Investigating the Generalization Ability of Parameterized Quantum Circuits with Hierarchical Structures

Abstract

Quantum computing provides prospects for improving machine learning, which are mainly achieved through two aspects, one is to accelerate the calculation, and the other is to improve the performance of the model. As an important feature of machine learning models, generalization ability characterizes models' ability to predict unknown data. Aiming at the question of whether the quantum machine learning model provides reliable generalization ability, quantum circuits with hierarchical structures are explored to classify classical data as well as quantum state data. We also compare three different derivative-free optimization methods, i.e., Covariance Matrix Adaptation Evolution Strategy (CMA-ES), Constrained Optimization by Linear Approximation (COBYLA) and Powell. Numerical results show that these quantum circuits have good performance in terms of trainability and generalization ability.