Good Afternoon. In the next 20 minutes, I'd like to give you a brief introduction to quantum computing
and the story of quantum computing addresses
the collision or intersection of two fields in science.
The first is the area of computer science
that explores the use of man-made machines
to solve mathematical problems.
And the second is the field of quantum science 
or quantum mechanics.
This is an area of science that lays down the foundations, the laws of physics,
that governs our universe down to the tiny, tiniest scales.
Now for many decades, these two fields of science had nothing to do with one another
until in 1985, we got to realize
that there is actually a very deep connection
between these two fields
and that basically gave birth 
to the field of quantum computing
today that i'll be talking about.
Now today's computers might be considered as perhaps humanity's greatest achievements.
or at least one of humanity's greatest achievements.
Really phenomenal pieces of equipment
that can do really amazing things.
And therefore, I think you'd be surprised to know
that the same concept of computing machines
that we have today,  these fascinating instruments,
are actually the same machine that Alan Turing
in 1936, thought of when he hypothesized
how would he construct a computing machine.
Now, some of you might know Alan Turing
from the movie "The Imitation Game"
a movie that aired about a year ago
exploring Alan Turing's work 
during the Second World War
as he basically deciphered or broke 
the Enigma, the Nazi encryption machine.
What Alan Turing had in mind when he
just hypothesized about a computing instrument,
(and he didn't build one), was a very very primitive piece of instrument.
And the concept was
let's imagine we have a very long piece of tape
And we can write on that tape,
we can have zeros and ones on it,
we have a head, a magnetic head or read-write head,
that can erase a bit there - zero - and turn it into one.
It can move right and left
And it does this based on instructions that are given to it
And the instruction that you see 
on the head right now is number four.
So, for the instruction number four, 
this computer here would see i have a zero.
So, my instruction is to replace the 0 to a 1
move to the right,
and  change my head instruction to number five.
This sounds like a very primitive computing instrument
But it turns out that this very basic concept 
is what's called the Turing Machine.
And everything computable 
can be calculated using that machine.
Now the bigger surprise, possibly, is that
that machine known as a Turing Machine
is in fact nearly identical to the
computers that we have today.
And so you can ask yourself, "what is the difference then
between our computers today
that look really fascinating and that primitive machine?"
And, in fact, the only difference is to some extent
the number of operations
that this machine can do per second.
In the early days, 1947, where
the first transistor was basically built
inside a chip, a semiconducting chip,
the number of operations we could do
is the order of ten or a hundred per second.
And over the course of 50 or 70 years
our computers have developed tremendously,
And today were able to basically run
maybe 10 to the 9 operations percent per second,
But the fundamental concept of computing
is exactly the same, or nearly exactly the same, 
as the Turing Machine.
A breakthrough in this stagnation occurred in 1985
by the physicist named David Deutch
who made a very peculiar statement.
And that statement is
"The ultimate limit of computaton 
is set by the laws of physics."
And as we know the laws of physics are governed by quantum mechanics.
And so the question is really
What is the link between computation 
and quantum mechanics?
So, to get you into the right mindset
about quantum mechanics,
I'd like to ask you a little riddle, and the riddle is
What is the difference between a classical mechanic (the one that fixes your car)
and a quantum mechanic?
Anybody have an idea?
Guess... it's okay.
Yeah?
So, a quantum mechanic can fix two cars at once.
This is an excellent answer.
My answer actually would have been that 
a quantum mechanic
could both drive and fix his car at the same time.
And I know this sounds counterintuitive
and it's okay. 
This is what happens with quantum mechanics.
It's very counterintuitive
but i like it to get into this mindset
where things that defy your intuition 
are not necessarily wrong
and just flow along.
And hopefully, you'll get a sense of why 
quantum mechanics helps with computation.
So, here's a zoom in on an atom,
an artist's rendering of an atom.
We have a nucleus that attracts electrons
and these electrons are surrounding the atom.
And, in fact, a more precise rendering of an atom 
is what I'm showing here,
where I have the nucleus
and the electron is depicted as a cloud,
rather than a particle
which basically tries to emphasize that 
it's living around this nucleus
all at once, all around.
OK?
Now, to highlight this element, I'm going 
to introduce two nuclei
and one electron.
And what you see up there
the electron is mostly surrounding the left nuclei.
And this means if I were to measure where is this electron amongst the two nuclei,
I'm always going to find it on the left.
And that's why I've written the letter L on the left.
I can also prepare these pair of nuclei
and one electron where the electron is on the right.
And if i were to measure where that electron is, 
 I'm always going to find it on the right.
It's deterministic.
And that's why I've labeled it right.
But, just like the riddle that I gave you
we can also prepare these two nuclei and one electron
in a way where the electron cloud is actually surrounding both nuclei
And to exaggerate things,
we can actually separate these two nuclei
such that we have one electron
who is actually equally hovering
around the two nuclei separated in space.
And if we were to ask now, where is that electron?
We would get two possibilities.
On occasion we will find it on the left,
and on occasion we will find it on the right,
but there is nothing the deterministic
that can predict the outcome of that experiment.
This is fundamentally unknown,
and therefore I've written the letters L & R on the side
because these are the possible outcomes 
of the experiment.
Now, to give you a sense of something 
that could be at two places
or do two things at the same time,
I'd like you to think of waves.
Waves are objects that are not local.
You see that you have a wave 
and its present at multiple places at the same time.
And that is the essence of how we can understand
features, certain features of quantum mechanics.
We know that waves have peculiar 
or particular manifestations.
For example, in one of the experiments downstairs
that you can go and explore,
there is a laser light that is shined on two slits.
And what we know is that when you 
shine waves on to two slits,
because of the non-local nature of the wave,
the wave can pass both on the right slit 
and on the left slit.
And what that does is give an interference pattern 
on the screen.
You're not getting the shadow
of the two slits on the screen,
you're  getting something more complex
and that more complex pattern indicates
that we have waves in the system.
So now let's just ask what would happen
if we replace this laser, with an electron gun.
And we're going to shoot electrons,
 particles, one at a time
through the double slits.
And when we do this experiment, what we find
is that on the screen we get spots.
For each electron we send, we get a spot
but you see the spots are messy, and it looks noisy.
But if we collect enough of these electrons,
eventually what we find is the pattern
that looks exactly the same as the pattern of waves
that we got when we did the experiment with waves,
 or light waves.
And what this suggests is that the electrons
are actually passing through the slits
both on the left and on the right
like our quantum mechanic, at the same time,
giving rise to an interesting pattern on the screen.
Note - we could not predict for any individual experiment
where we would find the electron
but the probabilities,
which are the intensities of these spots
is something that we can predict.
And, we see that we have high intensity stripes,
and we have low intensity stripes
at some other locations.
Let's take this now one step further
and consider 2 sets of pairs of nuclei and one electron,
one on the top and one on the bottom.
And I've prepared them in a way that
on the top the electron is on the left
and on the bottom, the electron is on the left,
And if I ask "what are the measurement outcomes?"
Where would I find my electron?
it's going to be left and left,
because that's how I prepared it.
I can do the same thing and
prepare the two electrons on the right
And ask "What is the measurement outcome?"
Deterministically, I'm always going to find it on the right.
But now let's introduce the superposition
and prepare the upper system in this left and right
and the bottom system in the left and right
and see what are the measurement outcomes.
And so the measurement outcomes are multiple.
I could find the electron on the left in the upper system
and left in the bottom system
I can find it left and right
and i can find right and left
and i can find right and right.
So, I have multiple possible outcomes that can come
when I perform the experiment,
but perhaps the most important thing to note
is that in this particular example
there are no correlations 
between the measurement outcome
on the top and on the bottom.
Note for example that for the outcomes left on the top
I can get both left and right on the bottom
And the same thing, if I have right on the bottom
I can get both left and right on the top.
They are uncorrelated.
They seemingly look entirely random.
But one thing that quantum mechanics allows us
is to prepare prepare system in a way
that has only a subset of the possible outcomes.
Okay?  And here i'm showing an example
where I've prepared the system where there are
only two possible outcomes:
left and left, and right and right.
And I want to emphasize why this is extremely creepy.
Let's imagine I send one pair
of these nuclei and electrons up to the moon,
and keep the other one here with you.
And I measure the one on the moon.
And I find left.
Since this system was prepared in this peculiar way
that the only measurement outcome possible
when the upper is left,
is that the other system is also left,
you see that even though i'm on the moon
you're going to measure left
and there's no way around it.
And if I were to measure right on the moon
you're gonna measure right on earth
And, it's gonna happen instantaneously.
So there's something very peculiar about 
what's happening here.
And this is something that if you blow up
to the classical or macroscopic scale,
would seem very, very unintuitive.
It's basically like describing a coin toss experiment
or two coin toss experiments
where if I measured left,
or heads on one,
the other one would automatically fall on heads,
and if I were to measure tails,
then deterministically the other one would fall tails.
And yet to begin with, I couldn't predict
what my measurement outcome could be at all,
it could be either heads or tails with equal probability.
This feature of quantum mechanics 
is different from superposition.
It's called entanglement.
And entanglement is a key element,
something that bothered Albert Einstein tremendously.
He struggled with this concept for many many years.
And he gave it this name "Spooky Action at a Distance"
because he really couldn't, you know, didn't like it.
And he actually spent many of his late days
trying to show why this kind of concept is not correct.
And he failed.
Today, we know that this description of superposition
and entanglement is consistent
with every single observation
we have about our universe
and so we have no indications of any violations 
of these concepts altogether.
So what's the connection with computing?
So, here is a classical bit.
When the system was deterministic,
the electron is always on the left.
Let's call that zero.
And when the electron is on the right, let's call that one.
That's our classical bit.
But here the quantum bit is the possibility
of not only having this bit being in 0 or 1,
but also being in the superposition of 0 and 1
at the same time, our quantum mechanic.
So let's take it a little bit further.
Suppose I had four bits.
I want to build a computer,
so this is a small computer with only four bits.
And these are classical bits for now
and I prepared them in the state 0.
All the electrons are on the left.
If I were to do a computation,
I would have to operate on these bits
and one operation would be a bit flip.
The bit flip will just change the location of the 2 nuclei,
And you see that we've switched bit number two 
from 0 to 1.
That's how a classical computer works,
it operates on the bits by flipping them
depending on various inputs that it has.
Let's look at this now from the quantum world.
So now we prepare these quantum bits,
they could be in these superpositions of zeros and ones
at the same time.
And, moreover, we have prepared them in a way that 
we can have multiple measurement outcomes
And you see here an example of all the bits
simultaneously zero,
together with a situation where all the bits 
are at the same time one.
And another instance where there is 0 1 0 1.
In fact, there are 2 to the 4 possible configurations 
of these bits.
Whereas the classical computer at any given instant
is at one of these possible configurations
at any given time,
you see that our quantum computer
is at many of these configurations at the same time.
In fact, it it could be in up to a number as large
as 2 to the N configurations at the same time.
This is really large when N, the number of bits,
gets to be very large.
When we do a bit flip operation on this computer,
note what happens
we're flipping the sides again of the two bits
so all the realizations, 
the possible measurement outcomes
switch zeros to ones and ones to zeros.
So, one single operation performs
changes the states of many possible outcomes at once.
You get a sense of parellelicity.
There is a very strong power embedded in
this kind of quantum computer.
So, if I want to compare these quantum computers
based on quantum bits and classical computers,
we argue that our classical computers 
are basically Turing machines.
There are no different from what Alan Turing 
envisioned many many years ago.
Whereas quantum computers that use
entanglement and super position
in fact, are more powerful than Turing machines.
This is, in fact, the first time in the
history of computer science
that we've been able to conceive a computing machine
that is more powerful than a Turing Machine.
So the question is:
Okay, so we have a more powerful computing machine,
What can we do with it? 
How would impact our lives?
So here's an example, 
it's a mathematical example of a problem
that quantum computers can solve 
much much better and faster
than a classical computer.
And the problem is
finding the prime numbers that 
construct a large number.
So, here is a number, 15,
and I'd like to ask you, 
what are the prime numbers that make it up? Yeah?
Three and five. That's correct.
So, when we discuss the difficulty of a problem
we always make the problem bigger and bigger.
So this was a two digit number.
Let's go to a three digit number.
So here we have the number 143.
Thirteen times eleven.
Boy, we have a quantum computer here.
13 x11 - that's absolutely correct.
Let's go one step further. 
Let's add one more digit - 4633.
Note, the computing time gets longer and longer.
That's the essence of a hard problem.
As the problem gets bigger,
the computing time gets bigger exponentially,
much faster than the size of the problem is growing.
Forty-one times one hundred thirteen.
What about a number that has a hundred digits?
I can tell you that a classical computer
would require a few months to figure that out.
Okay?
So, why is that interesting?
Why is factoring prime numbers a problem
that we would be interested in at all?
In fact, you're all interested in that because
you're using it every day many, many times.
It is the underlying concept of encryption.
When you send out a message or an email
your phone encrypts your message
and it uses a hard problem 
that is very hard to solve
so that any classical computer that would try to 
decipher your code
would take months or years to figure out 
what that code was.
Okay?
I want to emphasize that if we were to try and 
give this task to a quantum computer
for the same amount of time
we would only require one thousand quantum bits,
would be equivalent to one billion classical bits
for the same problem.
So, this is the power of a quantum computer.
So, what else can we solve with quantum computers?
In fact, we know a few problems,
quite a few, that quantum computers will
aid us in solving very effectively.
One we talked about is the encryption.
The other one is searching, or data mining,
searching in big databases.
It turns out the quantum computers
we know today
can do that more efficiently, more effectively, 
than a classical computer.
We can also of course use quantum computers
to simulate how nature behaves
on the microscopic scale,
where it is just governed by quantum mechanics.
There are, however, a very large list of problems
that we don't know yet,
whether quantum computers will be able to solve
more efficiently than a classical one.
The field is really is still in its infancy,
so we hope we will discover many, many more problems
that classical computers are weaker than quantum ones
but the answer is not known for many of those.
So, where we do we stand right now
with the question of classical computers 
and quantum computers?
So to give you a sense
the pathway or trajectory that classical computers 
have undergone is really tremendous.
We started in 1958, with the first integrated circuit.
We had only four elements,  four bits,
on that piece of semiconductor in the chip.
And in 1970, we already had a thousand bits.
And to give you a sense of the process that 
classical computers went thorugh
I show a picture of this hall here.
And let's imagine that people are bits.
We can probably fit into this space here
a thousand people.
And it will feel okay.
Maybe a little crowded, but okay.
And that's 1970.
By the year 1980, we would be able to fit
into this space, the entire visitors to a stadium,
a hundred thousand people.
So that's a little bit more crowded.
1995, we can fit here the entire population of Tokyo.
10 million bits.
And 2010, not even today,
we can fit the entire population of China into this room,
So, the process is really phenomenal
but what we need to understand 
is that this process cannot continue forever.
As we're shrinking things more and more,
to put more and more things into a small space,
the size of each bit is getting smaller and smaller
and we expect in the next 10 or 20 years
the extrapolation, the same development,
would require that our bit size would be
the size of individual atoms.
We won't be able to squeeze them further.
So, this miniaturization process 
is bound to reach an end,
and we're seeing it slow down already 
in the past several years.
In contrast, the trajectory of quantum computers
is really just beginning.
In 2000, we had one quantum bit
and today, we roughly have 10.
We are on a solid trajectory
but it is going to take a couple of more decades
to get to a scale where we have really a
large number of computers.
So my message is "stay tuned."
This is a really fascinating field 
that is developing today,
but don't start saving
to buy your next quantum computer.
Buy your classical one first.
It's going to take us a little bit of time.
Thank you.
[Applause]
