QuChaTeR: A Hybrid Quantum-Chaotic Temporal Framework for Earthquake Prediction

Abstract: Seismic prediction remains challenging due to the highly nonlinear and chaotic dynamics of earthquake signals. While classical deep learning models such as LSTMs and CNNs capture local temporal features, and quantum models offer richer state representations, their integration with chaos-driven mechanisms is underexplored. We introduce QuChaTeR, a hybrid architecture that combines wavelet-based preprocessing, chaotic maps, and variational quantum circuits with recurrent structures to enhance temporal feature extraction. Implemented in PyTorch and PennyLane, QuChaTeR is benchmarked against classical (LSTM, GRU, RNN, 1D-CNN, Reservoir Computing) and quantum-inspired (Quantum LSTM) baselines. On real-world seismic datasets, QuChaTeR consistently converges faster and achieves superior performance across multiple evaluation criteria. Despite promising results, scalability and quantum hardware limitations remain challenges. Overall, this work demonstrates how quantum-chaotic hybridization provides a practical pathway toward more accurate and robust earthquake prediction.

• The paper introduces QuChaTeR, a hybrid architecture combining wavelet preprocessing, temporal convolutional networks, chaotic LSTM perturbations, and variational quantum circuits for predicting earthquakes above magnitude 5.
• The model achieves 0.9634 test accuracy, 0.9682 recall, 0.9590 F1 score, and 0.9785 ROC-AUC, outperforming six classical and quantum baselines on the Earthquakes benchmark.
• The results are promising but require cautious interpretation because experiments use a small single dataset, noise-free quantum simulation, possible data-leakage risks, and no ablation studies, confidence intervals, or statistical significance tests.

QuChaTeR is a hybrid quantum-classical architecture for earthquake event prediction that combines temporal convolutional networks (TCNs), chaos-driven recurrent perturbations, and variational quantum circuits. The paper reports that this composite model outperforms a suite of classical and quantum baselines on a binary earthquake classification task, achieving 0.9634 test accuracy and 0.9785 ROC-AUC. This essay summarizes the architecture, experimental methodology, results, and limitations of the work.

Motivation and related work

The paper positions itself against two strands of prior research. Classical deep learning approaches to seismic time series — including Bi-LSTM models for earthquake occurrence prediction [Hamdi et al., 2024] and CNN-LSTM hybrids for geolocation-based risk forecasting [Sneka & Kanchana, 2025] — capture temporal dependencies but, according to the authors, struggle with the chaotic dynamics of seismic signals. Earlier work established the relevance of chaos theory to seismic prediction [Yi et al., 2010] and wavelet packet analysis for ground motion modeling [Yamamoto & Baker, 2013]. On the quantum side, hybrid quantum neural networks have been applied to tsunami prediction via earthquake data fusion [Dutta et al., 2025]. The paper's claimed contribution is the first framework combining chaotic dynamics, wavelet preprocessing, and quantum recurrent layers in a single architecture.

Dataset and preprocessing

Experiments use the Earthquakes dataset from the Time Series Classification Archive, collected by the Northern California Earthquake Data Center (1967–2003). The task is binary classification: predicting whether an earthquake of Richter magnitude greater than 5 will occur given 512 hours of preceding readings. The training set is heavily imbalanced (264 negative vs. 58 positive samples), which the authors address with SMOTE oversampling. Signals are Min–Max normalized, imputed, and decomposed with the Discrete Wavelet Transform into approximation and detail coefficients; the concatenated multi-scale coefficients form the feature vector, standardized to zero mean and unit variance.

A notable methodological concern is that SMOTE is applied before any train/test split is described in detail; if synthetic samples derived from test-adjacent data leak into training, reported metrics could be optimistic. The paper asserts an independent test set with "identical features but unseen samples," but does not specify whether resampling occurred strictly within the training partition.

Architecture

QuChaTeR fuses three components:

Temporal convolutional front-end: a TCN with dilated causal convolutions realizes a finite-order autoregressive operator of order $kd^{L}$, providing bounded temporal dependency and stable gradient propagation.

Chaotic LSTM: standard LSTM hidden states are perturbed by the logistic map $$\mathbf{z}_t = r\,\mathbf{h}_t \odot (1 - \mathbf{h}_t)$$ with control parameter $r \in (0,4)$, and the first two hidden dimensions are further updated by the Hénon map ($a = 1.4$, $b = 0.3$). The paper states a boundedness proposition: for these parameter regimes both maps remain bounded, yielding Lyapunov stability of the chaotic subsystem. The proof is brief and relies on coarse bounds on iterate magnitudes rather than a formal stability analysis; it also cites a 1992 workshop paper under the key "Shahi2022" whose bibliographic entry does not match its citation year, suggesting some reference hygiene issues.

Quantum variational embedding: each temporal representation is encoded into a Hilbert space via a parameterized circuit of $R_Y$ rotations, $R_Z$ data encodings, and CNOT entanglers across $Q$ qubits. Six Pauli-$Z$ expectation values are measured and mapped back through a learnable linear layer as a residual update to the hidden state, with differentiability via the parameter-shift rule.

The logistic map parameter $r^\ast$ is selected by Bayesian optimization over validation loss using Gaussian Process surrogates and Expected Improvement acquisition, converging to $$\mathbf{z}_t = r\,\mathbf{h}_t \odot (1 - \mathbf{h}_t)$$0. All experiments were run on PennyLane's default.qubit simulator — i.e., noise-free statevector simulation on classical hardware — not on actual quantum devices.

Experimental setup and qubit selection

All models train for 50 epochs with Adam and BCE loss (learning rate 0.001, except Reservoir Computing at 0.01). Qubit count was chosen by maximizing a generalization stability metric $$\mathbf{z}_t = r\,\mathbf{h}_t \odot (1 - \mathbf{h}_t)$$1:

Qubits	Train Acc	Test Acc	Gap	$$\mathbf{z}_t = r\,\mathbf{h}_t \odot (1 - \mathbf{h}_t)$$2
2	0.8813	0.8542	0.027	0.827
4	0.9612	0.8807	0.081	0.800
6	0.9902	0.9634	0.027	0.937
8	0.9527	0.9141	0.039	0.876

The 6-qubit configuration wins decisively, with a 0.9634 test accuracy and only a 0.027 generalization gap. It is worth noting that selecting hyperparameters (qubit count) by test-set performance, even via a composite metric, risks optimistic bias in the headline result.

Results

QuChaTeR leads every metric among seven evaluated models:

Model	Accuracy	Recall	Precision	F1	ROC-AUC
QuChaTeR	0.9634	0.9682	0.9501	0.9590	0.9785
CNN1D	0.9215	0.9083	0.9447	0.9258	0.9407
LSTM	0.9057	0.8815	0.9123	0.8969	0.9225
Quantum LSTM	0.8931	0.9052	0.8745	0.8891	0.9139
GRU	0.8553	0.8415	0.8624	0.8519	0.8829
Reservoir	0.8335	0.8188	0.8351	0.8266	0.8635
RNN	0.7918	0.7710	0.8035	0.7869	0.8323

The margin over the strongest classical baseline (1D-CNN) is roughly 4 accuracy points and 3.8 ROC-AUC points. Quantum LSTM shows higher recall than classical LSTM (0.9052 vs. 0.8815), which the authors interpret as evidence that quantum components help identify rare positive events — a claim consistent with, but not statistically tested in, the paper. Loss curves show quantum-containing models starting at higher loss and converging gradually, attributed to stochasticity in quantum simulation; the authors caution that final loss ordering does not fully reflect evaluation metrics.

No confidence intervals, multiple seeds, or significance tests are reported, so the robustness of the ~4-point improvement cannot be assessed from the paper alone. Given the small dataset (322 training samples before SMOTE) and the number of architectural choices tuned, variance across runs is likely non-trivial.

Limitations and open questions

The paper concedes several limitations explicitly. All quantum computation is simulated classically on a noise-free backend; behavior under realistic NISQ noise, decoherence, and shot sampling is untested, and the abstract acknowledges scalability and hardware constraints. The boundedness proof covers only a narrow parameter regime and assumes specific Hénon map bounds without addressing interaction effects between the chaotic perturbation and gradient-based training. Whether the chaotic component contributes meaningfully beyond what an equivalently sized classical network achieves — e.g., via ablation removing only the logistic/Hénon perturbations or only the quantum layer — is not reported, leaving open the question of which subsystem drives the gains. Finally, evaluation is confined to a single benchmark dataset; generalization to continuous-magnitude forecasting or other seismic regimes remains unverified.

Conclusion

QuChaTeR demonstrates that composing TCN feature extraction, bounded chaotic perturbations of LSTM dynamics, and variational quantum embeddings yields the best reported performance on the Earthquakes time-series classification benchmark, with 0.9634 accuracy and 0.9785 ROC-AUC against six classical and quantum baselines. The evidence is promising but rests on a single small dataset, noise-free quantum simulation, and no ablation or statistical testing. The most pressing open questions are the source of the performance gain among the three components and the transferability of the approach to noisy quantum hardware and larger seismic corpora.