Building a quantum analog of classical deep neural networks represents a fundamental challenge in quantum computing. A key issue is how to address the inherent non-linearity of classical deep learning, a problem in the quantum domain due to the fact that the composition of an arbitrary number of quantum gates, consisting of a series of sequential unitary transformations, is intrinsically linear. This problem has been variously approached in the literature, principally via the introduction of measurements between layers of unitary transformations. In this paper, we introduce the Quantum Path Kernel, a formulation of quantum machine learning capable of replicating those aspects of deep machine learning typically associated with superior generalization performance in the classical domain, specifically, hierarchical feature learning. Our approach generalizes the notion of Quantum Neural Tangent Kernel, which has been used to study the dynamics of classical and quantum machine learning models. The Quantum Path Kernel exploits the parameter trajectory, i.e. the curve delineated by model parameters as they evolve during training, enabling the representation of differential layer-wise convergence behaviors, or the formation of hierarchical parametric dependencies, in terms of their manifestation in the gradient space of the predictor function. We evaluate our approach with respect to variants of the classification of Gaussian XOR mixtures - an artificial but emblematic problem that intrinsically requires multilevel learning in order to achieve optimal class separation.
翻译:建立古典深层神经网络的量子类比是量子计算中的一项根本挑战。一个关键问题是如何解决古典深层学习固有的非线性问题,这是量子领域的一个问题,因为由一系列顺序统一变换组成的任意数量量子门的构成本质上是线性的。文献中已经对该问题进行了不同处理,主要是通过在单质变换层之间采用测量方法。在本文件中,我们引入了量子机器学习方法的配方,能够复制古典领域优等通用性(特别是等级特征学习)的深层机器学习的内在非线性。我们的方法概括了量子门门的任意性概念,由一系列顺序单质变形变形组成。 Qantum Kernal利用了参数轨迹, 即按模型参数在培训过程中的变化所划定的曲线, 能够代表不同层相异的趋同行为, 或形成等级相等同的可靠性依赖性差, 具体说, 我们的方法是将量级的神经坦坦坦涅尔内特核心内内尔研究模型模型模型模型模型的动态, 要求实现等级变形的等级变形的等级, 。我们评估了X 的等级变形变形的等级变形变形变形的等级变形的等级变形的等级变形的等级变形的等级变形变形。