Okay, good morning. So for the last lecture of the course, I was actually planning that

I sort of review the material that we covered, maybe try to emphasize some aspects that have

not been covered as much as I wanted, or just point to things which I consider important.

And okay, so maybe one short comment, because you asked whether I could change the date

of the exam, so now I unfortunately can't do this anymore.

I had actually shifted it upon a request and asked for a majority vote, it was sometime

around Christmas, and that made the decision for it, but like my schedule is too packed

that I can change things now.

Yeah, sorry.

Okay, so a bit of a recap of what the course covered.

I just, to start this, basically go through the contents in two slides.

So the first thing was a refresher of quantum mechanics.

Of course, there were things that I guess you're all very well familiar with, like what

states operators the evolution and measurements are, and the aspect which is there probably

a bit newer, but very relevant to this course is composite quantum systems, right?

Because that's where the whole advantage of quantum computing and the whole power is.

So in particular, in entangled states of several parts.

And then, sort of the main body of the course was discussing quantum algorithms, and I already

stress here for like perfect quantum computers, right?

So in all that part, the gates were always assumed to work as you write them in theory.

And so this started with a discussion of Deutsch's problem, but I put this now in the review

together with Simon's problem because they are in structure very similar.

Simon's problem is just the larger, in some sense, just a larger version of Deutsch's

problem to many qubits.

We also discussed, although it's not strictly a computing topic, teleportation.

And then there was a part comparing quantum and classical computers, which basically derived

that with a quantum computer you can run any classical computation with sort of a similar

effort.

But on the other hand, running a quantum computation or simulating what a quantum computer can

do can be exceedingly hard, which of course needs to be the case, otherwise we wouldn't

be interested in quantum computing.

So it's harder to implement, so there should be some gain for doing that.

And then here sort of the really important things are actually the quantum Fourier transform

and phase estimation.

Why that?

Because these two things are actually, so in particular phase estimation, which is built

on the quantum Fourier transform, is the main ingredient for Shor's algorithm for factoring

large numbers into primes and for the so-called HHL algorithm, which solves coupled systems

of linear equations.

Coming back to this word perfect, reality is not like that.

So that's why it has been this, well, people realized, okay, one will need error correction

to be able to run quantum computers.

So this was, like some basics of that were in the course, in particular, like a basic

introduction to the stabilizer formalism with applications to surface codes.

So you might remember the Tory code and like a high level discussion of planar surface

codes.

And then the last part was on this quantum computing with devices that where you deliberately

take into account that they have errors, which is called NISC for Noisy Intermediate Scale

Quantum Computers.

And there the main type of algorithm is this variational algorithms and in one version