Stefano Giagu

Graphs are versatile structures for the representation of many real-world data. Deep Learning on graphs is currently able to solve a wide range of problems with excellent results. However, both the generation of graphs and the handling of large graphs still remain open challenges. This work aims to introduce techniques for generating large graphs and test the approach on a complex problem such as the calculation of dose distribution in oncological radiotherapy applications. To this end, we introduced a pooling technique (ReNN-Pool) capable of sampling nodes that are spatially uniform without computational requirements in both model training and inference. By construction, the ReNN-Pool also allows the definition of a symmetric un-pooling operation to recover the original dimensionality of the graphs. We also present a Variational AutoEncoder (VAE) for generating graphs, based on the defined pooling and un-pooling operations, which employs convolutional graph layers in both encoding and decoding phases. The performance of the model was tested on both the realistic use case of a cylindrical graph dataset for a radiotherapy application and the standard benchmark dataset sprite. Compared to other graph pooling techniques, ReNN-Pool proved to improve both performance and computational requirements.

We investigate the possibility to apply quantum machine learning techniques for data analysis, with particular regard to an interesting use-case in high-energy physics. We propose an anomaly detection algorithm based on a parametrized quantum circuit. This algorithm was trained on a classical computer and tested with simulations as well as on real quantum hardware. Tests on NISQ devices were performed with IBM quantum computers. For the execution on quantum hardware, specific hardware-driven adaptations were devised and implemented. The quantum anomaly detection algorithm was able to detect simple anomalies such as different characters in handwritten digits as well as more complex structures such as anomalous patterns in the particle detectors produced by the decay products of long-lived particles produced at a collider experiment. For the high-energy physics application, the performance was estimated in simulation only, as the quantum circuit was not simple enough to be executed on the available quantum hardware platform. This work demonstrates that it is possible to perform anomaly detection with quantum algorithms; however, as an amplitude encoding of classical data is required for the task, due to the noise level in the available quantum hardware platform, the current implementation cannot outperform classic anomaly detection algorithms based on deep neural networks.