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

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.

A Hyperparameter Study for Quantum Kernel Methods

Quantum kernel methods are a promising method in quantum machine learning thanks to the guarantees connected to them. Their accessibility for analytic considerations also opens up the possibility of prescreening datasets based on their potential for a quantum advantage. To do so, earlier works developed the geometric difference, which can be understood as a closeness measure between two kernel-based machine learning approaches, most importantly between a quantum kernel and classical kernel. This metric links the quantum and classical model complexities. Therefore, it raises the question of whether the geometric difference, based on its relation to model complexity, can be a useful tool in evaluations other than for the potential for quantum advantage. In this work, we investigate the effects of hyperparameter choice on the model performance and the generalization gap between classical and quantum kernels. The importance of hyperparameter optimization is well known also for classical machine learning. Especially for the quantum Hamiltonian evolution feature map, the scaling of the input data has been shown to be crucial. However, there are additional parameters left to be optimized, like the best number of qubits to trace out before computing a projected quantum kernel. We investigate the influence of these hyperparameters and compare the classically reliable method of cross validation with the method of choosing based on the geometric difference. Based on the thorough investigation of the hyperparameters across 11 datasets we identified commodities that can be exploited when examining a new dataset. In addition, our findings contribute to better understanding of the applicability of the geometric difference.