Quantum Multiple Kernel Learning

TL;DR

This paper introduces a quantum multiple kernel learning method that combines quantum kernels using deterministic quantum computing, enhancing expressivity and outperforming single quantum kernel models in classification tasks.

Contribution

The paper proposes a novel quantum MKL approach leveraging DQC1 to estimate combined kernels without explicit computation of individual kernels, improving model expressivity.

Findings

Quantum MKL outperforms single quantum kernel models in classification accuracy.

The method efficiently estimates combined kernels using DQC1 without explicit kernel computation.

Simulations demonstrate the superiority of quantum MKL on synthetic and real datasets.

Abstract

Kernel methods play an important role in machine learning applications due to their conceptual simplicity and superior performance on numerous machine learning tasks. Expressivity of a machine learning model, referring to the ability of the model to approximate complex functions, has a significant influence on its performance in these tasks. One approach to enhancing the expressivity of kernel machines is to combine multiple individual kernels to arrive at a more expressive combined kernel. This approach is referred to as multiple kernel learning (MKL). In this work, we propose an MKL method we refer to as quantum MKL, which combines multiple quantum kernels. Our method leverages the power of deterministic quantum computing with one qubit (DQC1) to estimate the combined kernel for a set of classically intractable individual quantum kernels. The combined kernel estimation is achieved without explicitly computing each individual kernel, while still allowing for the tuning of individual kernels in order to achieve better expressivity. Our simulations on two binary classification problems---one performed on a synthetic dataset and the other on a German credit dataset---demonstrate the superiority of the quantum MKL method over single quantum kernel machines.