Variational Quantum Splines: Moving Beyond Linearity for Quantum Activation Functions

Activation functions within neural networks play a crucial role in Deep Learning since they allow to learn complex and non-trivial patterns in the data. However, the ability to approximate non-linear functions is a significant limitation when implementing neural networks in a quantum computer to solve typical machine learning tasks. The main burden lies in the unitarity constraint of quantum operators, which forbids non-linearity and poses a considerable obstacle to developing such non-linear functions in a quantum setting. Nevertheless, several attempts have been made to tackle the realization of the quantum activation function in the literature. Recently, the idea of the QSplines has been proposed to approximate a non-linear activation function by implementing the quantum version of the spline functions. Yet, QSplines suffers from various drawbacks. Firstly, the final function estimation requires a post-processing step; thus, the value of the activation function is not available directly as a quantum state. Secondly, QSplines need many error-corrected qubits and a very long quantum circuits to be executed. These constraints do not allow the adoption of the QSplines on near-term quantum devices and limit their generalization capabilities. This thesis aims to overcome these limitations by leveraging hybrid quantum-classical computation. In particular, a few different methods for Variational Quantum Splines are proposed and implemented, to pave the way for the development of complete quantum activation functions and unlock the full potential of quantum neural networks in the field of quantum machine learning.

Near Real-Time Detection Of Pipe Bursts in Water Distribution Systems

The research work presented in the thesis describes a new methodology for the automated near real-time detection of pipe bursts in Water Distribution Systems (WDSs). The methodology analyses the pressure/flow data gathered by means of SCADA systems in order to extract useful informations that go beyond the simple and usual monitoring type activities and/or regulatory reporting , enabling the water company to proactively manage the WDSs sections. The work has an interdisciplinary nature covering AI techniques and WDSs management processes such as data collection, manipulation and analysis for event detection. Indeed, the methodology makes use of (i) Artificial Neural Network (ANN) for the short-term forecasting of future pressure/flow signal values and (ii) Rule-based Model for bursts detection at sensor and district level. The results of applying the new methodology to a District Metered Area in Emilia- Romagna’s region, Italy have also been reported in the thesis. The results gathered illustrate how the methodology is capable to detect the aforementioned failure events in fast and reliable manner. The methodology guarantees the water companies to save water, energy, money and therefore enhance them to achieve higher levels of operational efficiency, a compliance with the current regulations and, last but not least, an improvement of customer service.