Good evening.

So in this last lecture I wanted to tell you something about the research we are actually doing

in the domain of applying neural networks.

And this will be specifically about applying classical neural networks for quantum devices.

So the talk I'll be giving to some extent has similarity to research talks I'm giving.

So you can also judge how it looks like when I talk about this in a research talk.

But let me just give the outline.

So first I will say something about the power of neural networks.

Of course I don't need to tell you because you have been to these lectures.

I'll give you an outline of machine learning for quantum technology.

So I'll talk a little bit about quantum computing and qubits

because that will be the background for much of it

and also what other people have been doing in this field in the last, say, two years.

And then I'll briefly recall reinforcement learning

because that will actually be the technique that we are using

for a specific challenge in quantum technology

and that will be quantum error correction.

So when I like to introduce neural networks,

I'd like to say that, well, your brain is very marvellous in many aspects,

but in particular it's very flexible.

So you see a picture of a light bulb that you have never seen before,

yet you recognize it as a light bulb.

And so it was the question, can we also build computers that are as flexible and robust

and very insensitive to the small details?

And the answer, of course, as you know, is artificial neural networks.

So this has been around for many decades,

but really many people have started paying attention only in 2012

because that was the year when one of these deep neural networks with many layers

was able to beat all the other approaches in a certain competition

that computer scientists organize.

This is the so-called ImageNet competition.

So you are provided with a million training pictures.

Then you can do with them whatever you want in your algorithm.

Typically, maybe you train your neural network on them,

but you can also do many other things.

And then afterwards you will be tested on pictures that your algorithm has never seen before,

and then it has to label these pictures correctly.

And then it is all about what's the fidelity,

what's the percentage of pictures that you label correctly.

So this was kind of a breakthrough, at least, that people became aware

how powerful neural networks had become in the meantime,

and therefore now there's really a rapid proliferation of applications

to image labeling, but also to translation or speech recognition and many other areas.

If we turn to physics, of course, physicists have investigated neural networks for quite a bit of time,

already back in the 80s,

but the recent revolution in physics as regards the application of neural networks dates back only, say, three years.

And so there have been more and more examples.

This is one example I already showed you, very obvious.

If you know that neural networks are good at image recognition,

then obviously they should be able to tell the paramagnetic phase from the ferromagnetic phase,