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Abstract

A quantum neural network (QNN) is an object that extends the notion of a classical neural network to quantum models for quantum data. We can create a QNN by parametrizing a quantum process and then using it to model unknown relations between quantum states. In this thesis, we explore how to use measurement-based quantum computation (MBQC) for quantum machine learning (QML) problems and propose a universal QNN in this framework. For numerics, we built MentPy, a Python package for simulating parametrized MBQC circuits. We study essential QML concepts analyzed in the gate-based literature, such as barren plateaus and expressivity, from the MBQC perspective. Using the proposed QNN, we solve several tasks, including learning a universal set of gates, a POVM with post-processing, a quantum instrument, and the classification of classical data. We also discuss how to train an ansatz under the hardware constraints imposed by photonic Gottesman-Kitaev-Preskill (GKP) qubits. Finally, we present a method to design ansatze that implement a specific set of gates. We use this construction to find the ground states of the transverse field cluster Hamiltonian using a variational quantum eigensolver (VQE) and calculate their string order parameter.