Provable advantages of kernel-based quantum learners and quantum preprocessing based on Grover's algorithm

TL;DR

This paper demonstrates that quantum preprocessing using Grover's algorithm can provide provable speedups in kernel-based learning, specifically in support vector machines, and enhances classical classifiers with quantum techniques.

Contribution

It introduces a novel quantum kernel leveraging Grover's algorithm and shows how quantum preprocessing can improve classical learning methods.

Findings

Quantum kernel with Grover's algorithm offers exponential speedup.

Quantum preprocessing combined with classical methods improves classifier accuracy.

Application to pattern matching demonstrates practical advantage.

Abstract

There is an ongoing effort to find quantum speedups for learning problems. Recently, [Y. Liu et al., Nat. Phys. $\textbf{17}$, 1013--1017 (2021)] have proven an exponential speedup for quantum support vector machines by leveraging the speedup of Shor's algorithm. We expand upon this result and identify a speedup utilizing Grover's algorithm in the kernel of a support vector machine. To show the practicality of the kernel structure we apply it to a problem related to pattern matching, providing a practical yet provable advantage. Moreover, we show that combining quantum computation in a preprocessing step with classical methods for classification further improves classifier performance.