Bayesian convolutional front-end based uncertainty-aware hybrid quantum-classical image classification

Quantum machine learning on noisy intermediate-scale quantum (NISQ) devices often suffers from noise sensitivity, small-data overfitting, and miscalibrated predictive confidence. We propose an uncertainty-aware hybrid Bayesian quantum neural network (BQNN) that couples a Bayesian convolutional front-end with a parameterized quantum circuit (PQC), forming a three-stage pipeline: Bayesian feature extraction, quantum state evolution, and classical decision making. For 28 ×28 grayscale inputs, the front-end uses an 8-filter 3 ×3 Bayesian convolution followed by 2 ×2 max-pooling and a fully connected layer to produce a 10-dimensional embedding, which is mapped to four rotation angles and encoded on 4 qubits. Two parameterized quantum circuit designs are considered for the quantum classification layer. On MNIST and Fashion-MNIST, repeated experiments over five independent random seeds show that the proposed BQNN variants consistently outperform the corresponding QCNN baselines. On MNIST, BQNN-2 achieves a mean best test accuracy of 95.46 ± 0.36%, a mean final test accuracy of 95.44 ± 0.38%, and a mean final test loss of 0.169 ± 0.012. On Fashion-MNIST, BQNN-1 attains the best mean overall performance, with a mean best test accuracy of 87.59 ± 0.62%, a mean final test accuracy of 87.49 ± 0.73%, and a mean final test loss of 0.385 ± 0.017, while BQNN-2 exhibits slightly smaller run-to-run variation. Additional representative comparisons with QNN baselines under the same training configuration further suggest faster convergence and higher peak accuracy for BQNN. Using 30 Monte-Carlo forward passes, BQNN achieves better calibration (ECE 0.007-0.009) than QCNN (ECE 0.016-0.020), thereby reducing overconfident predictions. Additional robustness experiments under noisy mixed-state simulation further show that, under depolarizing noise, BQNN consistently preserves higher peak test accuracy than QCNN across both circuit variants on MNIST, demonstrating improved robustness in NISQ-like noisy settings.