Thank you so much, Henriquet, for the invitation to Erlangen.

This is actually my first time in Erlangen, and I was really delighted to be reminded

actually that Emmy Noether was born here and studied here.

And Noether's theorem is actually one of my favorite theorems.

I'm a physicist, by the way, my background.

And of course, Noether's theorem is a beautiful way of seeing how mathematics actually impacts

something so deep in physics, like symmetry and conservation.

What I'm doing now is quantum computation.

Actually this is another example of where having a physicist's way of interpreting

the world, it really helps us rethink what we mean by algorithms.

So I mean, you guys, I'm sure most of you know much more about PDs than me.

So I work with Reza Jeng, who's an expert on PDs, and some of our other collaborators.

But what about the quantum simulation part of this talk?

What we really mean by that is actually what happens when your computer itself actually

obeys quantum dynamics and not classical dynamics, and the information now is embedded inside

your quantum states.

And now when we think about simulating PDs beyond Schrodinger's equation, then we also

need to modify the way we think about algorithms.

And I'll show you how we've been doing this in recent years.

So I don't need to explain ODs or PDs to you guys, and their importance in scientific computing.

But what we'll do say is that, as you very well know, in classical numerical algorithms,

a big problem is the cos of dimensionality.

So the high dimension, it becomes exponentially more difficult.

But what we do know is that if, a particularly good example of that is say, n-body Schrodinger

equations.

When you have high order, high dimensional equations, it becomes exponentially more difficult.

And this is when people like Paul Benioff and later Feynman suggested, well, what happens

if you want to simulate Schrodinger's equations on actually a quantum device itself, that

itself obeys Schrodinger's dynamics?

And there you can actually alleviate the cos of dimensionality.

And now we think, well, Schrodinger's PDs, that's just one particular PD.

What about all these other PDs that everyone's interested in?

So maybe if we can map these onto Schrodinger-like equations and put them on a real quantum device,

we can also help alleviate the cos of dimensionality for those problems as well.

So therefore, the very first step to do that is to actually do this mapping.

How do you turn non-Schrodinger-like equations into Schrodinger-like equations?

And this is something that we call Schrodingerization.

The name, I think, is self-explanatory.

And we'll introduce these a bit later on.

And since I have an idea that you guys are mostly classical, like numerical methods and

classical machine learning, I'll just say, give a little bit of background on quantum

computing and what we mean by quantum simulation.

So here, I talk about obviating the cos of dimensionality.

This is really saving on time complexity, all the time steps.

But actually, if you want to go beyond classical infrastructure and use quantum devices, it

can also help with other things, like memory, energy costs, communication, and so on, which

I won't talk about.

But also the fact that it's inevitable, because as our chips get smaller and smaller and smaller

and smaller, they will hit the quantum scale.

They'll no longer obey purely classical laws.