Effective Dimension Governs Generalization in Quantum Kernel Vision Models

2026-06-18

AI Summary

This work uncovers the counterintuitive mechanism by which entanglement enhancement and noise injection improve generalization in quantum vision models. Introducing the effective dimensionality \( d_{\text{eff}} \) as a unified metric, the study establishes—for the first time—that both entanglement structure and noise influence generalization through their modulation of \( d_{\text{eff}} \), linking this effect to implicit regularization. Combining quantum kernel analysis, spectral decomposition, and explicit modeling of depolarizing and amplitude damping noise, the authors derive measurable design principles, including an exact decomposition of the depolarizing kernel and a contraction bound under amplitude damping. Experiments demonstrate that, in overfitting regimes, amplitude damping noise boosts test accuracy by up to 13%, confirming an inverted-U relationship between effective dimensionality contraction and generalization performance, and closely matching theoretical predictions.

Abstract

Recent quantum vision models-quantum vision transformers and quantum convolutional networks-report two striking but unexplained empirical phenomena: (i) ansatze with more, or more uniformly distributed, entanglement generalize better, and (ii) injecting quantum noise can improve test accuracy rather than degrade it. These observations are currently treated as curiosities, discovered by grid search and explained, if at all, by hand. We show that both are manifestations of a single, measurable quantity: the \emph{effective dimension} $d_{\rm eff}$ of the (noise-shaped) quantum feature kernel. Working primarily with quantum-kernel vision models-a quantum feature map read out by a kernel classifier-we give a spectral account in which entanglement structure and quantum noise are two knobs that move $d_{\rm eff}$; in an overfitting regime, contracting $d_{\rm eff}$ acts as ridge-like regularization. We analyze the mechanism: an \emph{exact} decomposition of the depolarized kernel $K_p=(1-p)^2K+\tfrac{p(2-p)}{D}\mathbf{1}\mathbf{1}^\top$ with $d_{\rm eff}(K_p)\to1$, a contraction result (and its boundary) for amplitude damping, a kernel-machine capacity bound, and a capacity/alignment risk decomposition; the monotone contraction operative in our entangled experiments is verified empirically, not proven in general. Along the one-parameter depolarizing family the collapse is instead exact by construction; we use it only to confirm the kernel decomposition to machine precision and at up to $12$ qubits, not as evidence for $d_{\rm eff}$. Amplitude damping contracts $d_{\rm eff}$ and lifts test accuracy by up to $+13\%$ along an inverted-U sweet spot; the effect's sign flips between the over- and under-fitting regimes; noise injection matches an explicit spectral-filtering frontier. Our results organize two reported anecdotes into a single measurable principle for designing quantum-vision models.

Problem

• quantum vision models
• generalization
• entanglement
• quantum noise
• effective dimension

Innovation

• effective dimension
• quantum kernel methods
• entanglement structure
• quantum noise regularization
• generalization in quantum models