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.

Grant-Free Access for Massive IoT Based on Interference Cancellation and Massive MIMO

Recent years have witnessed an increasing evolution of wireless mobile networks, with an intensive research work aimed at developing new efficient techniques for the future 6G standards. In the framework of massive machine-type communication (mMTC), emerging Internet of Things (IoT) applications, in which sensor nodes and smart devices transmit unpredictably and sporadically short data packets without coordination, are gaining an increasing interest. In this work, new medium access control (MAC) protocols for massive IoT, capable of supporting a non-instantaneous feedback from the receiver, are studied. These schemes guarantee an high time for the acknowledgment (ACK) messages to the base station (BS), without a significant performance loss. Then, an error floor analysis of the considered protocols is performed in order to obtain useful guidelines for the system design. Furthermore, non-orthogonal multiple access (NOMA) coded random access (CRA) schemes based on power domain are here developed. The introduction of power diversity permits to solve more packet collision at the physical (PHY) layer, with an important reduction of the packet loss rate (PLR) in comparison to the number of active users in the system. The proposed solutions aim to improve the actual grant-free protocols, respecting the stringent constraints of scalability, reliability and latency requested by 6G networks.