# Quantum Kernels and the Cross-Section of Stock Returns: Anatomy of a Vanishing Advantage

arXiv: https://arxiv.org/abs/2607.20168 · HTML: https://mlsanity.com/paper/2607.20168/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 34 references that are in the map.
- First posted on arXiv 22 Jul 2026.

## Builds on (most cited first, 9 of 9)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (2021)
- [The Inductive Bias of Quantum Kernels](https://mlsanity.com/paper/2106.03747/) (2021)
- [Exponential concentration in quantum kernel methods](https://mlsanity.com/paper/2208.11060/) (2022)
- [Bandwidth Enables Generalization in Quantum Kernel Models](https://mlsanity.com/paper/2206.06686/) (2022)
- [Importance of Kernel Bandwidth in Quantum Machine Learning](https://mlsanity.com/paper/2111.05451/) (2021)
- [Numerical evidence against advantage with quantum fidelity kernels on classical data](https://mlsanity.com/paper/2211.16551/) (2022)

## Abstract (arXiv)

Do quantum kernels improve cross-sectional stock return prediction? We run a controlled horse race on the Chinese A-share market in which a quantum fidelity kernel, a projected quantum kernel, and a classical RBF control share identical training subsamples, solver, and tuning budgets, so that only the kernel is exchanged. On the main evaluation -- a point-in-time universe and 170 walk-forward windows (2012-2025) -- no quantum advantage exists: the fidelity kernel is indistinguishable from its RBF control (DeltaIC =+0.005, p=0.42), and a 2×2 design crossing kernel type with training budget (a Nystrom extension to the full ~38,000-observation windows) shows quantum kernels matching, but never beating, equal-budget linear models; after family-wise correction no pairwise difference among eleven models is significant, with point estimates favoring penalized linear regressions throughout. We then document how the opposite conclusion arises: a 60-window evaluation on a universe screened with full-sample information makes the same quantum kernel appear dominant on stability criteria and significantly better than neural baselines. Interaction characteristics from the anomalies literature help nothing, quantum or classical; a widened bandwidth grid reveals an interior optimum rather than the near-classical endpoint a coarse grid suggests; and the geometric difference, while large throughout (g gg 1), does not predict out-of-sample gains (ρ=-0.20). We propose protocol standards -- kernel-swap controls, budget-equalized comparisons, point-in-time universes, and multiplicity-robust inference -- for empirical claims of quantum advantage in finance.