Exploring the interplay between expressivity and trainability in quantum neural networks for image and audio data

Abstract

Quantum Machine Learning architectures consist of ansatzes, a Parameterized Quantum Circuit designed based on educated guesses about the problem to be solved. This design is the most critical aspect of developing a Quantum Neural Network (QNN) structure and has immense implications for its performance. This thesis investigates the expressivity of different ansatzess structures in QNN design through fidelity distribution analysis, which statistically compares the fidelity values between quantum states generated by an ansatz and random states sampled from the Haar measure. The expressivity and trainability of various ansatzes architectures are explored by leveraging different datasets from image and audio domains as test cases. The findings provide valuable insights into designing ansatzes for specific tasks and goals using QNN architectures, advancing the field of quantum machine learning.