Quantum Representation Learning.
Abstract: Variational quantum circuit is the main architecture used in quantum machine learning and variational quantum simulation tasks. However, despite its practical success, the theoretical guidance about which ansatz we should choose, and where the advantage should exist, is still unclear. In this paper, we study variational quantum circuits using the theory of ``neural tangent kernel"(NTK). We show that variational circuits are natural representation learners, because of non-linearity in the unitary operation depending on the variational parameters. We derive the dynamical equation of the loss function depending on the quantum NTK. Moreover, we study the ``frozen NTK" in the limit where the learning rate is small, and the ``meta quantum kernel" (quantum dNTK) as the leading order perturbative corrections. We also show that in the large width limit, the hybrid quantum-classical neural network could also be approximately closed to the Gaussian process, and the width is understood as the row sparsity of the operators used in the variational ansatz. Our work provides analytic controls of the training dynamics for arbitrary variational quantum ansatze.