Gaussian Kernel in Quantum Learning

TL;DR

This paper introduces a quantum version of the Gaussian kernel for support vector machines, demonstrating that it can be computed more efficiently than classical methods using quantum random access memory.

Contribution

It presents a novel quantum Gaussian kernel and analyzes its runtime complexity, showing potential exponential speedup over classical kernels.

Findings

Quantum Gaussian kernel has significantly faster runtime complexity.

Quantum random access memory enables efficient kernel computation.

Potential for exponential speedup in quantum SVMs.

Abstract

The Gaussian kernel is a very popular kernel function used in many machine learning algorithms, especially in support vector machines (SVMs). It is more often used than polynomial kernels when learning from nonlinear datasets, and is usually employed in formulating the classical SVM for nonlinear problems. In [3], Rebentrost et al. discussed an elegant quantum version of a least square support vector machine using quantum polynomial kernels, which is exponentially faster than the classical counterpart. This paper demonstrates a quantum version of the Gaussian kernel and analyzes its runtime complexity using the quantum random access memory (QRAM) in the context of quantum SVM. Our analysis shows that the runtime computational complexity of the quantum Gaussian kernel seems to be significantly faster as compared to its classical version.