Hybrid quantum-classical recurrent architectures have been proposed for capturing non-stationary, fat-tailed dynamics typical of financial time series, but most published evaluations compare a Quantum Long Short-Term Memory network only against plain Long Short-Term Memory on a single asset. This study contributes a controlled multi-baseline benchmark using four synthetic asset classes generated by calibrated Generalised Autoregressive Conditional Heteroskedasticity processes, comparing six architectures at a matched parameter budget below three hundred and fifty trainable parameters across five random seeds. The comparison set includes Long Short-Term Memory, Bidirectional Long Short-Term Memory, a compact Patch Time Series Transformer, Neural Basis Expansion Analysis, an Inverted Transformer, and a four-qubit Quantum Long Short-Term Memory with two variational blocks. Significance is established through Wilcoxon signed-rank tests, walk-forward validation across three expanding folds, depolarising-noise robustness sweeps, and a variational circuit depth ablation. The principal empirical finding is that compact classical recurrence dominates the benchmark on root mean squared error, while the quantum model exhibits the lowest seed-to-seed variance and the highest directional accuracy on the most volatile asset class.
Hybrid quantum-classical recurrent architectures have been proposed for capturing non-stationary, fat-tailed dynamics typical of financial time series, but most published evaluations compare a Quantum Long Short-Term Memory network only against plain Long Short-Term Memory on a single asset. This study contributes a controlled multi-baseline benchmark using four synthetic asset classes generated by calibrated Generalised Autoregressive Conditional Heteroskedasticity processes, comparing six architectures at a matched parameter budget below three hundred and fifty trainable parameters across five random seeds. The comparison set includes Long Short-Term Memory, Bidirectional Long Short-Term Memory, a compact Patch Time Series Transformer, Neural Basis Expansion Analysis, an Inverted Transformer, and a four-qubit Quantum Long Short-Term Memory with two variational blocks. Significance is established through Wilcoxon signed-rank tests, walk-forward validation across three expanding folds, depolarising-noise robustness sweeps, and a variational circuit depth ablation. The principal empirical finding is that compact classical recurrence dominates the benchmark on root mean squared error, while the quantum model exhibits the lowest seed-to-seed variance and the highest directional accuracy on the most volatile asset class.
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.
Quantum long short-term memory (QLSTM) models extend recurrent sequence learning with variational quantum circuits, but their optimization behavior can vary substantially across random initializations and temporal contexts. This paper evaluates a recursive QLSTM architecture against a standard QLSTM for one-step-ahead prediction of daily minimum and maximum temperature. Using daily weather observations from Toronto and identical training settings, we compare convergence, predictive accuracy, and generalization across input windows of 8, 16, and 32 days over 20 random seeds. The recursive model consistently reaches a near-optimal test loss earlier, reduces mean absolute error and root mean squared error, and exhibits a smaller generalization gap. These results indicate that recursive quantum feature transformations can improve stability and out-of-sample performance for compact hybrid quantum--classical temporal models.
In this paper, we present a reproducible benchmarking framework that systematically compares QML models with architecture-matched classical counterparts across three financial tasks: (i) directional return prediction on U.S. and Turkish equities, (ii) live-trading simulation with Quantum LSTMs versus classical LSTMs on the S\&P 500, and (iii) realized volatility forecasting using Quantum Support Vector Regression. By standardizing data splits, features, and evaluation metrics, our study provides a fair assessment of when current-generation QML models can match or exceed classical methods. Our results reveal that quantum approaches show performance gains when data structure and circuit design are well aligned. In directional classification, hybrid quantum neural networks surpass the parameter-matched ANN by \textbf{+3.8 AUC} and \textbf{+3.4 accuracy points} on \texttt{AAPL} stock and by \textbf{+4.9 AUC} and \textbf{+3.6 accuracy points} on Turkish stock \texttt{KCHOL}. In live trading, the QLSTM achieves higher risk-adjusted returns in \textbf{two of four} S\&P~500 regimes. For volatility forecasting, an angle-encoded QSVR attains the \textbf{lowest QLIKE} on \texttt{KCHOL} and remains within $\sim$0.02-0.04 QLIKE of the best classical kernels on \texttt{S\&P~500} and \texttt{AAPL}. Our benchmarking framework clearly identifies the scenarios where current QML architectures offer tangible improvements and where established classical methods continue to dominate.
Predicting the closing price of an equity remains stubbornly hard: price series are noisy, non-stationary, and shaped by feedback that breaks the assumptions of linear models. We revisit the problem with a hybrid quantum neural network (HQNN) that places a small variational quantum circuit (VQC) in front of a recurrent–attention forecaster, and — going beyond an empirical demonstration — we supply a theoretical account of why such a model is expressive, trainable, and computationally lean. The architecture works in two coupled stages. A four-qubit VQC first maps an amplitude-encoded feature vector through parameterised / rotations and CNOT–CZ entangling gates, with exact gradients supplied by the parameter-shift rule; the resulting expectation values form a compact quantum latent code. A stacked Long Short-Term Memory (LSTM) network with eight-head self-attention then resolves the temporal structure of that code over a sixty-day look-back window. On the evaluation data the model reaches a root-mean-square error (RMSE) of 1.74 USD, a mean absolute error (MAE) of 1.42 USD, and a coefficient of determination , ahead of a standalone LSTM (RMSE 3.45), a DCQ-GA Elman network (4.82), a blind-quantum-computing QNN (5.13), and a variational QNN–LSTM (3.97). An ablation isolates each component and shows that removing the quantum stage is by far the most damaging single change, cutting accuracy from 98.26% to 93.41%. Our theoretical contribution interprets the VQC as a truncated Fourier model whose accessible spectrum is set by the encoding depth, shows that the shallow four-qubit design sits well clear of the barren-plateau regime, recasts the circuit’s KL penalty as a quantum information bottleneck, and derives the sub-linear training-time scaling — about against the LSTM’s near-quadratic growth — that we observe empirically up to 100,000 samples. Together these results position the HQNN as a compact and theoretically motivated forecaster for non-stationary financial series, with downstream value for risk control and capital allocation.
Predicting the closing price of an equity remains stubbornly hard: price series are noisy, non-stationary, and shaped by feedback that breaks the assumptions of linear models. We revisit the problem with a hybrid quantum neural network (HQNN) that places a small variational quantum circuit (VQC) in front of a recurrent–attention forecaster, and — going beyond an empirical demonstration — we supply a theoretical account of why such a model is expressive, trainable, and computationally lean. The architecture works in two coupled stages. A four-qubit VQC first maps an amplitude-encoded feature vector through parameterised R_y/R_z rotations and CNOT–CZ entangling gates, with exact gradients supplied by the parameter-shift rule; the resulting expectation values form a compact quantum latent code. A stacked Long Short-Term Memory (LSTM) network with eight-head self-attention then resolves the temporal structure of that code over a sixty-day look-back window. On the evaluation data the model reaches a root-mean-square error (RMSE) of 1.74 USD, a mean absolute error (MAE) of 1.42 USD, and a coefficient of determination R^2=0.983, ahead of a standalone LSTM (RMSE 3.45), a DCQ-GA Elman network (4.82), a blind-quantum-computing QNN (5.13), and a variational QNN–LSTM (3.97). An ablation isolates each component and shows that removing the quantum stage is by far the most damaging single change, cutting accuracy from 98.26% to 93.41%. Our theoretical contribution interprets the VQC as a truncated Fourier model whose accessible spectrum is set by the encoding depth, shows that the shallow four-qubit design sits well clear of the barren-plateau regime, recasts the circuit’s KL penalty as a quantum information bottleneck, and derives the sub-linear training-time scaling — about O(N^0.62 ) against the LSTM’s near-quadratic growth — that we observe empirically up to 100,000 samples. Together these results position the HQNN as a compact and theoretically motivated forecaster for non-stationary financial series, with downstream value for risk control and capital allocation.
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.