Representation Learning via Quantum Neural Tangent Kernels

The idea of using quantum computers for machine learning has recently received attention both in academia and industry [1-13]. While proof of principle study have shown that some problems of mathematical interest quantum computers are useful [13], quantum advantage in machine learning algorithms for practical applications is still unclear [14]. On classical architectures, a first-principle theory of machine learning, especially the so-called deep learning that uses a large number of layers, is still in development. Early developments of the statistical learning theory provide rigorous guarantees on the learning capability in generic learning algorithms, but theoretical bounds obtained from information theory are sometimes weak in practical settings. The theory of neural tangent kernel (NTK) has been deemed an important tool to understand deep neural networks [15-21]. In the large-width limit, a generic neural network becomes nearly Gaussian when averaging over the initial weights and biases, and the learning capabilities become predictable. The NTK theory allows to derive analytical understanding of the neural networks dynamics, improving on statistical learning theory and shedding light on the underlying principle of deep learning [22-26]. In the quantum machine learning community, a similar first principle theory would help in understanding the training dynamics and selecting appropri-junyuliu@uchicago.edu