Quantum Statistical Inference

Understand

In this thesis, I present several results on quantum statistical inference in the following two directions.

• Firstly, I demonstrate that quantum algorithms can be applied to enhance the computing and training of Gaussian processes (GPs), a powerful model widely used in classical statistical inference and supervised machine learning.
• A crucial component of the quantum GP algorithm is solving linear systems with quantum computers, for which I present a novel algorithm that achieves a provable advantage over previously known methods.
• I will also explicitly address the task of encoding the classical data into a quantum state for machine learning applications.