Implementation of a Variational Quantum Classifier based on Grover's algorithm

In recent years, thanks to the improvement of quantum hardware fabrication, research interest in Quantum Computing (QC) has grown significantly. The quantum superposition and an accurate handling of complex probability amplitudes can be decisive in a large number of applications, reducing the computational complexity of data-intensive algorithms. Another branch advertised as a central future application that companies are investing in is Machine Learning (ML), which is able to abstract models from known data (training) and learning a way to predict the outcome of new ones (prediction). If these two areas are certainly growing, the focus is increasingly on the intersection discipline between them: Quantum Machine Learning (QML), typically declined in quantum computation applied on data generated by a classical system. After an in-depth analysis of the available scientific literature on QML, this thesis has been focused on the application of the Grover’s Search algorithm (GS) in the ML context, as it has proven quadratic speed-up in finding particular items in an unsorted database. Hence, due to the need of large dataset to train ML models, its application can be very powerful on ML problems that can be restated as search problem. In particular, this reformulation can be applied on a classification problem to assist the Variational Quantum Classifier (VQC), which is a trainable parametrized hybrid quantum-classical model. The hybrid approach is the one with a near-term perspective of application. Indeed, it divides the optimization procedure in two parts: one, implemented on QC, evaluates a cost function starting from a set of input parameters, the other, which is kept classic, tries to minimize the cost by updating the parameters. The contribution of this thesis is to broaden the gaze on quantum classifiers, which are very little investigated in literature, through the study and the implementation of a VQC model that exploits a structure based on the GS scheme in the learning phase. The model has been proposed in a recent study as Grover Based Learning Search (GBLS). This algorithm presents the possibility of implementing the GS reflection oracle with a trainable parametrized circuit: here lies the key-point that makes GBLS exploration interesting to improve QML classification, with a view to near-term application. The implementation has been developed through Python scripts and exploiting QISKIT libraries, with a particular focus on the qiskit_machine_learning one, an extremely recent and evolving library for the implementation of QML algorithms, intended for the elaboration approach of quantum gate array. A crucial point of this work is to understand more deeply the potential of these libraries and give a concrete example of their use with the implementation of the GBLS model, not actually embedded in them. The implemented GBLS model also wants to contribute to the quantum circuit library under development in VLSI Lab research group at Politecnico di Torino. In the dissertation, the validation of the model is reported, analyzing its functioning with the variation of training parameters (i.e. learning rate), input data and number of iterations of the algorithm. The obtained results on the computational cost and training/test accuracy show that GBLS can be a competitive strategy to expand the VQC scenario, and this thesis can be a starting point to make its benchmarking possible with other classifiers present in the state of the art.