Quantum tangent kernel methods provide an efficient approach to analyzing the
performance of quantum machine learning models in the infinite-width limit,
which is of crucial importance in designing appropriate circuit architectures
for certain learning tasks. Recently, they have been adapted to describe the
convergence rate of training errors in quantum neural networks in an analytical
manner. Here, we study the connections between the trainability and
expressibility of quantum tangent kernel models. In particular, for global loss
functions, we rigorously prove that high expressibility of both the global and
local quantum encodings can lead to exponential concentration of quantum
tangent kernel values to zero. Whereas for local loss functions, such issue of
exponential concentration persists owing to the high expressibility, but can be
partially mitigated. We further carry out extensive numerical simulations to
support our analytical theories. Our discoveries unveil a pivotal
characteristic of quantum neural tangent kernels, offering valuable insights
for the design of wide quantum variational circuit models in practical
applications.

量子切线核方法在无限宽度限制下分析量子机器学习模型表现的效率，对某些学习任务设计适当的电路架构至关重要。研究了量子切线核模型的可训练性和表达能力之间的联系。特别是对于全局损失函数，严密证明了全局和局部量子编码的高表达能力会导致量子切线核值向零的指数浓缩。而对于局部损失函数，由于高表达能力，此问题仍然存在，但可以部分缓解。通过广泛的数值模拟支持了我们的理论。我们的发现揭示了量子神经切线核的一个关键特征，为实际应用中宽量子变分电路模型的设计提供了有价值的见解。