The Quantum Path Kernel: A Generalized Neural Tangent Kernel for Deep Quantum Machine Learning
Abstract : 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.
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.
Neural Tangent Kernels are a recent development in the theory of neural networks. They describe the behavior of infinitely wide neural networks during training.
NTK helps in understanding the dynamics of gradient descent and the generalization properties of neural networks.
QML is an interdisciplinary area combining quantum physics and machine learning, aiming to leverage quantum computing to enhance ML algorithms.
Quantum algorithms and systems are inherently more complex to design, implement, and maintain compared to classical algorithms.
Requires expertise in both quantum computing and machine learning, which can be a barrier for many researchers and practitioners.
Current quantum hardware is still in the early stages of development, with limitations in terms of qubit count, coherence time, and error rates.
Noise and errors in quantum computations can affect the reliability and accuracy of QPK-based models.
The proposed Quantum Path Kernel (QPK) aims to address these limitations by extending the concept of neural tangent kernels into the quantum domain, creating a more generalized framework for deep quantum machine learning.
By leveraging quantum computing, QPK can provide more efficient training dynamics and improved generalization.
QPK might be better suited for handling larger and more complex neural network architectures.
Improved robustness to noise and errors in quantum computations, making it more practical for real-world applications.
By leveraging the principles of quantum computing, QPK can potentially offer exponential speedups for certain machine learning tasks compared to classical approaches.
Improved training dynamics and generalization capabilities, particularly for complex datasets and deep learning models.
QPK is designed to handle larger and more complex neural network architectures more efficiently than classical Neural Tangent Kernels (NTKs).
Better suited for high-dimensional data and large-scale problems that are computationally prohibitive for classical methods.
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