Architectural Sensitivity of Variational Quantum Circuits for Nonlinear Time-Series Forecasting under NISQ Noise

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.