GREG KROAH-HARTMAN:
Good afternoon.
Thanks everybody for coming,
also all the remote sites.
So we will kick off the Quantum
AI speaker series.
And we are very pleased and
honored that we have an
illustrous guest, John Preskill,
who will kick off
the speaker series.
John is actually based across
town and has been at Caltech,
where he's the Richard
Feynman Professor.
He's there since '83.
And previously, he got his
PhD. from Harvard.
So until the mid-90's, he did
more like traditional physics,
cosmology, elementary
particles.
But then switched to quantum
information and started IQI,
the Institute for Quantum
information at Caltech, where
many interesting results
were achieved.
And in his career, I think he
had 45 PhDs and 40 post-docs.
And I think this room here is
becoming testimony to it
because we are surrounded
by Preskill
post-docs and then PhDs.
And Sergio on our team
learned from John.
So it definitely left his mark
on the field of quantum
information.
And then just a few days ago, I
was told was that when John
has a guest who gives a talk,
then he is being introduced
with a poem.
And I thought oh, my god,
that's high bar.
But fortunately, Dave Bacon on
our team came through and he
put a little limerick together
to announce John.
So I will try this.
There was once a physicist named
John, who threw qubits
into the beyond.
Across the horizon they went.
But were they really spent
or destined to
become Hawking radiation?
So I approve.
I confess Dave's is a very
geeky limerick, even for
Google standards.
But maybe the last thing I
should say about John, I had
the pleasure to witness his
birthday symposium, which was
just a few months ago.
And that was quite a sight.
There was a lot of highly
decorated physicists, from
Nobel Prize winners
to winners of the
fundamental prize of physics.
And yeah, I was surrounded
by the worldly leaders of
physicists.
And he's highly respected
among them.
So I'm very happy that you are
going to give the first talk
in the series.
John.
JOHN PRESKILL: Can
you hear me OK?
Thanks a lot, Hartman.
And good job on the reading
of the limerick.
Thank you, Dave.
I haven't been introduced by a
limerick before, as I recall.
This is going to be a talk
about quantum physics.
But it's also to some extent
about technology.
Now, you guys know more about
technology than I do.
I have this laptop I think
it's pretty cool.
And we all recognize, I'm sure
you more than I, that
technology that seems impressive
to us now is going
to be replaced by the end of the
century by new technology
that we can't really expect
to imagine at this stage.
But it's fun to think about
future technologies.
I may not be the best qualified
to do that because
unlike many of you, I
am not an engineer.
I'm a theoretical physicist.
And maybe I'm not especially
knowledgeable about how
computers work.
But as a physicist, I know that
the crowning intellectual
achievement of the past
century has been the
development of quantum theory.
So it's natural to wonder about
how the development of
quantum theory in the 20th
century is going to impact
21st century technologies and
in particular information
technology.
Now, quantum theory is
over 100 years old.
But there are some ways in which
classical and quantum
systems differ that we are
really only appreciating
deeply in the last
couple of years.
And those properties have to do
with information encoded in
physical systems.
To a physicist, information is
something that we can encode
and store in the state of some
physical system like
the pages of a book.
But fundamentally, all physical
systems are really
quantum systems governed
by quantum physics.
So information is something that
we can encode and store
in a quantum system.
And information carried by
quantum systems has some
famously counter-intuitive
properties.
So physicists like to
speak about the
weirdness of quantum theory.
And we relish that weirdness and
take great delight in it.
But more recently, we're asking
more seriously whether
it's possible to put that
weirdness to work to exploit
unusual properties of quantum
information, to perform tasks
that wouldn't be possible if
this were a less weird,
classical world.
And that desire to put weirdness
to work has driven
the emergence of
a field we call
quantum information science.
Which from my perspective,
derives a lot of its
intellectual vitality from
three main ideas, quantum
entanglement, quantum computing,
and quantum error
correction.
And my goal in the talk is to
introduce you to these ideas,
if you're not already
familiar with them.
So starting at the beginning,
we know that we can express
classical information in terms
of bits, where we might think
of a bit as an object like a
ball that, can be either one
or two colors say
red or green.
And if I want to, I can
store a bit in a box.
And then later on if I open the
box, the color ball I put
in comes out again.
So we can recover a
bit and read it.
Quantum information, too, can
be expressed in terms of
indivisible units, what we call
quantum bits or qubits.
And for many purposes, it's
useful to think of a qubit as
an object stored in a box.
But where now, we can open the
box in two complementary ways,
two different ways to
prepare or observe
the state of a qubit.
And if I put information in door
number one or door number
two, then later on I can open
the same door again and the
color that I put in will come
out of the box, just like it
were a classical bit.
But if I say store information
in door number one and then
later on open a complementary
door, door number two, then
it's unpredictable
what we'll find.
It has probability one-half
of being red, probability
one-half of being green.
So if you're going to observe
quantum information, you have
to do it the right way.
If you do it in the wrong way,
you'll actually damage the
information.
And one reason why that's
important is appreciated if we
think about copying
quantum states.
If I had a quantum copying
machine, that would mean that
if I happened to have put
information in door number one
of a qubit, I could
make a copy.
And then I could open door
number one of the original and
the duplicate and out of
both I would find the
color that I put in.
Or if I put information in door
number two of the qubit,
I could make a copy and open
door number two on the
original and the duplicate.
And the color that I
had put in would
come out of both boxes.
But, in fact, there is
no such machine.
A machine that copies unknown
quantum states is not allowed
by the rules of quantum
mechanics.
And the reason is that to copy
what's inside the box, the
machine has to probe
what's inside.
And if it opens the right door,
the door that I used,
then it can copy the
information, no problem, just
as though it were classical.
But if it opens the wrong
door, it will damage the
information.
And at that point, it won't
be possible to make a high
fidelity copy.
So although we might be able
to clone a sheep, we can't
clone a qubit.
We can't copy unknown
quantum states.
Now, there are lots of
possible physical
realizations of qubits.
I'm going to mention
a couple of others
later on in the talk.
But just so you'll have
something concrete to think
about for the moment, you can
imagine a single photon or
particle of light which
has an electric field.
And that electric field can be
oriented either horizontally
or vertically, corresponding to
observing our qubit through
door number one and seeing
two possibilities.
Or we can imagine observing
it in these
45-degree rotated axes.
And that corresponds to opening
door number two, the
complementary door, to
observe the qubit.
The really interesting
differences between classical
and quantum information arise
only when we consider systems
with more than one part.
So suppose we have two qubits.
They can be far apart
from one another.
One is at Caltech,
in Pasadena.
The other is in the custody of
my friend, far away in the
Andromeda galaxy.
But a long time ago when these
two qubits were both on Earth
and could interact with one
another, they were prepared in
a particular state with some
interesting properties.
Namely, I can open my box in
Pasadena and open it through
either door number one
or door number two.
And either way, what comes out
of the box is random, has
probability one-half of being
either red or green.
And the same thing is true for
my friend in Andromeda.
He can open either box and
either way sees a random bit.
So neither one of us by opening
his box can acquire
any information.
It just generates
a random bit.
And that's kind of surprising
because with two boxes, we
ought to have been able to store
two bits of information.
So where is that information
hidden?
The answer for this particular
state of the two boxes is that
all the information is actually
encoded in the
correlations between
the two boxes.
For this particular state, if my
friend and I both open door
number one, we're guaranteed
to find the same color.
It could be red,
could be green.
But we always find the same one
if we open the same door.
And likewise, if we both open
door number two, we always
find the same color, probability
one-half of being
red, probability one-half
of being green.
But it's guaranteed to be the
same if we open the same door.
And there are four
distinguishable ways in which
a box in Pasadena could
be correlated
with a box in Andromeda.
We could either see the same bit
or opposite bits when we
both open door number one or we
both open door number two.
We've chosen one of
those four ways.
So that's two bits
of information
stored in the boxes.
But what's unusual is the
information is locally
inaccessible.
We can't acquire any of that
information by looking at the
boxes one at a time.
And that property of quantum
information, that it can be
stored nonlocally, shared
between two distantly
separated systems, is what we
call quantum entanglement.
And that's the really central,
essential way in with quantum
information is different from
classical information.
Correlations themselves are
not such an unusual thing.
We encounter them all the
time in daily life.
I normally wear two socks
that are the same color.
It means that if you look at
my left foot, then you know
for sure what color
to expect when you
look at my right foot.
Yeah, Hartman just tried it.
It worked.
And that's a correlation.
And you might say it's kind
of similar with the boxes.
If I want to see what my friend
is going to see when he
opens store number one in
Andromeda, I can open door
number one in Pasadena.
If I want to know what my friend
is going to see when he
opens door number two, I can
open door number two.
So aren't the boxes are really
just like the socks?
No, they're really different.
There's a big difference
between this quantum
correlation and classical
correlation.
An essential difference is
there's just one way
to look at a sock.
But we have these two
complementary ways of looking
at a qubit, of opening
a quantum box.
And that means that the
correlations among qubits are
richer and more interesting
than correlations among
classical bits.
This phenomenon of quantum
entanglement is an old thing.
It was discussed quite
explicitly by Einstein in a
famous 1935 paper, with
two collaborators.
And to Einstein, quantum
entanglement was so unsettling
as to indicate that something
is missing from our current
understanding of the quantum
description of nature.
And that paper induced some
interesting responses,
including one from Schrodinger
later that year, which was
especially insightful.
And Schrodinger described
entanglement this way.
He said the best possible
knowledge of a whole does not
necessarily include
the best possible
knowledge of its parts.
What he meant was that even if
we know exactly how those two
boxes were prepared, know
everything about those two
boxes, we are still helpless to
predict what will be found
when we open one of the boxes
in Pasadena or Andromeda.
And it was Schrodinger who
suggested, using the word
"entanglement" or "entangled"
to describe that situation.
He also said it's discomforting
that the theory
should allow a system to be
steered or piloted into one or
the other type of state at the
experimenter's mercy, in spite
of his having no access to it.
Schrodinger meant isn't it odd
that it's up to me to decide
by opening door number one or
door number two whether I will
know what my friend will see
when he opens door number one
or door number two?
But Schrodinger also understood
that these
correlations don't enable us
to send a message from
Pasadena to Andromeda
instantaneously.
No matter what I do, my friend
opens either door number one
or door number two and just
finds a random bit, learning
nothing about what I did
and receiving no
information from me.
Now, this phenomenon or idea
of quantum entanglement did
not advance very much for
30 years after that.
Until the mid-'60s, when John
Bell started us thinking about
quantum entanglement in a
rather different way.
Not just as something weird,
but something potentially
useful, a resource that we
can use to do things.
Specifically, Bell described
games that two players can
play, Alice and Bob.
It's a cooperative game.
Alice and Bob are on
the same side.
They're both trying to win.
The way the game works is that
Alice and Bob receive inputs
and they are to produce outputs
which are correlated
in a certain way, depending on
the inputs that they receive.
And if they receive some
correlated bits before the
game began, they're allowed to
consult those correlated bits.
But under the rules of the game,
Alice and Bob cannot
communicate between the time
that they receive the inputs
and the time that they
produce their output.
And for this particular game, if
they play the best possible
strategy, they can win with a
probability of success 3/4,
averaged over the inputs that
they could receive, if we
assume they're uniformly
distributed.
But there's a quantum
version of the game.
It's the same game.
But now, Alice and Bob are
permitted to use entangled
qubits that were distributed
before the game began.
And by making use of that
entanglement, they can play a
better quantum strategy and
win the game with a higher
success probability,
above 85%.
So the quantum correlations
are good for something.
They allow you to win this game
with higher probability.
And experimental physicists have
been playing the game for
decades now and they keep
winning with this higher
probability of success that Bell
showed us is possible in
quantum physics.
So these quantum correlations,
stronger than classical
correlations, really do
seem to be part of
the way nature behaves.
Now, to Einstein quantum
entanglement was kind of
disgusting.
And he called it spooky
action at a distance
in a derisive tone.
This sounds even more derisive
when you say it in German.
But it doesn't matter
in physics what
Einstein things, right?
Nature is the way experiments
reveal her to be.
And we have to learn to
love her as she is.
Quantum entanglement is really
part of the world.
OK.
So in a world with quantum
correlations, we can use those
correlations to do things that
we wouldn't be able to do if
all correlations
were classical.
Boxes are not like socks.
You can win a game with
a probability of
85% instead of 75%.
Is that really a big deal?
Yeah.
This is a really,
really big deal.
And to appreciate why it's a
big deal, we really should
think about systems
with many parts.
Now suppose, for example,
that I have a book.
It's 100 pages long.
It consists of a hundred
subsystems, each a page.
If it were a classical book
rather, with bits printed on
every page, you could read a
single page and you'd know 1%
of the content of the book.
10 pages, you'd know 10% of
the content of the book.
But suppose it's a highly
entangled quantum book.
Then if you look at the pages
one at a time, what you see is
really just random gibberish,
which tells you nothing about
the content of the book, if it's
a highly entangled book.
If you want to distinguish one
entangled quantum book from
another, you can't tell the
difference by looking at the
pages one at a time because the
information isn't printed
on individual pages.
Almost all the information is
encoded in the correlations
among the pages.
If you want to distinguish one
such book from another, you
have to make a difficult
collective observation on many
pages at once, perhaps
more than half the
pages in the book.
If I have a quantum system
consisting of qubits, and a
rather modest number of qubits,
just a few hundred, if
I wanted to give a complete
description of all the ways in
which those qubits are
correlated with one another, I
would have to write down a
huge amount of classical
information, more bits than
the number of atoms in the
visible universe.
It will never be possible, even
in principle, to write a
description like that down.
There's too much classical
information to describe this
extravagant correlation of just
a few hundred qubits.
And that property of quantum
information, that we can't
hope to describe it using
classical information, was
intriguing in particular
to the Caltech
physicist Richard Feynman.
And it led Feynman to make the
suggestion in the early 1980s
that if we could process
quantum bits instead of
classical bits, operate a
scalable quantum computer,
we'd be able to perform tasks
that would be beyond the
capability of any conceivable
digital computer.
So Feynman's idea was that if
we can't even write down in
terms of classical bits the
state of a few hundred qubits,
then perhaps by processing the
qubits, we'd be able to
perform a task that we
can't emulate with
ordinary digital computers.
When Feynman was making this
suggestion in the early 1980s,
there was an undergraduate at
Caltech, concentrating in
mathematics, named Peter Shor.
And Shor, like all Caltech
undergraduates, had to take
our core curriculum.
Everybody at Caltech has to
learn quantum mechanics, even
if you major in music.
We don't have a lot
of music majors.
Everybody has to learn quantum
mechanics when you're a
sophomore and Peter did.
And as far as I know, that was
the most advanced class in
physics that he took.
But like many Caltech
undergraduates, he remembered
what he learned as a sophomore
about quantum physics.
And he drew upon that knowledge
about 13 years later
to make an amazing discovery.
Shor, in 1994, realized that if
you could build a quantum
computer, it would be able to
solve certain problems like
finding the prime factors of
large composite integers very,
very quickly.
That for a quantum computer,
factoring would not be much
harder than multiplying
numbers together.
And when I first heard about
this, as Hartman said in the
introduction, this was in 1994,
I didn't know much about
computer science or
cryptography.
I was working on particle
physics, and cosmology, and
gravitational physics.
But as soon as I heard
about this, I was
really amazed and stunned.
Because I understood the
implications are quite
remarkable.
That the boundary between hard
problems and easy problems,
the problems that we should be
able to solve some day with
advanced technologies versus the
problems that we never any
hope of solving, that boundary
is different than it otherwise
would be because this is a
quantum world instead of a
classical world.
I thought it was one of the most
interesting things I had
ever heard in my scientific
life.
And it lead me eventually to
change the direction of my own
research toward quantum
information and quantum computing.
Just to clarify what I'm talking
about, I'm talking
about the scaling of the
resources that we need to
solve the problem.
A hard factoring problem
nowadays is
factoring 193 digits.
That's been done by a network of
a few hundred workstations
collaborating over the internet
in a few months.
But from what we know about
the scaling of the best
classical algorithms for
factoring, if that same
hardware were used to try to
factor a 500-digit number, it
would take longer than the
age of the universe.
So that's not something that we
expect to happen, factoring
500-digit numbers in the
very near future
with classical computers.
Now, let's imagine that I have
a quantum computer with the
same clock speed as that
classical computer.
It can perform the same number
of basic operations per second
as the classical computer, but
now on qubits instead of bits.
And then we would be able
to factor, using Shor's
algorithm, the 193-digit number
in about a tenth of a
second and the 500-digit
number in two seconds.
Now, there's a completely
different scaling of the
resources we need with the
size of the input to the
problem when we run
Shor's algorithm.
But who cares about factoring?
People do care about factoring
because the presumed
difficulty of factoring is the
basis of widely used, public,
key cryptography schemes.
There are other problems that
quantum computers can break
which are alternative ways
of doing public key.
When quantum computers are
widely available, we won't be
able to protect our privacy in
the same way that we're doing
it now using current
public key schemes.
Alternatives exist.
But it's still not exactly clear
how we will best protect
our privacy in the post-quantum
world.
That's a ongoing subject
of discussion.
But the more important thing,
more broadly, that we learn
from Peter Shor's algorithm is
that there's an interesting
classification of problems.
There are problems which
are classically hard
and quantumly easy.
Problems that we can't solve
with reasonable scaling of
resources with classical
computers, but which we can
with quantum computers.
And so it becomes an urgent
question, what lies in that
intermediate region that's
quantumly easy
and classically hard?
And we still have a lot to
learn about that I think.
We do know that quantum
computers have limitations.
They can't speed
up everything.
It seems that spectacular
speedups are possible only for
problems with a special
structure.
And in particular, we don't
think that quantum computers
can dramatically speed
up problems which are
NP-complete, the hardest
problems for which we can
efficiently verify the solution
with a classical computer.
In the worst case, we can't do
much better than brute force
search for the answer
in that case.
Quantum computers can speed up
brute force searching, but not
exponentially, only
quadratically, a more
modest speed up.
It's important to keep in mind
though that quantum computers
can also solve problems that are
not in NP, problems where
we can't check the answer with
a classical computer.
And indeed, the most natural
application for quantum
computers is to simulate the
time evolution of quantum
systems with many particles,
many parts, which might be of
interest in chemistry or in
the quantum field theories
that physicists use to describe
elementary particles.
So, for example, we can ask
about the type of problem that
I as a particle physicist
used to worry about.
Suppose we want to consider a
high energy collision between
particles and we'd like to be
able to sample accurately from
the possible states of many
particles that could be
produced in that high
energy collision.
And at least in some cases,
we've shown that that
simulation can be done with
efficient scaling of resources
on a quantum computer, which we
don't believe is the case
classically.
So it may be that a quantum
computer is capable of
simulating efficiently any
quantum process that can occur
in nature, though that's still
an open question, in
particular with regard to
processes in which both
quantum mechanics and gravity
are important.
So quantum computers would have
wonderful capabilities.
We'd love to have them.
Lots of people around
the world are
working on quantum computing.
So why don't we have
them already?
What's the big delay?
Well, it's really, really,
really hard.
And part of what makes it hard
is that quantum systems are
more susceptible to error, to
the damaging effects of noise,
than classical systems.
Physicists sometimes like to
speak about a quantum state of
a cat, which is a superposition
of the live and
dead state of a cat, or in
this case, the more human
case, of a awake and
sleeping cat.
Now, we never observe in our
everyday lives that kind of
superposition of
macroscopically
distinguishable states.
And we understand why
that's the case.
Because no real cat can be
perfectly isolated from its
surroundings.
And the interactions with the
environment very quickly in
effect measure the cat,
projecting it onto a state
which is either completely
alive or completely dead.
That's a process that
we call decoherence.
And decoherence is actually very
important for helping us
understand why classical
physics works so well.
Why, when we consider
macroscopic systems, we don't
usually have to worry about
quantum phenomena.
It's because decoherence
is extremely
fast for big systems.
Now, a quantum computer, when
we manage to build one, may
not be much like a cat.
But it will, like a cat,
inevitably interact at some
level with its environment.
There will be decoherence.
And so the quantum computer will
crash unless we can find
some way of fighting off
decoherence, of preventing
sources of error from making
the quantum computer fail.
Errors are a problem, even
in the classical
world, as we all know.
I have many bits that
I cherish and I
would hate to lose.
And everywhere, there are
dragons lurking, who take
delight in tampering with those
bits and flipping them
from red to green,
or whatever.
But we know ways of protecting
ourselves from the dragons.
We can encode information
redundantly.
So that if I have a bit that I
want to be sure to keep, I
can, for example, store backup
copies of the bit.
That's an example of a simple
code, which can be used to
protect against errors.
The dragon might come along
and flip the color
of one of the balls.
But as long as the dragon
hasn't had a chance to
interact with more than one
ball, I can employ a busy
beaver of the sort we have
many of at Caltech.
And we can ask the beaver, if
he sees the one ball is a
different color than the others,
to recolor that ball
so that all three match.
And so as long as only one of
the balls has been damaged, we
can recover the original encoded
state and protect
against errors.
So we'd like to use the same
concept of protecting
information from error through
redundant storage in the
quantum world.
But there are some potential
obstacles.
As we've already discussed,
we can't copy
unknown quantum states.
So I can't take the state of a
quantum computer and store a
backup copy in case the
original gets damaged.
And there are more things that
can go wrong with quantum
information than with classical
information.
It could be that the dragon will
come along and open door
number one of a qubit and flip
the color of the ball and
reclose the box.
That would be like a bit
flip that occurs
in a classical bit.
But it's also possible that
the dragon could open door
number two and change the
color of the ball.
That's what we call a phase
error in quantum information.
It really has no analog in
the classical world.
And there's another
way of thinking
about these phase errors.
Another way a phase error, an
error through door number two
could occur, would be for a
dragon to open door number
one, look at the color of the
ball, and not flip the color,
but just remember the color,
make a record of
what the color is.
And that record will damage the
information if we try to
look at the qubit through
the door number two.
And in many physical situations,
it's easier to
remember or record the value of
a bit than to flip a bit.
And that means these phase
errors are particularly
pervasive and hard
to avoid in many
types of physical systems.
In fact, if we want to resist
decoherence, it means we have
to somehow prevent the
environment from learning
about the state of the quantum
computer during the course of
the computation.
If some record is left behind of
what the intermediate state
of the quantum computer was,
that will cause the quantum
computer to fail.
If a quantum computation was
successful, then it should be
that if you ask the quantum
computer after its done, what
did you just do while you were
factoring that huge number, it
should always answer I forget
because no record was left
behind of the state
of the computer at
intermediate times.
So we really need to do a kind
of secret computation,
completely sealed off from the
surroundings if we want a
quantum computer to succeed.
When we're done with the
computation and we have the
result, it's OK to broadcast
that to the world and tell
everyone what the answer is.
But we can't have any record
left behind of the state of
the quantum computer during the
course of the computation
because that will cause the
computation to fail.
So we have to figure out a way
to encrypt the processing that
we're doing.
And really our enemy here
is entanglement.
It is entanglement between our
quantum computer and its
environment, which drives
decoherence.
And the way to fight off that
entanglement is to use
entanglement to our advantage,
to store information in a
highly entangled state.
If I want to store one logical
qubit, it is possible to do
that if I have five physical
qubits, in such a way that if
the dragon comes along and looks
at one of those five
qubits, the dragon can't acquire
any information about
what the logical state
is of the qubit by
looking at that one box.
This is just like the 100-page
book I described earlier.
The state of the five qubits
is highly entangled.
So if you want to know what the
information is stored in
that five-qubit book, you can't
learn that information
by looking at a single qubit.
It's not there.
It's in the correlations
among the qubits.
And we can again ask the
beaver to help us out.
After the dragon has done
something, and we don't know
what, we can ask the beaver to
make some kind of collective
observation on the five qubits,
which we can do with
the quantum computer.
And from that information learn,
not the state of the
logical qubit that we're
trying to protect.
We don't want anyone, even the
beaver, to know what that is.
But what damage has occurred,
which of the boxes has been
damaged, what needs to be done
to repair the damage.
And then the beaver can
reinstate the original encoded
state, if only one of the
qubits has been damaged.
So that's the principle of
quantum error correction.
And how do we actually
get this to work?
Well, we'll see.
But one hero of the story is my
colleague, Alexei Kitaev.
I first met Alexei in 1997, on
his first visit to the US.
He came to Caltech and gave a
talk on the first day we met.
And I made these notes.
And it was really one of the
most exciting days of my
scientific life to talk to
Kitaev that way because I
learned from him an idea which
I felt could potentially be
transformative about quantum
error correction.
And what I learned from Kitaev
is the connection between
error correction and topology.
"Topology" is the word
mathematicians use if they
want to describe properties of
objects that remain invariant
when we smoothly deform the
object without tearing it.
And likewise, we would like
the way a quantum computer
processes protected information
to remain
invariant when we deform
the computer by
introducing some noise.
So we'd like to make use of
physical interactions that
have topological features.
Physicists have known
about such
interactions for a long time.
For example, I can consider an
electron interacting with a
magnetic flux tube.
And if that electron is carried
around the flux tube,
even though it never penetrates
inside to interact
directly with the magnetic
field, the quantum state of
the electron will be modified.
And that modification is really
a topological property.
It stays the same
if we deform the
trajectory of the electron.
The only thing that matters is
the winding number of the
electron around the flux tube.
There are more exotic types of
topological interactions that
can occur in two-dimensional
media, where there are
point-like particles which
we call anyons.
Non-abelian anyons in particular
have the property
that I can consider a system of
many of these particles in
a two-dimensional media.
And there are lots of quantum
states we can construct of
these many anyons, a number
of states which are all
distinguishable, which
is exponential in
the number of particles.
But all of these quantum states
locally look the same.
We can't see any of the
information that distinguishes
one state from another
by looking at the
particles one at a time.
OK.
The environment might
interact with the
particles one at a time.
But that doesn't allow any
information about the encoded
state to leak to the
environment.
And we can process the
information just by performing
exchanges of the particles,
having particles swap places
to get a different quantum
state, which can be a logical
operation in a quantum
computer.
So we can imagine operating a
topological quantum computer,
that's what I learned from
Kitaev in 1997, which we could
initialize by preparing pairs
of these particles in the
two-dimensional medium,
anyons.
And then process information
by performing a sequence of
exchanges or swaps of the
particles, so that their world
lines in 2 plus 1 dimensional
space-time trace out a braid
in that three-dimensional
space.
And then we can read out the
information at the end by, for
example, bringing the particles
together pairwise
and observing whether they
disappear, whether they
annihilate or not.
And what makes this idea
beautiful is that the
computation is intrinsically
resistant to decoherence.
If we keep the temperature low
so there are a lot of stray
anyons wandering around, if we
keep the anyons far apart from
one another, except at the very
beginning when we create
the pairs and the very end when
we annihilate the pairs,
then there's no way for the
information that's being
processed to leak to
the environment.
And if we perform the
right braid, we'll
get the right answer.
So it's topologically protected
quantum computation.
So that looks pretty
good to a theorist.
But how are we actually going
to build the system that has
such non-abelian anyons that
could be the basis of the
hardware for a quantum
computer?
Well, here we can make use of
another idea which Kitaev and
others have developed, a trick
for cutting electrons in half.
You can think about
it this way.
We can imagine a wire which
is superconducting.
"Superconducting" means the
wire conducts electricity
without any resistance.
And there are really two types
of superconducting conducting
wires, what we call conventional
or ordinary
superconductors and something
called a topological
superconductor.
And at the boundary between
these two types of
superconductivity sits
an object we
call a Mayorana fermion.
What's unusual about a
topological superconductor is
that we can add one extra
electron to this topological
superconductor and that
electron dissolves and
disappears.
In so doing, it actually changes
the state of this pair
of Mayorana fermions
at the edge.
Now, each Mayorana fermion
individually doesn't change in
any perceptible way.
But the pair of Mayorana
fermions does.
And that can be used to store
a qubit of information.
Experiments have been done
to look for this effect.
They are not yet conclusive.
They'll have to be repeated
and made more convincing.
But there are at least
preliminary indications that
this type of a topological
superconductivity in Mayorana
fermions can be realized in
systems that experimental
physicists know how to build now
using semiconductors and
superconductors.
Of course, we'd like to
be able to process the
information by doing some
kind of braiding of
these Mayorana fermions.
And that is in principle
possible.
If we have a network of wires,
we can manipulate the position
of a Mayorana fermion by
adjusting some voltage gates,
which determines where the
boundary is between
conventional and a topological
superconductor.
So I can take one of the
Mayorana fermions and park it
around the corner of a
t-junction, move the first one
over to the left, and then
unpark the other one.
And so if we've achieved an
exchange of two Mayorana
fermions, that would be like an
elementary logic gate in a
quantum computer.
So this type of experiment
hasn't been done yet.
We're hopeful that it
can be done in the
next couple of years.
And that would be a potential
step towards building one type
of quantum hardware.
But apart from any technological
implications, it
would be a real milestone for
physics to realize this type
of exotic topological
interaction between particles
in some system that physicists
can control.
So I've talked about hardware.
I would like to mention that
there are a variety of
different ways of developing
hardware that are under
development, many of which
look very interesting.
And in particular, it's timely
to talk about ion-trap
technology because Dave
Wineland's work in that area
was recognized by the most
recent Nobel Prize in
physics last year.
Wineland and others have, over a
couple of decades, developed
ion-trap technology.
They have the ability to store
individual atoms, which have
an electron stripped off.
So they're electrically
charged.
They're ions.
They can be stored with
electromagnetic
fields for a long time.
And although each one is just
an individual atom, we can
encode a qubit by imagining that
each atom is either in
its lowest energy state, its
ground state, or in some
long-lived, excited state.
And if I want to read out the
state of the qubit, that's
actually pretty easy.
We can illuminate the ions
with laser light.
And if we choose the frequency
of the light suitably, then
the ions will remain dark
it they're in the green
state of the qubit.
If they're in the red state,
they will interact strongly
with the light and fluoresce.
So they'll glow visibly.
And we can read out a series
of 0s and 1s that way, when
we're ready to read out
our quantum computer.
But, of course, we want to do
more than just read out.
We want to be able to process
the information.
So we have to be able
to perform logic
gates on pairs of qubits.
We've got to get the
qubits to interact.
And in this case, we would use
the electrostatic repulsion
between ions for that purpose.
We can do something like this.
I can pick out an ion in a trap
and address it with a
pulse laser, choose the
frequency and duration of that
laser pulse properly so that
if the ion is in the red
state, nothing will happen.
If it's in the green state,
the ion makes a transition
from the green to
the red state.
And at the same time, because
of those interactions, a
vibrational mode of all the ions
in the trap is excited.
And then I can pick out another
ion in the trap and
address it with the pulse laser,
choose the frequency
and duration of that pulse in
such a way that nothing will
happen if the ions are
not vibrating.
But if they are vibrating,
that ion will undergo a
transition from one state
to the other and the
vibration will stop.
So what I've done is
I've picked out
two ions in the trap.
And if the first ion
had been red,
nothing would have happened.
If it's green, then both
ions make a transition.
And so if I start out with a
superposition of red and green
for the first ion, I get a
correlated quantum state, an
entangled pair of qubits
for the pair of ions.
And the quantum computation
would consist of many such
steps, each one an entangling
operation acting
on a pair of ions.
At least that cartoon is the way
a theorist would describe
what goes on in Wineland's
lab.
If you go to his lab at NIST in
Boulder, Colorado and look
around, you're in for
kind of a shock.
Because underlying that cartoon
is a great deal of
technical complexity, which
might make you pessimistic
about the prospects for scaling
up ion traps to
thousands or millions
of qubits.
Well, it's going to be
very, very hard.
Wineland and others have an
idea of how to do it.
But it looks very difficult.
We don't know whether that
will succeed or not.
On the other hand, there are
other ways of realizing qubits
physically, which are making
rapid progress.
One makes use of
superconductivity again, but
in a different way than I
described in the case with
Mayorana fermions.
We can use superconducting
wires to store quantum
information.
And although for practical
reasons this isn't the best
way to do it, and you'll learn
about better ways to do it
when John Martinez is here in
a month or two, you can
visualize how we could store
information by thinking of a
closed loop of superconducting
wire with a
persistent current flowing.
And the current can flow
either clockwise or
counterclockwise around
the hoop.
Those are the two
distinguishable
states of the qubit.
And what's remarkable about
that encoding is that the
information is encoded in a
collective state of billions
of electrons.
And yet, we can treat it like
a single unit of quantum
information and protect it
and manipulate it quite
accurately.
Another possibility is to use a
single electron, which has a
magnetic field, a spin, where
its north pole can be oriented
either up or down.
So that's a qubit.
And what's remarkable about that
encoding is it's just one
little electron.
But yet we can address it,
prepare its state, manipulate
its state, get two such qubits
to interact with a good
accuracy using current
technology.
And both of these technologies
have been advancing
impressively in the last
couple of years.
And there are a number of
others, a number of other ways
that have been proposed and
are under development for
proceeding with building
quantum hardware.
And we just don't know at this
stage which of these is going
to turn out.
Or maybe it'll be none of these
and some other idea that
hasn't been proposed yet.
Each of these technologies has
advantages and disadvantages.
Perhaps the systems of the
future will use hybrid
technologies, where we combine
together different types of
qubits so we can take advantage
of the strong points
of each of these technologies.
No matter how we build the
hardware, we're going to have
to do error correction, as
I described earlier.
And actually the best idea we
have about how to do this
error correction in a reasonably
efficient manner
goes back to these topological
encodings of information that
I mentioned.
The best idea we have is that
if you're going to use ions,
or electron spins, or
superconducting circuits, you
can, by getting such systems
to interact in a prescribed
way, make them behave like these
topological media that I
described, that support
anyons.
And so we can use that
system to store
quantum information robustly.
But that will only work
effectively if our gates are
good enough.
We have to have a low enough
rate of error per gate in
order for these error
correction ideas to
effectively protect a quantum
computer against the damaging
effects of noise.
We would like the probability
of error per gate to be
considerably less than 1% in
order to have reasonably
efficient error correction
schemes.
And the hardware is advancing
and getting into that
interesting regime where we can
do two qubit gates with
the required accuracy
for quantum error
correction to be effective.
So how far do we have to go
before we can build factoring
machines that can really
outperform what can be done
with classical computers?
Well, let's say we want to break
the RSA scheme as it's
usually implemented
these days.
That means we have to factor
a 2048-bit number.
Well, you know you can do that
with a classical computer.
It's just question
of resources.
John Martinez has done these
estimates, which I'm
stealing from him.
If you want to factor a 2048-bit
number, then you just
have to cover 1/4 of the land
area of North America with a
server farm.
Now, that would cost about a
million trillion dollars.
The power requirement would be
about a million terawatts,
which is about 100,000
times the world's
power output today.
The bad news is you have to run
the algorithm for 10 years
to get the answer and it would
consume the world's supply of
fossil fuels in a day.
So what if you tried to do this
with the existing quantum
technology, which Martinez has
been a leader in developing?
Well, we just do it
by brute force.
If we want to factor this
number, we need something like
10,000 logical qubits,
error-free qubits.
In order to achieve that, based
on the types of error
rates that we think are
achievable or nearly
achievable with the current
technology, we would need
about 10 million physical
qubits, keep them far enough
apart so we have lots
of room to cool them
and bring in wires.
And then the current cost,
Martinez estimates, of making
a really good qubit in his
lab is about $10,000.
So we could get these 10 million
physical qubits if we
were willing to spend
a $100 billion.
And then we could run the
algorithm in 16 hours.
It would consume 10 megawatts.
OK.
So actually this is a somewhat
rosier outlook than maybe the
current situation because it's
such a huge engineering
challenge to scale things
out when we don't know
exactly how to do it.
But it indicates that we can
imagine in coming decades that
this can really be a practical
technology.
We've just got to bring
the cost down a
bit, below $100 billion.
And you'll hear more about
that from Martinez.
So there are three questions
about quantum computers than
I've discussed so far.
Why do we want to build one?
Well, for one thing, because
quantum computers would be
able, perhaps, to simulate any
process that occurs in the
quantum world.
That could be important in
chemistry, and material
science, and from a physicist's
point of view, in
simulating exotic physical
phenomenon, that particle
physicists like me, or like
I used to be, care about.
Can we really build one?
Well, we don't know of an
obstacle in principle that
will prevent us from succeeding,
if we use these
principles of quantum
correction, and we can make
the hardware good enough.
And as far as we can tell,
it ought to work.
How are we going to do it?
That's still far from clear.
These different approaches to
quantum hardware that I
quickly summarized for you
are all being developed.
It's important that they
all be developed.
Because we really don't know
which is going to turn out, if
any of them, to be the best
scalable technology.
But you know, I am
not an engineer.
I'm a theoretical physicist.
So I get excited about the
potential ways in which what
we're learning by thinking about
quantum computing can be
applied to problems at the
frontiers of physics.
And there are many applications
of quantum
information processing
to physics.
Many of them have to do with
what we call the monogamy of
entanglement, a difference
between classical and quantum
correlations that I haven't
emphasized so much so far.
Classical correlations
are polygamous.
They can be shared
by many parties.
Adam and Betty both read
the newspaper.
They have the same
information.
They become correlated
with one another.
And nothing prevents
Charlie from
reading that same newspaper.
So now, all three of them
are correlated.
And Charlie is just as strongly
correlated with Betty
and with Adam, as Adam and Betty
are with one another.
And the rest of us in the room
can read the newspaper.
And everybody joins in
on the correlation.
Quantum correlations
are different.
We say they are monogamous.
They are harder to share.
If Adam and Betty are strongly
entangled, if they are fully
entangled, as entangled as
possible with one another,
then neither Adam nor Betty
has the ability to be
correlated with any
other system.
Likewise, if Betty is fully
entangled with Charlie, then
Betty and Charlie cannot be
correlated at all with Adam.
So that's what we mean when
we say the entanglement is
monogamous.
It can be shared two ways.
And that monogamy can be
frustrating because Betty
might want to be entangled with
both Adam and Charlie.
But if she wants to entangle
with Charlie, she has to
sacrifice some of her
entanglement with Adam in
order to do so.
That feature, that monogamy
of entanglement, has many
ramifications.
One is in quantum
cryptography.
If Adam and Betty are nearly
fully entangled with one
another, if they can verify
they are very highly
entangled, for example by
playing Bell's game and
winning, and then they will
know that they have very
little correlation with anyone
in the outside world who would
be a potential eavesdropper.
They can use their entanglement
to generate a
secret key that they share, a
random string of numbers that
Adam has and Betty has, but
which the outside world knows
very little about.
And then with a little bit of
processing, they can amplify
that privacy so that they are
assured that the world outside
knows nothing about their key.
And they can safely use it
to encrypt and decrypt a
classical message.
With information theoretic
security, no attack by the
eavesdropper will succeed in
breaking such a protocol.
Monogamy is very important in
the study of quantum matter.
We might have a system
of many electrons.
And the interactions among the
electron make them want to
entangle with one another.
But if electron A is to entangle
with electron B, then
it's going to give up some of
its ability to entangle with
other electrons in the
system that it
wants to entangle with.
And so the system will have to
arrive at some compromise to
relieve that frustration, that
inability to entangle with
many particles at once to the
best degree possible.
And there are qualitatively
different ways in which the
many-body state can find and
entangled a state of matter,
which correspond to different
phases of matter, that can't
be smoothly changed
one to another.
Classifying the different phases
of quantum matter is
really a problem in
understanding the types of
entanglement that can be shared
by many particles.
And monogamy is also important
in the study of black hole
physics, which has been a
subject that's been quite
active over the last
year or so.
Let me just take a few minutes
to tell you about
what's been going on.
Actually, we've known for a long
time, nearly 40 years,
that black holes, although
classically they are objects
from which nothing can escape,
actually emit radiation
because of quantum effects.
We think a black hole, if it
forms from a collapse of
matter, will eventually
evaporate completely through
this emission of Hawking
radiation.
And normally when systems get
thermalized and behave like
they have some characteristic
temperature and radiate, like
black holes do, we believe
that such processes are
microscopically reversible.
In principle, they could
be run backwards.
Information doesn't really
get destroyed.
But it gets scrambled, put
into a form which is
very hard to decode.
But which, in principle,
can be decoded.
So we think, black holes, like
other quantum systems, ought
not to destroy information, just
scramble it, making it
hard to decode.
But black holes are different
than other systems in an
important way.
They have a highly deformed
geometry, which I've tried to
indicate here in this diagram.
Here, time is running upward.
This black line represents the
event horizon, the boundary
between the outside and the
inside of a black hole.
And this green line is a
slice of constant time,
a space-like surface.
But just think of it as
one particular time.
But because of the distorted
geometry, it has
this unusual shape.
Which means that the collapsing
matter from which
the black hole form, and most
of the outgoing Hawking
radiation emitted as the black
hole evaporates, are at the
same time, cross the single
space-like slice.
And so if information really
comes out of a black hole in a
highly scrambled form, it means
information at the same
time is at two different places,
inside the black hole
and outside.
But remember, I told you that
we can't copy quantum
information.
So we're kind of stuck here.
If black holes don't destroy
information, then it seems
that they are a quantum
copying machine.
That they were able to clone
a quantum state, taking the
information encoded in the
collapsing matter and printing
it in this outgoing
Hawking radiation.
And that caused great
puzzlement.
But for about 20 years, we have
had an idea about how the
situation is resolved, which
is called black hole
complementarity.
It's a kind of crazy idea.
It is that we should not think
of the outside system, the
Hawking radiation, and the
inside system, the collapsing
matter, as two different
parts of a big system.
We should think of them as
two complementary ways of
describing the same system.
There's, so to speak, door
number one and door number two
of black hole physics, two
complementary descriptions of
the same system.
And that's not at all obvious.
And that we actually need to
understand the black holes
better to clarify exactly
why it occurs.
But the idea is that this
isn't really cloning.
It's just we have two
descriptions of the same physics.
One is appropriate for someone
who falls into the black hole,
the description of the
information in
the collapsing body.
The other is appropriate for
someone who stays outside.
That's the information
imprinted
in the Hawking radiation.
This idea of a black hole
complementarity is intended to
reconcile three beliefs
which seem reasonable.
Black holes don't destroy
information.
They merely scramble it.
Secondly, that an observer who
falls through the horizon, the
boundary between inside and
outside of a black hole,
doesn't notice anything unusual
upon entering the
black hole.
Everything seems normal.
Until later on, when the party
will inevitably be torn apart
by very strong gravitational
forces, deep
inside the black hole.
And physics seems perfectly
normal from the point of view
of someone who stays outside
the black hole.
But what has recently been
argued is that these three
things can't simultaneously
be true.
And the problem is this.
That if we consider an old black
hole, which has been
radiated for a long time,
information is starting to
leak out of it we
it evaporates.
That means that the recently
emitted radiation, system B,
has to be highly entangled
with radiation that was
emitted earlier, which
I called system C.
But we also know that if a
freely falling observer,
falling through the horizon,
sees not a lot of particles,
but something that just looks
like empty space, empty space
actually has a lot of
entanglement between and
outside the black hole, B, and
the region inside, A. So this
recently emitted radiation has
to be highly entangled with
the inside of the black hole.
It also has to be
highly entangled
with earlier radiation.
And that's a problem.
Because system B can't be highly
entangled with both A
and C. That violates monogamy.
And so we're really confused
about what this means.
What has been suggested is
that we should give up on
assumption 2, that freely
falling observers don't think
everything is smooth and nice
and normal when they cross
from the outside to the inside
in the black hole.
In fact, there is no inside.
And they just hit a
seething firewall.
The singularity, where you get
torn apart, is actually right
at the horizon.
That's the suggestion which has
been promoted recently.
And it's crazy.
Because if you just solve
the equations of general
relativity to see what the
geometry of a black hole
should be, that's not
what you find.
You find in fact the geometry
should be very smooth as you
cross the horizon.
So we're really confused
about this.
The reason I'm telling you about
it is that this debate
could have occurred
20 years ago.
But it's occurring now I think
because the gravitational
physicists and string theorists
are more accustomed
now to thinking about their
physical systems from the
point of view of quantum
information and entanglement.
And that's a change which is
occurring throughout many
areas of physics.
Physics is a broad subject.
We have the frontier of short
distances, in which we study
the elementary particles and
their interactions; the
frontier of long distances,
the evolution of the whole
universe and the properties
of the early universe.
But there's another frontier,
also very exciting and very
active, which you could call
the complexity frontier or
entanglement frontier, the
study of highly entangled
systems with many parts.
That encompasses quantum
computing, trying to
understand phases of quantum
matter, and all the different
ways in which systems of many
particles can be entangled.
That's an area in which
we can expect great
progress in this century.
At Caltech, we have a center
devoted to the exploration of
this entanglement frontier
from many points of view.
And the IQIM has a slogan, which
is nature is subtle,
where we are playing on
Einstein's famous statement,
"Subtle is the Lord, but
malicious He is not."
Einstein, for all his audacity
and genius, underestimated the
subtlety of nature when he
dismissed quantum entanglement
as spooky action
at a distance.
And what we're trying to do in
quantum information science
these days is to enjoy and
relish and explore and exploit
ultimately the subtlety of the
quantum world and all its
facets and ramifications.
Thanks for listening
to me today.
AUDIENCE: So I remember--
I noticed thinking when you
were talking about how you
have to isolate the material,
the quantum computer, from
outside observation that my
immediate responses, and I
thought as an engineer, was
like man, that's got to be
really tough to debug if
something's going wrong.
So I was wondering so what are
the implications there for how
you would program it?
Do you have to have like a
mathematical proof that your
program is correct?
Because it doesn't seem like
you could examine what it's
doing when it's executing.
JOHN PRESKILL: So the question
is if what I said is true,
that in order for a quantum
computer to work it has to be
completely isolated from the
outside world and we're not
able to look inside at what it's
doing or in the course of
a computation, how would
we ever debug it?
How would we as--
or you as engineers--
manage to figure out how to
fix it when it's broken?
Well, the answer--
I mean I don't think there's
any answer that's
surprising to you.
You would have to, in the
process of developing a
quantum computer, benchmark
different subroutines by
running them and seeing how
well they performed.
You can break it all.
The big computation you can't
simulate with a classical
computer because that's the
whole reason you're building a
quantum computer.
The pieces of a computation,
you can simulate.
You can compare such simulations
to the operation
of the quantum hardware.
Then you can try to scale
up to larger and
larger quantum circuits.
And in cases where you're doing
computations for which
it is easy to know what the
answer is, make sure you're
getting the right answer.
If it's not working, then look
at the individual parts of
that circuit and try to improve
their performance.
And there's no deep
answer to that.
It's just sort of the
obvious answer.
AUDIENCE: You mentioned
earlier that quantum
techniques don't work equally
well on all problems.
Some of them give exponential
speedup, some of them only n
squared, that sort stuff.
I was wondering if you could
give any further intuition on
what kinds of problems fall
into the different?
JOHN PRESKILL: Yeah.
So I think the question is,
I said that there are some
problems that quantum computers
can achieve
spectacular speedups, many
problems for which we think
that's not possible.
And so what's the intuition
about whether a problem lies
in one class or the other
or what's a nice
characterization?
Well, we don't have the complete
answer to that.
I did say that we do not expect
exponential speedups to
be possible for NP-hard
problems.
We think that in such cases
even a quantum computer
wouldn't in the worst case be
able to do much better than a
brute force search.
And they can speed that up a
little bit, but not a lot
compared to classical systems.
So first of all, we're talking
about if we want to stay
within the class NP, where we
can check the answer easily
with a classical computer, about
a rather special class
of problems, which are outside
P. So they're classically
hard, but not NP-hard.
Factoring is a candidate
for being in the
intermediate class.
So other problems which are
outside P, which we think
can't be solved in polynomial
time with a classical
computer, but are not NP-hard,
are candidates for quantum
algorithms.
But that's probably not exactly
the right answer.
And I also tried to emphasize
that we don't have to limit
ourselves to NP.
There are things that quantum
computers could do that we
wouldn't be able to
check classically.
We could check a quantum
computer with another quantum
computer, things like
simulation problems,
simulating quantum systems
with many parts.
And I think the most potential
that we currently know from
our current understanding
of quantum computers for
nontrivial applications involve
such simulation of
quantum systems.
AUDIENCE: Could you say
something about the robustness
of entanglement?
So when you were talking about
quantum computing, it seemed
like entanglement was this
very delicate thing.
And you had to worry about the
decoherence problems that when
two particles interact with
the outside world, the
entanglement is lost.
But with this black hole
problem, it seems like the
entanglement was
indestructible.
And that was why these
three propositions
couldn't all be true.
JOHN PRESKILL: Well,
entanglement is
indestructible, even outside the
context of the black hole
problem, in the sense that if
you have systems that are
entangled with one another,
although they may interact
with the environment, that
doesn't really destroy the
entanglement.
It just means that the
entanglement can now only be
detected if we look at
entanglement between
subsystems that include
the environment.
So the problem is that
we don't control the
environment very well.
So if we look at just the system
that we can control and
don't pay attention to the
environment, then it can
appear that the entanglement
is lost, even though it's
really there.
In the case of the black hole
problem, I was really talking
about this issue of principle,
of whether entanglement is
there or not, not whether it's
there in a form that we can
control or even decode easily.
Which actually is an
interesting question of principle.
Is it a really hard problem to
do the decoding that could
detect this entanglement?
And if it's a really hard
problem, do maybe the laws of
physics tell us that this
entanglement doesn't really
have an operational meaning?
AUDIENCE: So it sounds like it
might be very difficult for
humans to build such
a computer.
Do such computers exist in
natural settings where some
spontaneous result appears
quite naturally, like for
instance in superconductivity
where some physical state is
just emergent from a large
group of particles.
And the way they actually are
doing it is a quantum
computer, but we don't know
how it's happening?
JOHN PRESKILL: Right.
So the question is for humans,
it may be hard to realize
large-scale quantum computers.
Are there ways in which
nature does it?
Are there natural processes in
which quantum computation
occurs, so-to-speak
spontaneously?
Yeah.
I mean it's sort of-- you know
it was hard for us to build a
hydrogen bomb.
But the Sun does it.
In fact, it was hard to build a
fission bomb, but there was
a spontaneous uranium reactor
in Africa because too much
uranium was collected
in one place.
So is quantum computation
occurring by such naturally
occurring process somewhere?
I don't know.
My guess is that if we really
want large-scale quantum
computers, which are hard to
simulate classically--
well, I mean there are lots of
things going on in physics
labs for which that might be a
fair statement, that there are
states of quantum matter.
One famous one is the
high-temperature
superconductors, which we don't
understand very well
microscopically how they work
because haven't so far been
able to simulate them on
classical computers.
So maybe that system is, by
simulating itself, is
performing a quantum computation
in some sense.
Or more broadly, whenever a
quantum system evolves forward
in time, it is in
a sense behaving
like a quantum computer.
But I'm afraid that's probably
too broad a notion of what we
mean by a quantum computer.
My guess is that nature
has a way of
realizing quantum computers.
The way is to allow engineers
to evolve, who build them.
And that's probably the
way nature does it.
GREG KROAH-HARTMAN: Maybe we
conclude it here and thank
John for a beautiful talk.
JOHN PRESKILL: All right.
Thanks for listening.
