Importance of Quantum Machine Learning

Advantage of Quantum Kernels

We will discuss the application of Quantum Computing in Machine Learning. This is a very exciting area of research in Quantum Computing. To understand this we start with a classical machine learning problem i.e. Linear Classification Problem. We have two sets of data that we want to classify into two separate categories denoted by dots and crosses.

It’s easy to classify this into two discrete groups using a single line.

However, classifying this can be harder if the data is more complex e.g.

So there isn’t a single line that can be used to classify the data into two discrete groups. So to solve this problem we need to map this data into a higher dimensional space called a feature space. So the visualization will be:

Now we can easily classify the above data:

This mapping of data from a lower dimension to a higher dimension can be done using the kernel function denoted by :

Kernel functions work by taking some underlying features of the original dataset and using that to map those data points into this high-dimensional feature space. Kernel functions are incredibly powerful and incredibly versatile but they do face problems like giving poor results or increasing time complexity with increasing complexity of the dataset e.g. Time Series Dataset where data is very complex and at a very high frequency.

But quantum computers can provide an advantage in this space since they can access much more complex and higher dimensional feature spaces(Hilbert Space) than classical computers. This can be done because we encode our data into quantum circuits which gives a exponentially compact representation of the data and the resulting kernel functions are difficult to replicate on a classical machine and these kernel functions can perform better. IBM researchers proved that quantum kernels can provide exponential speed up over their classical counterparts for certain classification problems.

QISKIT RUNTIME is used to build quantum machine learning algorithms with built-in tools such as sampler primitive. These are some predefined programs that help us optimize workflows and execute them efficiently on quantum systems.

Let’s consider the linear classification problem:

• We have our data and we have encoded it into our quantum circuit.
• We then use the Sampler Primitive to obtain quasi-probabilities(It relaxes Kolmogorov’s axioms of probability) indicating the relationship between the different data points and these relationships constitute the kernel matrix Kij.
• This kernel matrix can be used in a Classical Support Vector Machine to predict new classification labels.

Thus ability to constitute a higher dimensional kernel matrix gives a motivation to study and research Quantum Machine Learning.

Credit for the above blog: I have gained this information from a video on Quantum Machine Learning by IBM Technology. Thank You Abby Mitchell for such a wonderful explanation of the above concept. Check out the video at:
https://www.youtube.com/watch?app=desktop&v=NqHKr9CGWJ0

Originally published at https://aanshsavla.hashnode.dev.