Tanja Döhler | Searcharxiv

arXiv2026

Learning Temporal Patterns in Financial Time Series: A Comparative Study of Quantum LSTM and Quantum Reservoir Computing

This study explores quantum and classical hybrid architectures for financial time-series fore casting, focusing on Quantum Long Short-Term Memory (QLSTM) networks and Quantum Reservoir Computing (QRC), using univariate and multivariate lag structures on real financial data. We assess how lag embeddings affect predictive accuracy and robustness. Data are en coded into quantum states via amplitude encoding, enabling efficient representation of normalized lagged observations under realistic qubit constraints. The recurrent dynamics of QLSTM and the reservoir of QRC are implemented as parameterized quantum circuits, while classical optimizers train the readout and, where applicable, variational circuit parameters. We benchmark quantum models against classical LSTM and reservoir computing using common error like metrics. Our results show that, with suitable lag selection and amplitude encoding, quantum-enhanced archi tectures match classical baselines in univariate settings and can modestly outperform them in multivariate regimes with correlated inputs, where expressive encodings are most beneficial.

quant-ph↗

arXiv2026

Variational Quantum Conditional Boltzmann Machines for Time-Series Forecasting: Architectures, Symmetric Hyperparameter Evaluation, and a Nonlinear Benchmark

In this study, we developed and evaluated four conditional energy-based forecasting architectures: a classical Gaussian-Bernoulli CRBM, a hybrid quantum-classical QCRBM, a full-register QQRBM, and a lag-feature QFeatureQRBM with complete derivations of their conditional distributions, Contrastive-Divergence gradients, and hybrid training, bridging the energy-based formulation and the implementation-level quantum computation. Unlike prior comparisons, our evaluation enforces symmetric hyperparameter optimisation: classical and quantum-specific hyperparameters receive an equally thorough grid search across thirteen structured experiments. We test on two data classes, a Gaussian-process dataset (GP) generated with real financial data and the input-driven NARMA-10 nonlinear benchmark. Across both regimes we find no systematic evidence of a quantum advantage at the available sample size: no quantum architecture improves on the best classical baseline. The fully quantum QQRBM and QFeatureQRBM are significantly worse, whereas the hybrid QCRBM is statistically indistinguishable from the strongest classical CRBM on both datasets. A power analysis bounds this null result: at n = 12 only medium-to-large effects are detectable, so small advantages cannot be excluded. An iso-parameter (matched-budget) comparison reaches the same conclusion: the classical CRBM is lowest at three of the four budgets and no CRBM-vs-QCRBM difference is significant at any budget.

quant-ph↗