Image Classification Using CNN-QNN Hybrid Model with Optimized Correlated Features

Quantum Neural Networks (QNNs) are often limited by the number of available qubits and the accumulation of noise in deep circuits. While classical deep learning typically employs decorrelation techniques (like whitening or orthogonalization) to reduce redundancy, it remains unclear how these classical feature statistics interact with the entanglement-based processing of QNNs. This paper investigates whether intentionally controlling the correlation of classical features can enhance the performance of hybrid CNN-QNN models without increasing quantum circuit depth.

The authors propose a hybrid architecture where a classical CNN extracts latent features, which are then passed through a correlation-regularization module before being encoded into a Variational Quantum Circuit (VQC). The regularization module uses a covariance-based loss function to force the off-diagonal entries of the feature correlation matrix toward a target constant. The researchers mathematically derived the QNN output using the Heisenberg picture to understand how input correlations propagate through the quantum circuit. They validated their hypothesis using Monte Carlo simulations and empirical tests on three binary classification tasks: CIFAR-10 (automobile vs. truck), Fashion-MNIST (shirt vs. coat), and radar micro-Doppler signatures (robotic dogs vs. non-robots).

The study reveals that there is an optimal regime for feature correlation in hybrid quantum-classical models. Specifically, the mathematical derivation and simulations indicate that an average feature correlation of approximately 0.5 maximizes classification accuracy. Inducing this moderate correlation consistently outperformed models with low (decorrelated) or high (redundant) correlations across all tested datasets. Furthermore, this approach reduced the variance in classification accuracy, suggesting that aligning classical feature statistics with the quantum entanglement structure provides a more stable and effective learning environment for NISQ-era quantum devices.