



01807nas a2200145   4500008004100000245009300041210006900134260001400203520133200217100001601549700002701565700001701592700001501609856003701624       2023                        eng d00aAnalyzing Convergence in Quantum Neural Networks: Deviations from Neural Tangent Kernels0 aAnalyzing Convergence in Quantum Neural Networks Deviations from  c3/26/20233 a<p>A quantum neural network (QNN) is a parameterized mapping efficiently implementable on near-term Noisy Intermediate-Scale Quantum (NISQ) computers. It can be used for supervised learning when combined with classical gradient-based optimizers. Despite the existing empirical and theoretical investigations, the convergence of QNN training is not fully understood. Inspired by the success of the neural tangent kernels (NTKs) in probing into the dynamics of classical neural networks, a recent line of works proposes to study over-parameterized QNNs by examining a quantum version of tangent kernels. In this work, we study the dynamics of QNNs and show that contrary to popular belief it is qualitatively different from that of any kernel regression: due to the unitarity of quantum operations, there is a non-negligible deviation from the tangent kernel regression derived at the random initialization. As a result of the deviation, we prove the at-most sublinear convergence for QNNs with Pauli measurements, which is beyond the explanatory power of any kernel regression dynamics. We then present the actual dynamics of QNNs in the limit of over-parameterization. The new dynamics capture the change of convergence rate during training and implies that the range of measurements is crucial to the fast QNN convergence.</p>1 aYou, Xuchen1 aChakrabarti, Shouvanik1 aChen, Boyang1 aWu, Xiaodi  uhttps://arxiv.org/abs/2303.14844