machine learning. This is a very exciting area of  quantum computing research and lots of classical  
machine learning. This is a very exciting area of  quantum computing research and lots of classical  

machine learning developers are understandably  excited about the potential applications within  
machine learning developers are understandably  excited about the potential applications within  

their own field. So to get started, let's talk  about a classical machine learning problem that  
their own field. So to get started, let's talk  about a classical machine learning problem that  

is one this very common linear classification. So  if we start with two sets of data that we want to  
is one this very common linear classification. So  if we start with two sets of data that we want to  

classify into two separate categories, let's draw  them here. We're just going to have three dots  
classify into two separate categories, let's draw  them here. We're just going to have three dots  

and three crosses, all on a single linear plane  here. If the data is arranged like this, it can  
and three crosses, all on a single linear plane  here. If the data is arranged like this, it can  

be pretty easy to classify this into two discrete  groups. We can draw a single line in the middle  
be pretty easy to classify this into two discrete  groups. We can draw a single line in the middle  

here and now we've classified them, but this  can be a lot harder if our data is more complex.  
here and now we've classified them, but this  can be a lot harder if our data is more complex.  

For example, if our data is arranged like this,  perhaps with the crosses in the middle. Now, there  
For example, if our data is arranged like this,  perhaps with the crosses in the middle. Now, there  

isn't a single line that we can draw on this plane  to classify the data into two discrete groups.  
isn't a single line that we can draw on this plane  to classify the data into two discrete groups.  

So in order to solve this problem and classify  this data, what we need to do is we need to map  
So in order to solve this problem and classify  this data, what we need to do is we need to map  

this data into a higher dimensional space,  which we're going to call a feature space.  
this data into a higher dimensional space,  which we're going to call a feature space.  

Then if we've mapped the  data, for example, like this.  
Then if we've mapped the  data, for example, like this.  

We can now see because we've mapped this data  into a high dimensional space. There is now a  
We can now see because we've mapped this data  into a high dimensional space. There is now a  

much easier way to classify this. So how do  we do this step of transferring our data,  
much easier way to classify this. So how do  we do this step of transferring our data,  

mapping it into a high dimensional feature  space? To do this, we can use kernel functions.  
mapping it into a high dimensional feature  space? To do this, we can use kernel functions.  

Kernel functions work by taking some underlying  features of the original dataset and using that to  
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  
map those data points into this high dimensional  feature space. Kernel functions are incredibly  

powerful and incredibly versatile, but they  do face problems. Sometimes they just get poor  
powerful and incredibly versatile, but they  do face problems. Sometimes they just get poor  

results, and also the compute runtime can explode  as the complexity of the data sets increase.  
results, and also the compute runtime can explode  as the complexity of the data sets increase.  

If you're an experienced machine learning  developer, perhaps you've seen this already.  
If you're an experienced machine learning  developer, perhaps you've seen this already.  

If you're dealing with data that has very  strong correlations, or perhaps if you're  
If you're dealing with data that has very  strong correlations, or perhaps if you're  

dealing with time series forecasting where the  data is very complex and at a high frequency,  
dealing with time series forecasting where the  data is very complex and at a high frequency,  

but quantum computers have the potential  to provide an advantage in this space.  
but quantum computers have the potential  to provide an advantage in this space.  

They can be useful because quantum  computers can access much more complex  
They can be useful because quantum  computers can access much more complex  

and higher dimensional feature spaces  than their classical counterparts can.  
and higher dimensional feature spaces  than their classical counterparts can.  

And they can do this because quantum computers  can we can encode our data into quantum circuits,  
And they can do this because quantum computers  can we can encode our data into quantum circuits,  

and the resulting kernel functions could be very  difficult or even impossible to replicate on a  
and the resulting kernel functions could be very  difficult or even impossible to replicate on a  

classical machine, as well as this, those  kind of functions also can perform better.  
classical machine, as well as this, those  kind of functions also can perform better.  

In 2021, IBM researchers actually proved that  quantum kernels can provide an exponential  
In 2021, IBM researchers actually proved that  quantum kernels can provide an exponential  

speed up over their classical counterparts for  certain classes of classification problems.  
speed up over their classical counterparts for  certain classes of classification problems.  

As well as this. There is a lot of research going  into improving Quantum kernel with structure,  
As well as this. There is a lot of research going  into improving Quantum kernel with structure,  

data and kernel alignment. So as you  can see, this field is incredibly  
data and kernel alignment. So as you  can see, this field is incredibly  

exciting. There's a lot of research going on  in this space. And you can use Qiskit Runtime  
exciting. There's a lot of research going on  in this space. And you can use Qiskit Runtime  

to easily build a quantum machine learning  algorithms with built in tools such as the  
to easily build a quantum machine learning  algorithms with built in tools such as the  

sampler primitive, which primitives are unique to  the IBM's Qiskit Runtime. These are essentially  
sampler primitive, which primitives are unique to  the IBM's Qiskit Runtime. These are essentially  

predefined programs that help us to optimize  workflows and execute them efficiently on  
predefined programs that help us to optimize  workflows and execute them efficiently on  

quantum systems. Let's take, for example, our  linear classification problem. Let's say we  
quantum systems. Let's take, for example, our  linear classification problem. Let's say we  

have our data and we've encoded it into a quantum  circuit. We can then use the sampler primitive.  
have our data and we've encoded it into a quantum  circuit. We can then use the sampler primitive.  

To obtain quasi-probabilities indicating  the relationships between the the different  
To obtain quasi-probabilities indicating  the relationships between the the different  

data points and these relationships  can constitute our kernel matrix.  
data points and these relationships  can constitute our kernel matrix.  

And that kernel matrix can then be evaluated and  used in even a classical support vector machine  
And that kernel matrix can then be evaluated and  used in even a classical support vector machine  

to predict new classification labels. So if you're  ready to get started learning more about quantum  
to predict new classification labels. So if you're  ready to get started learning more about quantum  

machine learning, you can check out the links in  the description for more information about Kiska  
machine learning, you can check out the links in  the description for more information about Kiska  

runtime as well as the quantum machine learning  course that's available on the Qiskit textbook.  
runtime as well as the quantum machine learning  course that's available on the Qiskit textbook.  

I hope you've enjoyed this content. Thank  you very much for watching. [00:00:00][0.0]
I hope you've enjoyed this content. Thank  you very much for watching. [00:00:00][0.0]