Building Continuous Quantum-Classical Bayesian Neural Networks for a Classical Clinical Dataset

TL;DR

The paper tackles uncertainty-aware medical image classification by proposing a Quantum-Classical Bayesian Neural Network (QCBNN) that fuses a classical CNN with a quantum circuit to generate continuous stochastic weights under a Bayesian framework. It systematically evaluates multiple parametrized quantum circuit (PQC) architectures, comparing them to a classical Bayesian baseline on the BreastMNIST breast ultrasound dataset, and analyzes predictive performance, uncertainty calibration, and weight distributions. The findings indicate that certain PQC designs with learnable entanglement and constrained rotation can achieve stronger uncertainty-aware performance and even surpass the classical benchmark in some metrics, offering practical insights for designing future hybrid quantum-classical models in medicine. These results advance understanding of how PQC architecture choices influence uncertainty representation and inform the development of more trustworthy clinical AI systems.

Abstract

In this work, we are introducing a Quantum-Classical Bayesian Neural Network (QCBNN) that is capable to perform uncertainty-aware classification of classical medical dataset. This model is a symbiosis of a classical Convolutional NN that performs ultra-sound image processing and a quantum circuit that generates its stochastic weights, within a Bayesian learning framework. To test the utility of this idea for the possible future deployment in the medical sector we track multiple behavioral metrics that capture both predictive performance as well as model's uncertainty. It is our ambition to create a hybrid model that is capable to classify samples in a more uncertainty aware fashion, which will advance the trustworthiness of these models and thus bring us step closer to utilizing them in the industry. We test multiple setups for quantum circuit for this task, and our best architectures display bigger uncertainty gap between correctly and incorrectly identified samples than its classical benchmark at an expense of a slight drop in predictive performance. The innovation of this paper is two-fold: (1) combining of different approaches that allow the stochastic weights from the quantum circuit to be continues thus allowing the model to classify application-driven dataset; (2) studying architectural features of quantum circuit that make-or-break these models, which pave the way into further investigation of more informed architectural designs.

Figures (11)

• Figure 1: General architecture of proposed continuous hybrid quantum-classical BNN model. The top gray part represents a classical CNN architecture, while the bottom green part represent the quantum weights sampler and the bottom blue part represents the trainers for the quantum sampler. The quantum sampler comprises multiple modules: classical noise, a PQC generator and a post-processing step that computes expectation values of each qubit. The only part that requires a quantum hardware is the quantum generator, while all the other components are performed classically. The trainers of the sampler include a discriminator and a prior.
• Figure 2: Different PQC architectures, inspired by the literature. All architectures contain an embedding block, trainable block with rotation gate $R$ parametrized by $\theta$ followed by measurement of all qubits.
• Figure 3: Overview over predictive performance metrics and uncertainty-related metrics for \ref{['fig:matic_i']}-\ref{['fig:romero']} PQCs.
• Figure 4: Weights distribution density estimated from 100 inference passes through the model and consists of all samples across all convolutional filters combined.
• Figure 5: Accuracy on the test set and certainty level difference between correctly and incorrectly identified samples weighted by ensemble size (see \ref{['eq:difference']}).