Power and Limitations of Parameterized Quantum Circuits*

In recent years, the study of parameterized quantum circuits (PQCs) has gained significant attention in quantum machine learning and near-term quantum information processing. These circuits are known for their potential to approximate complex functions and their ability to encode data efficiently. However, our understanding of the power and limitations of PQCs is still quite limited. In this talk, we will delve into the power and limits of parameterized quantum circuits in several essential tasks. We will analyze the expressivity and capability of PQCs in terms of approximating functions, learning quantum states, and encoding classical data. We will also discuss the potential of designing quantum algorithms by combining PQCs and existing algorithmic tools. Overall, this talk aims to shed light on the power of PQCs and their potential advantages in near-term quantum applications. This talk is mainly based on arXiv:2205.07848, 2206.08273, 2310.07528.