Reports that hybrid quantum-classical models outperform classical ones in financial forecasting rarely rest on controlled comparisons. We examine this question with QuantFormer, a transformer in which variational quantum circuits compute the queries, keys and values of attention. Our first evaluation, which trained on synthetic data from a quantum generative adversarial network and tested on next-day returns, was inconclusive because no model, quantum or classical, beat a constant forecast of zero, so the differences in error between models reflected noise. We therefore repeated the comparison on the five-day range-based volatility of five assets, with three controls: a classical twin of identical design, an exact classical surrogate that can represent every function of the circuits, and the HAR econometric model. With training on 2019-2022 and testing on 2023, all neural models forecast volatility with skill, but none matched HAR (R²_oos=0.40, against 0.28-0.33 for the neural models on average). QuantFormer ranked the outcomes as well as the classical models, although its R²_oos ranged from 0.16 to 0.38 across random seeds because runs over-predicted the calm 2023 market by different amounts. A tenfold smaller learning rate for the circuits halved this spread and raised the mean R²_oos of QuantFormer to 0.33, level with the classical models but not above them. From these results we derive a checklist for evaluating quantum forecasting models.

Quantum Machine Learning,Variational Quantum Circuit,attention mechanism,Volatility forecasting,HAR model,Forecast Evaluation