Quantum Kernel Alignment with Stochastic Gradient Descent

TL;DR

This paper introduces a quantum kernel alignment method using an extended Pegasos algorithm with stochastic gradient descent, enabling efficient training and alignment of quantum kernels for support vector machines, especially on non-stationary data.

Contribution

It extends Pegasos to the quantum domain and demonstrates its ability to simultaneously train SVMs and align kernels, outperforming existing methods.

Findings

Effective quantum kernel alignment with high accuracy

Outperforms existing quantum kernel alignment techniques

Particularly effective for non-stationary data

Abstract

Quantum support vector machines have the potential to achieve a quantum speedup for solving certain machine learning problems. The key challenge for doing so is finding good quantum kernels for a given data set -- a task called kernel alignment. In this paper we study this problem using the Pegasos algorithm, which is an algorithm that uses stochastic gradient descent to solve the support vector machine optimization problem. We extend Pegasos to the quantum case and and demonstrate its effectiveness for kernel alignment. Unlike previous work which performs kernel alignment by training a QSVM within an outer optimization loop, we show that using Pegasos it is possible to simultaneously train the support vector machine and align the kernel. Our experiments show that this approach is capable of aligning quantum feature maps with high accuracy, and outperforms existing quantum kernel alignment techniques. Specifically, we demonstrate that Pegasos is particularly effective for non-stationary data, which is an important challenge in real-world applications.