What I wanna talk about is -
what was said a couple of times today -
that quantum mechanics is difficult.
"I don't understand quantum mechanics"
"Quantum mechanics is very hard"
What I wanna talk about is: what's hard?
What's the hard thing about quantum mechanics?
I mean - everything's hard!
If - you know - sperm and an egg come together,
and a baby comes out.
That's pretty hard to understand.
But, somehow,  we don't walk around obstetrics hospitals
and say "Oh, it is so hard to understand
how this happens"
So, that, we have gotten used to.
Although, it is impossible to understand. It's impossible
to understand how you can take a neuron and a neuron
and another neuron, and put them together.
And, all of the sudden, you get consciousness
That's very hard to understand.
But, somehow, quantum mechanics has this reputation
that goes even beyond that.
Maybe I can just say, for a minute,
what it is that makes it hard about quantum mechanics
And, it is this idea that something doesn't have a state
until it is measured
You have probably - I think just even being anywhere in global world culture -
you have probably heard this idea that
something doesn't have a state until it is measured.
And, you say: "Okay, fine - something is indeterminate"
and I don't mean that it is indeterminate.
I mean that it doesn't have a state.
Usually, indeterminate means "you don't know it".
But, this is something different.
I wanna give you an example of what I mean by
indeterminate.
Then I will tell you about topological - and then, we will be done.
By then, they will have gotten this fixed and finished.
If you have a microwave oven in your house,
or in your laboratory - as we do -
and you look in it.
It's okay, you can look through
the little holes in the grid.
You know what -
I don't need it anymore!
I don't need it anymore, I am gonna tell you the story that I am gonna tell you.
A better story, anyway.
You look in the microwave oven
Forget this!
You look in the microwave oven
and you can't see anything. You can see your food going around.
But, you can't see the microwaves.
And, they are pretty powerful - they are powerful enough
to cook your food.
But, you can't see them.
Now, you can see visible light
and the reason you can see visible light is because
the way that the light interacts with your eye
is that all of the energy from a photon
has to deposit all of its energy onto one retinal cell
and the energy of a microwave isn't enough
to make the cell fire, so you can't see the microwaves
But, you can see the visible light.
So far so good?
Okay, good.
Now -
go out at night and look at the star in the sky
that is all you need to do to in order to see all the weirdness
of quantum mechanics and I literally mean all
of the weirdness of quantum mechanics.
Just look at a star.
Why?
Because the light from the star
is coming from
atoms inside the star
that give off radiation.
And, the radiation that comes out from the star is going in
all different directions at the same time.
Now, remember -
I said that the direction or the
state - what direction the light is going - is
indeterminate and that was the hard part.
So, don't think of the light coming out of the star
like a shower head that is spraying light
in all different directions.
Think that the light that is coming out of the stars is indeterminate -
what direction it's coming isn't known yet.
But, then -
I stick my eye in front of the light
and one photon of light goes into my eye
and I see it!
And, all of the sudden, that light is
determined; where it is.
Now, why should that bother you? Why is that hard to understand?
It's hard to understand because
another possibility was that the light
came out of the star and went the other way,
away from the earth
in the opposite direction.
That was a possibility
until
it hit my eye
and as soon as it hit my eye, suddenly,
all the other possibilities became impossible.
But, someone in my eye had to shout out,
all the way across the universe:
"You can't be there anymore"
"That location is now no longer possible"
"It's in his eye"
Now, you can ask - what if I hadn't put my eye there?
Well, then, there would still be a possibility that should be
on the other side of the universe.
How long did it take for the message to get
from
the shouter that says that it's impossible over
to the other side of the star
on the other side of the galaxy going out the other direction.
How long did that take?
Now, Einstein would tell you that you can't send messages
faster than the speed of light
but we are talking about light.
The answer is the information gets out there
instantaneously.
All the way over there instantaneously
that photon can't be there
Don't like it?
That's okay; maybe you don't like where babies come from.
But you don't have a choice - that's the way it works.
Now, why are we here today and why is Microsoft
concerned with these beautiful, fantastic
crazy-sounding ideas from quantum mechanics?
Because if you had a chip
and you had a transistor on a chip, and it was ON
or it was OFF. When it was ON,
it let electricity flow
and when it was OFF, it didn't let electricity flow.
And, the electricity flow to another chip on the other side
and that one was ON or OFF
and let the electricity go to the other side.
As soon as it measures the state of this
transistor,
just like the photon on the far side of the star,
it would determine whether or not
that transistor over on the other side of the chip was ON or OFF,
when I measure this transistor being ON or OFF.
And, how long will it take for the information to get
from the measurement of this transistor
to that one being determined?
Instantaneously.
This measurement
would set that transistor
and that's possible,
but it's never been built
and that's why Microsoft is here.
Because you can make a chip in which the laws of physics,
a 100 years old and indisputable,
show up on a chip.
Now -
topological was in my title.
Topological is written on the squares out there - what's that all about?
The problem is that this measurement
business of making things real sometimes happens when
you don't want it to happen.
Anything can measure - you don't need a conscious mind to
do the measurement. Anything that accidentally touches
that transistor will crash it,
and determine its position and the next position
and the next position.
Sometimes you don't want that to happen and you have to prevent it from happening.
Enter topology.
What is topology? Topology is the study
- we have field's medal winning topologists
in the audience - and I am gonna explain what topology is.
It's the study of shapes that
don't care if they are distorted a little bit but
have some character of their shape.
I think the best example that I can give
and it is the title of my presentation
but, since I am not going through my slides, I am just gonna show you with my belt.
It's the easiest way to do it.
If I have a loop like this in my belt
there's no twists in that belt.
That's the title of my
presentation.
If I twist this one time like this
and put my belt back together - if you have ever done this when you putting your belt on
in the morning and it gets a twist in it. You can't get the
twist out.
The twist is stuck, if this thing comes all the way back around.
I can even count how many twists it is
and that information can't get out of my belt.
It's stuck.
It's recorded in this thing and
it can't be removed,
but there's something else that's interesting about the twist in my belt,
which is
there's nowhere on my belt, where I can look
and see whether it's twisted.
I can't see the twists from anything,
which means that quantum mechanical measurement
that crashes the transistor
also can't see whether there's a twist
in the belt.
If you could store the information in a way
in which there are twists.
Then, you can prevent accidental measurement.
That's the topological
quantum states that is the basis of the machines
that we are trying to built. We are trying to put twists in.
Now, the thing that make this interesting is,
in the original Bohr model of
1913,
when he described the orbitals of atoms
and the transitions in between them,
so that you could see what colour light was. You could ask
how did those orbits get to be this specific size that they were
and the answer is: each orbit
has a twist in it. Each orbit has the same number of twists
of the electron that goes around in the circle.
So, in a way, the Bohr orbits themselves
all the way from 1913 were
topologically encoded so that
they would stay fixed, so that they couldn't
vary and that the light coming out of atoms were the same.
So, it's built in deeply to the
history and the understanding
of quantum physics that you could encode things
in ways that you can't see when you look at any one part of it.
If you could make a machine in which the
transistors not only encode the information
that lets the measurement take place instantaneously.
But, that the information is encoded
topologically in the twists
of something, which is extended throughout the system.
You can store the information, immune from measurement.
That's what Peter Krogstrup is trying to do
in those machines over there.
Now,  if we could do it,
who cares?
I mean it would be a fantastic revolution to be able
to make a quantum system on a chip
that was as immune to decoherence
as the orbitals of Bohr's atom.
But, what's critically important is that we already
know from theoretical mathematics and theoretical
physics, that if you could build a machine like that;
the problems that cannot be solved,
using today's computers - what do I mean by cannot be solved?
That means using the fastest
known algorithms of these computers, they will still take the age of the universe
in order to solve these problems. Let's call that the definition of
cannot be solved.
What's an example
of a problem that can't be solved?
Well, how to design a drug
that binds to a site
in your body.
It's too complicated of a problem.
It is known that if we have the algorithms that use these
quantum mechanical principles, then we can
solve those problems.
It's just that the machines don't exist.
So, you will have to come back in a few years,
after Peter has had a wack at it for a while,
to see whether we have been able to
encode information
in twists so that it can't be measured,
so that we can build a chip,
in which the simultaneous states
become determined so that the chip
can act like the light that we see every day,
where the observation makes it real,
only when you want to.
