Curator's Take
This article shows that the ability of quantum policies and value functions to generalize is governed more by the Fisher‑effective dimension—an entanglement‑driven measure of circuit complexity—than by sheer parameter count, providing a fresh PAC‑Bayesian lens on why highly connected PQCs often overfit. By demonstrating that entangled architectures consistently exhibit larger train‑test gaps across supervised, bandit and reinforcement‑learning tasks, the work gives practitioners a concrete metric for ranking circuit designs when data are limited, something traditional parameter‑counting bounds cannot do. The findings suggest that modestly entangled or shallow connectivity may be preferable in near‑term quantum RL applications, though high return variance in multi‑step policies means the ordering can blur as more samples become available.
— Mark Eatherly
Summary
Parameterized quantum circuits (PQCs) are increasingly used as policies and value functions in quantum reinforcement learning, yet it remains unclear when and why quantum policies generalize. We give a PAC-Bayesian account in which generalization is governed not by the raw number of circuit parameters, but by the effective dimension of the Fisher geometry induced by the circuit. This quantity is inflated by entanglement, making entangling connectivity an independent axis of complexity.In controlled experiments that fix the number of trainable rotations and vary only entanglement, we find that circuits with larger Fisher effective dimension exhibit larger train-test gaps, while parameter count is a weak predictor. The resulting bound acts primarily as a ranking certificate: it correctly orders circuits with identical parameter count, which parameter-counting bounds cannot do. We validate this mechanism across supervised classification, quantum contextual bandits, and value-function generalization, where entangled circuits consistently generalize worse than non-entangled circuits of equal parameter count, with gaps shrinking as sample size increases.Our strongest evidence comes from low-variance decision models, including single-observable classifiers, value heads, and one-step policies. In end-to-end multi-step policy learning, entanglement effects remain statistically significant but high return variance leaves the full ordering only partially resolved. Partial-correlation analysis shows that Fisher effective dimension screens off entangling pattern, and controls for training accuracy, readout, and optimizer rule out major optimization confounders. The effect also persists on an IBM Heron quantum processor under real noise. Overall, our results reframe quantum policy design around an entanglement--generalization trade-off rather than expressivity alone.