  To accelerate the process of materials design, materials science has
increasingly used data driven techniques to extract information from collected
data. Specially, machine learning (ML) algorithms, which span the ML
discipline, have demonstrated ability to predict various properties of
materials with the level of accuracy similar to explicit calculation of quantum
mechanical theories, but with significantly reduced run time and computational
resources. Within ML, graph neural networks have emerged as an important
algorithm within the field of machine learning, since they are capable of
predicting accurately a wide range of important physical, chemical and
electronic properties due to their higher learning ability based on the graph
representation of material and molecular descriptors through the aggregation of
information embedded within the graph. In parallel with the development of
state of the art classical machine learning applications, the fusion of quantum
computing and machine learning have created a new paradigm where classical
machine learning model can be augmented with quantum layers which are able to
encode high dimensional data more efficiently. Leveraging the structure of
existing algorithms, we developed a unique and novel gradient free hybrid
quantum classical convoluted graph neural network (HyQCGNN) to predict
formation energies of perovskite materials. The performance of our hybrid
statistical model is competitive with the results obtained purely from a
classical convoluted graph neural network, and other classical machine learning
algorithms, such as XGBoost. Consequently, our study suggests a new pathway to
explore how quantum feature encoding and parametric quantum circuits can yield
drastic improvements of complex ML algorithm like graph neural network.
