I was blown away for most of the day

by the power and the ubiquity of computers.

Not only the fantastic graphics that we've seen,

but to even recognize that musicians these days

have a stage filled with computers as part

of their performance was to me very surprising.

I want to reduce the essence of computers

down to their smallest working part.

For the purpose of talking about a resource.

A resource that may be useful for increasing the speed of computers.

And one which interestingly is not used today.

It's a resource that lives inside of atoms

and it's one that we hope to develop as time goes on.

This picture is the working part of every computer.

It's the transistor. It's made out of a semiconductor.

Semiconductor is something that's either a conductor or an insulator

depending on whether a voltage is applied to it.

The fact that you can control electricity with electricity

means that you can make a machine that can compute.

As we've heard today these are getting smaller and smaller.

And in fact are approaching the atomic scale.

Only a few hundred or thousand atoms across.

Constitutes the wires that are inside

of these computer that are around us.

This little device invented in 1947 is now everywhere.

Right now we manufacture

about 10 billion transistors every second.

Most of you probably have 100 million or so

transistors in your pocket right now.

We live in a world filled with these little objects.

But I would like to contrast the way these objects work with

the world of atoms that Don was just talking about

in the previous talk.

Let's think of these transistors as little switches.

As I said, they can be turned on and off with electricity.

But for all intents and purposes they're on-off switches.

We can call them 0s and 1s if we like this binary notation.

Or if we're interested in eventually

moving to spins, which we'll do in this talk,

we can think of them as spinning this way,

or spinning the other way, up or down.

But in any case they represent some binary structure.

The resource that I'd like to talk about,

the one that's not used in computation

but which lives inside of every atom

and makes the world around us work is Quantum Mechanics.

Quantum Mechanics says that switch can be

up and down at the same time.

Just like the particle that can go through 2 slits

or any other quantum state

a transistor can be on and off

according to the laws of Quantum Mechanics.

What that means is that you can imagine a machine

that's consistent with all the laws of physics

in which every one of those

10 million, 100 million transistors

in your pocket was simultaneously on and off.

And not just those two states, but in fact

every one of the exponentially many states

that can be formed by imagining

every one being on or off

and every one that's on can then turn another one on or off

but of course it is either on or off

and it then does or doesn't turn the next on or off, etc.

That power lives inside

of the world that we understand of atoms.

But we don't use it.

And it's a strange world.

In moving from the world of atoms

to the world of macroscopic objects

we have to forgo our intuition

and I'll give you an example of that.

Take a Helium atom

the same atom that's in Helium balloons.

The two electrons that form the shell

of the Helium atom have a particular orientation

with respect to this spin that I talked about.

The angular momentum spinning up or spinning the other way.

And that is that they're in some configuration

of these two spins. Now what Quantum Mechanics

allows and I should mention this quote of

"Spooky Action at a Distance"

is something from Einstein

who never quite bought this story of Quantum Mechanics

and you'll see why in a second.

Let's take the two electrons in the Helium atom

and for the language of the day,

I'll call them Up and Down

I won't say which one's is Up and which one's Down.

One of them's Up and the other one's the opposite direction

so they can fill in the first shell.

And I want to take those two electrons

and without disturbing them separate them in space.

And I want to give one over here,

the first seat here, do you mind if I toss you one

of these electrons you have to grab it.

OK, here you go. You got it? Got it. OK

And I need another one over here.

Michael can you help me out here?

There's the second electron.

Now, what I would like you to do -

we didn't disturb the electrons

we distributed them very gently -

is to measure yours. Is it Up or Down?

(Inaudible) Charlie: It's Up.

Charlie: Michael? Michael: It's Down.

Charlie: Down. (Laughter)

Well that was interesting. OK.

That's right, because we didn't disturb them.

Let's do it one more time, just for fun.

Here you go. Got it?

Michael? Good!

Wait, I have an idea. Turn your detector sideways.

Now is it East or West? (Inaudible)

Michael did you hear what he said?

You're not listening, right?

East!

Michael, yours is? West!

How did you know what his was?

That's a resource.

Thats's what Quantum Mechanics provides.

Quantum Mechanics says that that singlet,

the two electrons in the Helium atom,

if you could control them and even separate them,

even separate them to the outer reaches of the Galaxy,

If you make a measurement,

yours becomes the opposite.

And that's a powerful kind of communication.

Not quite enough to violate Special Relativity.

Because immediately as soon as he measured his,

yours became something.

And we don't use that

in any machines that we build these days.

And yet there's little doubt that it's true.

But imagine building some complicated machine.

A bit like a cat or something.

And saying that all of these things were together.

Now Schrödinger commented on the possibility

of putting a cat like this together

and said we can even think of some ridiculous cases.

I'm not going to read the quote but you understand that

the quantum state is going to either knock the cyanide bottle over

and it's going to either kill the cat.

And the whole cat is going to be either alive or dead simultaneously.

And Schrödinger illustrated this point

to represent how impossible such a system was.

But in fact Schrödinger set us up on that one.

Because Schrödinger created

a situation in which if you created the conditions to preserve

the simultaneous superposition of all of these states

it would have certainly killed the cat.

There wouldn't be any air in the room. It would be very low temperature.

But computer chips are very happy to work under those conditions.

And so there is no rule that says that

we couldn't make a catlike chip that would

be very happy to work at Absolute zero or near, in vacuum, etc.

And what if we could?

There are examples of problems,

Scott Aaronson told you a little bit about them earlier today.

I don't know if Rives was paying attention during that talk

but I want some help from Rives

on the first question on this test.

Two prime numbers, smallish, smallish prime numbers,

whose product is 15. Can you help me out?

Rives: It depends on what you mean by prime. (Laughter)

What's your definition of prime?

Charlie: I will exclude 1 for the sake of brevity.

R: Yeah, you wouldn't be the first person today.

I'll go with 3, 5 my final answer.

C: Fantastic. You did graduate High School.

(Laughter)

I think I'm going to need Carl Feynman for this one.

This one's a little bit harder.

Carl I don't know if you're here? Yeah!

(Inaudible)

It's unfair, It's unfair. It's a hard question.

The answer is 41 x 113.

And what's interesting about the example

is not only is it a hard question for Carl Feynman

it's a hard question even for computers.

That is if you take two numbers

that are pretty big and multiply them together

that goes like a snap.

But if you take the thing that you got when you

multiplied them together

and try to break them apart

you're in real trouble.

In fact what I mean by that

is that if the numbers are a thousand bits long

it would take the age of the universe for even the best computer

to solve the problem.

Now if you could build one of these machines

that took advantage of the superposition

that let all the transistors

in the circuit be in multiple states at the same time

it becomes a very easy problem.

Our job, and by our I mean, in my laboratory

and the laboratory of several colleagues and friends who are here,

we're trying to build these chips

and we're building them out of semiconductors

only in this case we're using the spin,

we're doing the same kind of transformations

where we separate the electrons to produce

the same kind of entangled states.

And how far are we?

We have about one working.

So maybe it's about the equivalent of 1947

when this was invented, the transistor.

And we can see as we go along using

either carbon nanotubes or gallium arsenide, or Silicon

the kinds of machines that we had to build

and we're at the level now of 1 or 2

or on a good day 3 transistors

And we're waiting for the day that we have...

not a hundred billion, but the 300 that we heard about earlier,

that would produce an exponential number

of quantum states and allow computation.

We're not there yet. We're still building these chips.

Here's a carbon nanotube with gates on it that produces

one such spin based quantum chip

and for the next one, and the next one

and the next 50 and the next 500 after that

we're going to have to wait a few more TED meetings.

Thank you. (Applause)