Now 2 to the 250 is larger than the
number of atoms in the Universe,
so even if I had the computer the size of the Universe, 
I wouldn't be able to store
enough data to represent the state of a
very simple molecule.
My name is Tom O'Brien and I just
finished my PhD studying applications of
quantum computing, and how a quantum computer might be good at doing chemistry.
And I'd like to tell you 
a bit today about why you might want
to use a quantum computer to
solve problems in chemistry.
So for me to do this, I should begin by telling you a
little bit about why classical computers,
why your laptop, or why large
supercomputers are particularly bad
at solving problems in quantum chemistry.
And I want to do this by starting with
the world's simplest molecule, 
which is dihydrogen.
So dihydrogen, or the hydrogen molecule, 
has two nuclei.
One on the left and one on the right.
Left and right just because. 
And then each of these nuclei
has an electron flying around. Let's
label these guys:
A spin up electron flying around the left atom,
and we can make a spin down electron 
flying around the right atom.
I'm just using the up and down labels to 
distinguish the two electrons right now.
Now when you have each of these atoms in isolation,
the electrons just tend to fly
around them by themselves.
But when I put the two of them together, I have to ask
myself the question, namely:
Will this electron stay on the left atom,
 or will it move across and jump on the right?
Quantum mechanics says that actually I'm
allowed to have my cake and eat it too here.
The electron might want to do both:
it can be in a superposition
of being on the left atom and on the right atom.
And for me to try to find the optimal 
or the lowest energy configuration,
I need to consider all of these possibilities.
So for me to do this for this very simple
system, I can just build a table.
So for the 'up-spin electron' that could be
around the left atom,
Or it could be around the right atom.
That's two possibilities.
The 'down-spin electron'
that could also be around the left atom,
or it could be around the right atom.
That's two possibilities.
And then there
are two competing forces that I need to
consider to balance out the electrons,
to balance out a superposition 
of these four possibilities.
The first one is the electrostatic force.
Electrons repel each other.
So these want to be
as far away from each other as possible.
The second force is the kinetic
force, which roughly means
electrons like to move about.
They like to be in as many places 
as they can at the same time.
They want to be free.
When you write down this table 
and you want to build your superposition,
you have that the electrons being free
would just prefer to be in as many boxes as possible.
Whereas the electrostatic repulsion
wants to force the electrons to either
be up in this box,
where you have one on the right and one on the left,
Or in this box down here, which has the same.
Balancing out the four combinations
to balance out the strength of these two forces,
means I have to really
consider a number in each of these boxes.
Now this is a really simple problem,
because there are only four numbers,
and the reason why there were only four numbers,
 is because there were only two electrons.
Two electrons gave me four numbers, 
which is two to the two.
However, a relatively small molecule can still
have hundreds of electrons.
And at the point where I have 250 electrons, 
then this means I need to consider
approximately 2 to the 250 numbers to
describe the state of the entire system.
Now 2 to the 250 is larger than the
number of atoms in the Universe,
So even if I had a computer the size of the
Universe I wouldn't be able to store
enough data to represent the state of a
very simple molecule.
So if I want to use a computer, I have to do some kind
of approximation to solve this.
I mean a classical computer, my desktop.
But a quantum computer avoids this by being an artificial molecule.
Let me briefly show you how that occurs.
A computer is made out of qubits and the
qubits that I've been studying
in my PhD are called transmon qubits.
And a transmon qubit has two superconducting islands
sitting at about 20 millikelvin in a very, very cold fridge.
And these are connected by a weak link.
Because they're super
conductors, charge can slosh about,
it's very free to move. There's no
resistance.
Charge is free to move between the left and the
right islands.
And the laws of quantum mechanics say that it does this
coherently.
The charge can be in a superposition of being on the left island and being on the right island.
If a single transmon, let's call this
guy T1,
then T1 has the possibility 
of being in plus left and plus right.
That gives me two possibilities that I have to consider
when I'm describing this system.
If I have another transmon,
T2, this also has charge on the left or on the right.
You can see that I'm building up exactly 
the same table that I have above,
In exactly the same way.
Because this is behaving like an artificial H2 molecule.
As I add more transmons to this system 
it'll grow in exactly the same way
as the electronic system has up here.
So my research has
been about trying to describe
the control of this system and how to
actually use it to mimic
the artificial molecule, and use it to extract
data from these quantum systems
so that we can get data out, 
that we actually can solve problems
that we actually find useful.
And so that we can deal with the the noise that limits the
precision of these devices,
and that they don't simulate to nature, 
where the noise is much more reduced.
