Graph Quantum Neural Tangent Kernel (GraphQNTK):这一模型基于图神经切核,利用无限宽度的量子图神经网络进行图分类任务。它是当前处理大规模图数据的主要量子图神经网络算法之一,但仍然面临量子设备规模有限的问题。 4. 核心思想 4.1 自我图分解处理策略 为了克服量子设备上量子比特数量的限制,作者提出了自我图分解策略...
When the targeted value of loss function crosses the minimum achievable value from above to below, the dynamics evolve from a frozen-kernel dynamics to a frozen-error dynamics, showing a duality between the quantum neural tangent kernel and the total error. In both regions, the convergence ...
For example, recent advancements in theoretical machine learning show that training neural networks with large hidden layers is equivalent to training an ML model with a particular kernel, known as the neural tangent kernel19,20,21. Throughout, when we refer to classical ML models related to our...
The black curve indicates exact values obtained by ED. In d, f, g the green, blue, and orange points each indicate the results predicted by the ML model trained by a (modified) Dirichlet kernel, neural tangent kernel, and Gaussian kernel, respectively. Full size image...
Using kernel properties, neural tangent kernel theory, first-order perturbation theory of the Kerr non-linearity, and non-perturbative numerical simulations, we show that quantum enhancements could happen in terms of convergence time and generalization error. Furthermore, we make explicit indications on...
Despite the great promise of quantum machine learning models, there are several challenges one must overcome before unlocking their full potential. For instance, models based on quantum neural networks (QNNs) can suffer from excessive local minima and barren plateaus in their training landscapes. Rece...
It is clear in these formulas that the propagator kernel is radially symmetric, and that all information from the initial data travels at finite speed. Both equations also possess a well-known dispersive property that |u(x,t)|≤C|t|−1/2 provided the initial data are sufficiently smooth ...
NTKs define a kernel between any pair of data examples, describing the evolution of deep neural networks during their training by gradient descent. In the infinite-width limit, for instance, neural networks using a Gaussian distribution described by this kernel can yield results c...
Despite the great promise of quantum machine learning models, there are several challenges one must overcome before unlocking their full potential. For instance, models based on quantum neural networks (QNNs) can suffer from excessive local minima and barren plateaus in their training landscapes. Rece...
of native gates, a crucial application for the quantum computing industry that typically uses exponential-size training data, can be sped up significantly. We also show that classification of quantum states across a phase transition with a quantum convolutional neural network requires only a very ...