What question did this study set out to answer?

This research aims to enhance quantum machine learning performance by developing a hybrid Bayesian quantum neural network (BQNN) that addresses noise sensitivity and overfitting.

June 3, 2026Open Access

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

Key Points

This research aims to enhance quantum machine learning performance by developing a hybrid Bayesian quantum neural network (BQNN) that addresses noise sensitivity and overfitting.
Utilized a Bayesian convolutional front-end for feature extraction on 28x28 grayscale images.
Designed two parameterized quantum circuit variants for classification tasks.
Conducted experiments on MNIST and Fashion-MNIST datasets using repeated random seeds.
BQNN-2 achieved a test accuracy of 95.46% with a final test loss of 0.169 on MNIST.
BQNN-1 reached a mean test accuracy of 87.59% with a final test loss of 0.385 on Fashion-MNIST.
BQNN showed better calibration and accuracy in the presence of noise compared to QCNN.

Abstract

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.

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Wang et al. (Mon,) studied this question.

synapsesocial.com/papers/6a1fc76ddee9eb8c0dce84d8 https://doi.org/https://doi.org/10.1038/s41598-026-51827-x

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