Approximating a wavelet kernel using a quantum computer

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2023

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Machine learning and quantum computing are both fields which have gained a significant amount of popularity and attention in recent years. The intersection of these two fields, quantum machine learning, looks at whether quantum computers can aid or improve classical machine learning methods, or whether quantum computers can perform machine learning tasks which classical computers cannot. In this thesis we explore different implementations of quantum machine learning algorithms on near term quantum computers, and the limits of these systems. We focus on support vector machines and kernel methods, which are a form of supervised machine learning. We examine whether using quantum kernels to search for a quantum advantage over classical computers is suitable, and why it may be wise to search for quantum advantages using other methods. Lastly, we construct a quantum circuit which can approximate a wavelet kernel with a mean squared error over sample plots of 9.09 × 10−9 , by estimating the Fourier coefficients of the kernel. We hope that this can be used as a starting point for performing wavelet analysis on quantum computers.
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