  Advances in classical machine learning and single-cell technologies have
paved the way to understand interactions between disease cells and tumor
microenvironments to accelerate therapeutic discovery. However, challenges in
these machine learning methods and NP-hard problems in spatial Biology create
an opportunity for quantum computing algorithms. We create a hybrid
quantum-classical graph neural network (GNN) that combines GNN with a
Variational Quantum Classifier (VQC) for classifying binary sub-tasks in breast
cancer subtyping. We explore two variants of the same, the first with fixed
pretrained GNN parameters and the second with end-to-end training of GNN+VQC.
The results demonstrate that the hybrid quantum neural network (QNN) is at par
with the state-of-the-art classical graph neural networks (GNN) in terms of
weighted precision, recall and F1-score. We also show that by means of
amplitude encoding, we can compress information in logarithmic number of qubits
and attain better performance than using classical compression (which leads to
information loss while keeping the number of qubits required constant in both
regimes). Finally, we show that end-to-end training enables to improve over
fixed GNN parameters and also slightly improves over vanilla GNN with same
number of dimensions.
