Variational quantum circuits (VQCs) have been proposed as promising models for nonlinear learning tasks in the noisy intermediate-scale quantum (NISQ) era. This study presents a hybrid classical-quantum framework for nonlinear time-series forecasting that integrates causally-filtered Hidden Markov regime detection with multiple VQC architectures. Four circuit architectures are defined as an explicit [Formula: see text] factorial design that isolates circuit depth from entanglement topology (shallow: depth 1/linear; ring: depth 1/ring; deep: depth 4/linear; heavy: depth 4/ring), each with reported qubit count, parameter count and gate count, and are evaluated under an analytic depolarizing/readout noise model. Three nonlinear classical baselines (support-vector regression, gradient boosting, and a multilayer perceptron) are compared alongside a linear autoregressive (AR) baseline, and the Hidden Markov Model (HMM) regime feature is fit only on training data and propagated causally into the test set to remove look-ahead leakage. Across 20 Monte Carlo replicates, we find that every VQC architecture is outperformed by every classical baseline, including plain linear AR (paired t-tests, all [Formula: see text]; Cohen’s d up to 4.8). Within the VQC family, circuit depth - not shallowness - is associated with better performance (deep/heavy [Formula: see text] shallow/ring), while entanglement topology alone has little independent effect once depth is controlled. An ablation removing the HMM-derived feature shows it contributes negligibly to forecast accuracy in this setting. Under this confound-controlled design, we find no evidence of a forecasting advantage for the tested VQC architectures over classical linear or nonlinear baselines, which we report as a cautionary result for claims of near-term quantum advantage in forecasting.
Variational quantum circuits (VQCs) have been proposed as promising models for nonlinear learning tasks in the noisy intermediate-scale quantum (NISQ) era. This study presents a hybrid classical-quantum framework for nonlinear time-series forecasting that integrates causally-filtered Hidden Markov regime detection with multiple VQC architectures. Four circuit architectures are defined as an explicit [Formula: see text] factorial design that isolates circuit depth from entanglement topology (shallow: depth 1/linear; ring: depth 1/ring; deep: depth 4/linear; heavy: depth 4/ring), each with reported qubit count, parameter count and gate count, and are evaluated under an analytic depolarizing/readout noise model. Three nonlinear classical baselines (support-vector regression, gradient boosting, and a multilayer perceptron) are compared alongside a linear autoregressive (AR) baseline, and the Hidden Markov Model (HMM) regime feature is fit only on training data and propagated causally into the test set to remove look-ahead leakage. Across 20 Monte Carlo replicates, we find that every VQC architecture is outperformed by every classical baseline, including plain linear AR (paired t-tests, all [Formula: see text]; Cohen’s d up to 4.8). Within the VQC family, circuit depth - not shallowness - is associated with better performance (deep/heavy [Formula: see text] shallow/ring), while entanglement topology alone has little independent effect once depth is controlled. An ablation removing the HMM-derived feature shows it contributes negligibly to forecast accuracy in this setting. Under this confound-controlled design, we find no evidence of a forecasting advantage for the tested VQC architectures over classical linear or nonlinear baselines, which we report as a cautionary result for claims of near-term quantum advantage in forecasting.
This study investigates classification performance and trainability of variational quantum classifiers on near-term noisy quantum hardware across circuit depth and qubit count regimes within the context of quantum computing and machine learning, an area of growing scientific importance given its implications for hybrid quantum-classical algorithm design and practical NISQ hardware benchmarking for near-term quantum advantage assessment. Using gradient-based parameter optimization of parameterized quantum circuits with hardware noise modeling via density matrix simulation and physical execution on IBM Eagle processors, we examine expressibility of parameterized circuits enabling nonlinear decision boundaries in feature Hilbert space, with trainability constrained by barren plateau gradients at large qubit counts in 96 circuit architectures (4 qubit counts x 4 depths x 6 ansatz families) evaluated across 5 classification datasets with 20 random initialization seeds each drawn from IBM Quantum Eagle (127-qubit) and Falcon (27-qubit) processors with noise mitigation via zero-noise extrapolation. Results indicate that 10-qubit, 4-layer VQC achieves 84.2% classification accuracy on the best benchmark, within 3.8 percentage points of classical SVM, but gradient variance decays exponentially with qubit count (variance halving per 2 added qubits), confirming barren plateau scaling (p < 0.001), with 84.2% accuracy, 3.8 pp gap to classical SVM baseline as the primary quantitative benchmark. Concordance between primary and confirmatory measurement approaches exceeded 93%, validating the analytical framework. These findings contribute empirically to quantum computing and machine learning and carry actionable implications for the design of programs and policies targeting hybrid quantum-classical algorithm design and practical NISQ hardware benchmarking for near-term quantum advantage assessment.
The practical value of quantum machine learning must be derived from efficiency rather than scale, as current NISQ processors support only small, shallow circuits. This paper evaluated whether variational quantum circuits (VQCs) can reduce the trainable parameter count in an image classification scenario while preserving accuracy. Experimentation compared quantum classifier heads to parameter-matched classical heads on an identical set of frozen features drawn from the Fashion-MNIST dataset by a CNN. 9 configurations of a quantum circuit crossed 4, 6, and 8 qubits with 1, 2, and 4 entangling layers, each matched to a multilayer perceptron with an approximately equal parameter count. The linear probes served as a floor baseline for all 105 runs across 5 random seed values. 7 out of 9 quantum-based configurations met the mean test accuracy of no more than 1 percentage point below its matched classical head, enforced by the pre-specified criterion. The 2 failures were single-layer circuits, with each falling roughly 8 points below its matched classical head and 12 points below the circuit-free linear probe; in total, 6 configs with 2+ layers passed, with the smallest at 74 trainable parameters. The general trend noticed was that accuracy increased progressively with depth. The 4-layer circuits exceeded the linear probe at every qubit count and produced the highest accuracy at 6 and 8 qubits. The simulation ran noiselessly; VQCs preserved accuracy at the matched parameter budget when depth was given, showcasing depth rather than qubit count gating performance.
Time-series forecasting is vital across sectors such as finance, energy, and environmental science, where accurate future predictions drive informed decision-making. Traditional statistical methods and deep learning models like LSTM and Transformers, while effective, often struggle with high-dimensional data and long-term dependencies. In this paper, we propose a hybrid quantum-classical model that utilizes Parameterized Quantum Circuits (PQCs) to capture complex temporal patterns in multivariate time-series data. Our architecture integrates a classical encoder, a quantum variational processor, and a classical decoder, trained end-to-end using gradient-based optimization. Experiments conducted on benchmark datasets—electricity load, stock prices, and weather forecasting—demonstrate that the hybrid model consistently outperforms classical baselines in terms of Mean Squared Error (MSE), Mean Absolute Error (MAE), and R² score. Robustness analysis confirms the model’s resilience to moderate quantum noise, while an ablation study highlights the performance gain from quantum components. This work showcases the potential of hybrid quantum-classical approaches on Noisy Intermediate-Scale Quantum (NISQ) devices and lays a foundation for scalable, real-world quantum machine learning applications.
Forecasting temporal dynamics underpins many areas of science and engineering, from large-scale atmospheric prediction to nanoscale quantum control. Classical approaches, including autoregressive models and deep neural networks, have advanced sequential learning often at the expense of known model order, or large dataset and parameters, resulting in computational cost. Here, we investigate whether quantum entanglement can serve as a resource for temporal pattern learning using shallow and structured quantum circuits. We have proposed a Quantum Time Series (QTS) framework that encodes normalised sequential data into single-qubit rotations and captures temporal correlations through forward and cross-entanglement layers. Among several encoding schemes, phase encoding-based sparse entanglement provides hardware efficiency by scaling to larger qubit systems with linear circuit depth and two-qubit complexity of [Formula: see text] for qubit size n. This offers a reduction in parameters and depth compared with deep variational quantum circuits such as Heisenberg-inspired circuits, and random-parametric unitary architectures. Experiments on synthetic and geophysical datasets show that shallow QTS circuits reproduce complex temporal pattern from limited data by leveraging structured quantum entanglement. Executions on IBM's Heron and Eagle-class processors demonstrate robustness and scalability up to 100 qubits. These results suggest that structured entanglement may offer a short-term memory effect for time-series analysis, providing a scalable route for near-term quantum applications.
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.
Variational quantum circuits (VQCs) are a leading approach to quantum machine learning on near-term devices, yet it remains unclear which circuit architecture yields the best accuracy-parameter trade-off on classical tabular data. We present a systematic empirical comparison of four VQC families -- multi-layer fully-connected (FC-VQC), residual (ResNet-VQC), hybrid quantum-classical transformer (QT), and fully quantum transformer (FQT) -- across five regression and classification benchmarks. Our key findings are: \textbf{(i)}~FC-VQCs achieve 90-96\% of the R2 of attention-based VQCs while using 40-50\% fewer parameters, and consistently outperform equal-capacity MLPs (mean R2=0.829 vs.\ MLP720's 0.753 on Boston Housing, 3-seed average); \textbf{(ii)}~FC-VQC's Type~4 inter-block connectivity provides partial cross-token mixing that approximates the role of attention -- explicit quantum self-attention yields only marginal gains on most datasets while significantly increasing parameter count; \textbf{(iii)}~expressibility saturates at circuit depth~≈3, explaining why shallow VQCs already cover the Hilbert space effectively; \textbf{(iv)}~LayerNorm on the fully quantum transformer improves classification accuracy, suggesting normalization is important when all operations are quantum; \textbf{(v)}~in our noise study on Boston Housing, FQT degrades gracefully under depolarizing noise while QT collapses. All results are validated across three random seeds. These findings provide practical architectural guidance for deploying VQCs on near-term quantum hardware.