Is quantum advantage the right goal for quantum machine learning?

This paper was released a couple of days ago in Axiv, authored by one of the leading researchers in the field of quantum machine learning-- Dr Maria Schuld. In case you are familiar with her research works and publications, you would tell her approach to quantum machine learning; quantum kernel theory. In the quantum kernel method, one does not have to worry about finding the right variational circuit ansatzes or about barren plateaus but pays the price of having to compute pairwise distances between data points. These pairwise computations are dubbed as kernel methods in classical machine learning theory. Furthermore, in the kernel method, access to feature space is facilitated through kernels or the inner product of feature vectors. With an appropriate Algebraic powered lens, one could observe the structural mathematical relationship between the quantum models and the classical kernel methods. This bridge between quantum machine learning and kernel methods is formed by the observation that quantum models map data into a high dimensional feature space in which the measurement defines a linear decision boundary.

This feature space is defined as the space of complex matrices enriched with the Hilbert-Schmidt inner product - which is the space where density matrices live in!

?Hold on with this Mathematical jargon! let us discuss some key insights from the paper:

'The dominant goal in quantum machine learning is to show that quantum computers, with their properties like entanglement and interference, offer advantages for machine learning tasks of practical relevance'. Therefore, let us say we decide to let go of the goal of beating classical machine learning for a moment, what other meaningful questions can we ask in this research field?

What is the good building block of quantum models?

How can we bridge quantum computing and classical learning theory to gain a better understanding of quantum machine learning?

?Machine learning may turn out to be one of the hardest applications to show a practical quantum advantage given that models perform exceedingly well when deployed even in the most complicated industrial settings. The question about whether quantum computers can play a role in practical machine learning applications is therefore still open and there is no foreseeable future of when answers could come by.

?I will leave you with the rest of the questions and the link to the paper below. There are answers there and there are other thought-provoking discussions from the authors.

Link to the [Paper](https://arxiv.org/pdf/2203.01340.pdf)

signing out.

Cheers.