expressivity.