Scaling Laws for Hybrid Quantum Neural Networks: Depth, Width, and Quantum-Centric Diagnostics

TL;DR

This paper investigates how hybrid quantum neural networks' performance and quantum properties scale with circuit depth and qubit count, providing practical guidance and evaluation protocols.

Contribution

It offers a systematic study of scaling laws in hybrid quantum neural networks, analyzing performance and quantum metrics across datasets and parameter regimes.

Findings

Performance saturates at certain depths and qubit counts

Quantum metrics correlate with predictive performance

Guidelines for selecting (Q, L) in hybrid QNNs

Abstract

Hybrid quantum neural networks are increasingly explored for classification, yet it remains unclear how their performance and quantum behavior scale with circuit depth and qubit count. We present a controlled scaling study of hybrid quantum-classical classifiers along two axes: (1) increasing the number of quantum layers L at fixed qubits Q, and (2) increasing the number of qubits Q at fixed depth L. Across multiple datasets, we evaluate predictive performance using Accuracy, PR-AUC, Precision, Recall, and F1, and track quantum-specific metrics (QCE, EEE, QGN) to characterize how quantum properties evolve under scaling. Our results summarize scaling trends, saturation regimes, and dataset-dependent sensitivity, and further analyze how quantum metrics relate to predictive performance. This study provides practical guidance for selecting (Q,L) in hybrid QNN classifiers and establishes a consistent evaluation protocol for scaling analysis.