Adaptive pruning algorithm using a quantum Fisher information matrix for parameterized quantum circuits

Quantum machine learning is a promising application for near-term quantum computers. However, parameterized quantum circuits (PQCs) for machine learning are prone to redundancy because the number of gates in the circuit cannot be determined beforehand in order to achieve desired performance. Thus, adaptive pruning algorithms for the redundant circuits would be needed. In this study, we propose adaptive pruning algorithms using a quantum Fisher information matrix in which the number of hyper-parameters for the algorithms is one or zero. In order to reduce the computational demand regarding parameter pruning, the Fisher-Rao norm using the quantum Fisher information matrix instead of using the Fisher information matrix is adopted. We conducted numerical experiments on six regression tasks: two synthetic and four real-world tasks. The results demonstrate the effectiveness of adaptive pruning on performance and realizing compact circuits. In addition, from analysis of the generalization error bound for PQCs using the empirical Rademacher complexity and the classical Fisher-Rao norm, we found that for the absolute cost function, redundant PQCs exhibit over-parameterization. However, PQC generalization performance could be inferior to that of classical linear deep neural networks.