Fundamental Machine Learning Routines as Quantum Algorithms on a Superconducting Quantum Computer

TL;DR

This paper evaluates the practical performance of quantum algorithms like HHL and Quantum Support Vector Machine on superconducting quantum computers, highlighting their strengths and limitations for specific problem types.

Contribution

It provides a numerical analysis of the HHL and Quantum SVM algorithms' performance on real quantum hardware, identifying conditions for success and areas for improvement.

Findings

HHL performs better on diagonal matrices than on sparse Hermitian matrices.

Quantum SVM is more effective for binary classification than multi-label tasks.

Performance can be improved with further algorithmic and hardware advancements.

Abstract

The Harrow-Hassidim-Lloyd algorithm is intended for solving the system of linear equations on quantum devices. The exponential advantage of the algorithm comes with four caveats. We present a numerical study of the performance of the algorithm when these caveats are not perfectly matched. We observe that, between diagonal and non-diagonal matrices, the algorithm performs with higher success probability for the diagonal matrices. At the same time, it fails to perform well on lower or higher density sparse Hermitian matrices. Again, Quantum Support Vector Machine algorithm is a promising algorithm for classification problem. We have found out that it works better with binary classification problem than multi-label classification problem. And there are many opportunities left for improving the performance.