(ambient music)
- Good evening, everyone.
I'm Joel Moore,
the interim chair of the
Berkeley Physics Department,
and it is my great pleasure
to welcome you this evening
to the annual J Robert
Oppenheimer Lecture.
Since 1998, Berkeley Physics
has had the opportunity
to bring truly
world-renowned theoretical
physicists to campus
to speak in honor of J Robert
Oppenheimer and his legacy.
This lecture series occurs every spring,
and it highlights trends, discoveries
and groundbreaking research
in theoretical physics,
and it was made possible
through the generosity of
Jane and Robert Wilson.
Before introducing tonight's lecturer,
I would like to say a little bit about
the Berkeley Physics
Department and some news, and
say a little bit more about
Oppenheimer and his legacy
and what he particularly means
in the present time.
To start with, Oppenheimer
was a theoretical physicist
and created the first school
of theoretical physics
in the US at Berkeley.
He came to Berkeley
one year after Ernest Lawrence,
who was maybe the largest figure
in Berkeley's experimental
physics program,
and between them, they turned Berkeley
into one of the best departments
to do physics in the world.
Oppenheimer's achievements in physics,
I would normally tell you a lot about.
These include the
Born-Oppenheimer approximation
for molecular weight functions
and work on the theory of
electrons and positrons,
the Oppenheimer-Phillips process infusion,
and various other things.
I would like to focus tonight
on another aspect of
Oppenheimer's career, which is
what he did after he was at Berkeley.
You may have heard that he
was the scientific leader
of the Manhattan Project,
the project to create the atomic bomb.
And in that capacity, he was
an incredible scientific manager.
And normally, management is
not the most exciting thing
to talk about.
The particular point I would make
is that Oppenheimer put together
an unbelievable collection of talent.
And this is not so much a
scientific thing to me as it is
being able to recognize very smart people
and get them together and
then get out of the way,
I think is Oppenheimer's
great achievement.
And one point I would like
to make about that talent is,
some of it was born in the US,
like Richard Feynman, for example,
but a great deal of it was not.
Much of it was immigrant,
and, of that part, much
of that was refugee.
And I think a great deal
of America's leadership
in post-war physics came
to that Manhattan Project,
came from that Manhattan
Project generation.
And that's why if you try
to talk with physicists
about politics, you'll get
widely different opinions.
Even with Oppenheimer, you
will get different opinions on,
was Oppenheimer sufficiently
careful about security?
Was the atomic bomb a
worthwhile exercise, and so on.
Physicists are very
capable of disagreeing.
You will very rarely hear a physicist say,
in fact, never in my experience,
that American physicists
have not benefited greatly
from international collaboration
and from people coming
from other countries,
and I think that's
probably worth remembering.
So, Oppenheimer's progress as the father,
the founding father
of the American School
of Theoretical Physics
was to ask,
what a talk was about,
or what a piece of physics was about,
what was learned by it,
and what were the remaining
unsolved problems,
and we continue to ask
those same questions,
and that's the theme of tonight's lecture.
So, as I mentioned, the
Oppenheimer Lecture we've had
since 1998, and it's become
a very nice tradition
in our physics department,
and there are new things
happening that I believe
will last at least as well
and become new traditions,
and I wanted to call your
attention to a couple of those.
One is, tonight is a night for theory,
but we have created a
new experimental program
at the undergraduate level, Physics 5,
with a beautiful new laboratory
that I think is going to make Berkeley,
if it isn't already,
the best place to learn
experimental physics as an
undergraduate in the world.
We have a new center for
quantum coherence science,
which is actually very connected
to the kind of work that
you'll hear about tonight.
It's very much in the same theme,
that certain fundamental ideas
of quantum mechanics unify
a vast number of different
areas of physics.
So that's one of our main priorities
in research at the moment.
And then lastly, in order to
link physics with the outside world
in the same way that Oppenheimer did,
we have a new industrial
partnership program,
called Berkeley Physics Partners, or BP2,
and I would be happy
to talk with you about
any of these things,
but I think, with that, let me move on to
a little bit more about science
and the Oppenheimer Lecture, and
our distinguished guest
tonight, Professor Preskill.
So, Oppenheimer lecturers,
since 1998, have included
six Nobel laureates
and distinguished figures
from all areas of theoretical physics,
ranging from astrophysics,
to condensed matter,
to cosmology,
to atomic and molecular physics.
Tonight, we have an
unusually broad speaker
in that Professor Preskill's lecture
on quantum computing and
the entanglement frontier
will take us on a journey
into quantum entanglement
and the various aspects of
physics that it unifies.
So, Professor Preskill comes to us
from the California
Institute of Technology,
better known as Caltech.
He is the Richard P Feynman professor
of theoretical physics there,
and he's also director of The Institute
for Quantum Information
and Matter at Caltech,
and that institute, which has
existed for quite some time now,
I believe it started in 2000,
was one of the first to
recognize that notions
of quantum information are very powerful
in linking the work of physicists
in different disciplines.
Getting back to Professor Preskill,
he received his PhD in
physics in 1980 from Harvard
and moved rather quickly
to Caltech in 1983.
He is a member of the National Academy.
He is a two-time recipient
of the Associated Students
of Caltech Teaching Award.
He's mentored more than 50 PhD students
and more than 45 postdoctoral
scholars at Caltech,
and many of those,
a few of those are here, I believe,
and many of those have
gone on to be leaders
in their research areas.
So if I had to pick a few
sentences to sort of summarize
the theme of his research,
at least since 2000 or so,
he's especially intrigued
by the ways that our
deepening understanding
of quantum information
and quantum computing
can be applied to other
fundamental issues in physics,
such as the quantum
structure of space and time.
Aside from his research papers,
his celebrated lecture notes
from his Caltech course
on quantum computation,
which, by this time, includes
a great deal of things
that I wouldn't necessarily
call computation,
they've exerted a profound influence
on the development of the subject.
And I would say that Caltech has become
one of the leading centers
for theoretical research
on quantum information
and quantum computing.
Our own center for quantum
coherence science has
a different emphasis in some ways,
it's based on what Berkeley leads in,
but it's fair to say that one of our
intellectual progenitors
in setting up this new center was
what's been done at Caltech.
So, Preskill has been described as
less weird than a quantum
computer and easier to understand.
I agree with the second part,
and the first, I'll reserve
judgment until after the talk,
but we are thrilled to
add Oppenheimer lecturer
to his very long list of accolades.
Please join me in welcoming
Professor John Preskill.
(applause)
- Thank you very much, Joel, for the
beautiful introduction.
And I'm deeply honored to be here
to carry on the tradition
of the Oppenheimer Lecture
and to join the roster of
great scientists who
have preceded me here.
I'm going to be talking
about quantum physics,
but also about information.
Everybody knows that
information technology has had
a huge impact on our everyday lives,
but we also recognize that
information technology
that seems impressive to us
today is going to be surpassed
in the future by new technology
that we can't really
expect to imagine today.
It's interesting just the same
to speculate about future technologies,
and I may not be the
ideal person to engage
in that type of speculation.
I'm not an engineer, I'm
a theoretical physicist
and I can't really claim to
be deeply knowledgeable about
how computers really
work, but as a physicist,
I do know that the crowning
intellectual achievement
of the 20th century was the
development of quantum theory,
and it's natural for a
physicist to wonder how
the development of
quantum theory in the 20th century
will impact 21st-century technology.
Quantum theory is, of course,
an old subject by now,
but some of the deep ways
in which quantum systems
are different from classical systems
we've only come to appreciate
relatively recently.
And a lot of those differences have to do
with the properties of information
encoded in physical systems.
To a physicist, information
is something we can encode
and store in the state
of a physical system,
like, for example, the pages of a book,
but fundamentally, all physical systems
are really quantum systems
governed by quantum mechanics,
and so information is something
that we can encode and store
in a quantum state.
And physicists have
appreciated, for a long time,
that information carried
by quantum systems
has some notoriously
counterintuitive properties.
That's why we like to
speak about the weirdness
of quantum theory,
and we relish that weirdness and
find great enjoyment in it.
But we're also starting
to ask more seriously
in recent years whether it's possible
to put the weirdness to work
to exploit the 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 derives much of
its intellectual vitality
from three central ideas,
which are quantum entanglement,
quantum computing,
and quantum error correction,
and my goal in the talk
is to introduce you to these ideas.
I'd like to start at the beginning.
We all know that any amount of
digital classical information
can be expressed in terms
of indivisible units,
bits of information,
and we might think of a
bit as a physical object,
like a ball, which can be
either one of two colors.
Now if I want to, I can store a bit
inside a box,
and then later on, if I
want to recover the bit,
I can open the box, and
the color that I put in
comes out again, so I can
read the bit accurately.
And when I speak of quantum
information, what I mean is
information carried in a quantum system,
and it, too, can be expressed in terms
of indivisible units,
what we call quantum bits,
or qubits for short.
And for many purposes,
it's useful or instructive
to envision a qubit as an
object stored inside a box.
Where we're now, we have the
option of opening the box
through two complementary doors,
which correspond to two different ways
in which we can prepare or observe
the state of the qubit.
And you can put information
in door number one of the box
or door number two, and if, later on,
you open that same door again,
the color ball that you put
in comes out again,
just as though the
information were classical.
But if I put information into a qubit
through door number one, for example,
and then later on, I observe the qubit
through door number two,
observe it in the complementary way,
then no one can predict what we'll find.
There's a 50% probability
that the ball is red
and 50% that it's green.
So if you want to read
quantum information,
you have to do it the right way.
If you do it the wrong way,
then you will unavoidably
damage the information.
And one consequence of
that we can appreciate,
if we think about copying a quantum state.
If I had a quantum copy machine,
that would mean that if I happen to have
put information through door
number one of our qubit,
I can make a copy of the qubit,
and then if I open the
original and the copy
through door number one,
then the color ball that I put in would
come out of both boxes.
And likewise, if I happen
to have put information
in door number two of the original Qubit,
once I build a copy, I
could open door number two
on the original and the duplicate,
and the color that I put in
would come out of both boxes.
But, in fact, no such quantum
copying machine is possible.
It's not allowed by the laws of physics.
We can't make high-fidelity copies
of unknown quantum states.
And the reason why not is that
in order to make the
copy, the copy machine has
to probe inside the box,
and if it guesses right and
uses the same door that I did,
then it will be able
to copy the information
just as though it were classical,
but if it guesses wrong
and opens the wrong door,
that will damage the information
and there won't be any way
to build a high-fidelity copy.
So although we might be
able to clone a sheep,
we can't clone a qubit.
Now I've described qubits
in an abstract way,
which I think is a useful
way to think about them,
but a qubit always has
some physical realization,
and I'll give a few other examples later,
but just so you'll have something concrete
to think about.
We could consider, for example, the qubit
to be a polarization state
of a single particle of light, a photon.
A photon has an electric
field, and if it's oriented
either horizontally or vertically,
that corresponds to looking
through door number one of the box,
and if the polarization is tilted
to the 45-degree rotated axes,
that corresponds to door number two.
So, for example, we could make a
horizontally polarized
state of a single photon
and observe it through the tilted axes,
and what we would generate
is just a random bit.
But the really interesting ways
in which quantum information
is different from classical information
we can only appreciate
if we consider states
of more than one qubit.
So let's imagine we have two qubits,
and they could be far
apart from one another.
One at Caltech in Pasadena,
the other in the custody of my friend
in the Andromeda Galaxy.
And some time ago, these two
qubits were both on earth
and they interacted in a
certain way that prepared
a correlated state of the two qubits
which has some unusual properties.
Namely, I can open my box in Pasadena
through either door number
one or door number two,
and either way, what I
find is just a random color
with the 50% probability of
being either red or green,
and the same thing is true
for my friend in Andromeda.
He can open the box through
either door number one
or door number two
and just finds a random bit.
So neither one of us
finds any information in the boxes
by opening a box in Pasadena or Andromeda,
which seems kind of funny,
because with two boxes,
we should have been able
to store two bits of information.
But where has that
information been hidden?
The answer in this case is that
all the information is actually
encoded in the correlations
between what happens when
you open the box in Pasadena
and when you open it in Andromeda.
Because it turns out, for this
particular correlated state
of the two qubits,
if I open door number
one, what I find might be
red or green, but if
my friend in Andromeda
also opens door number one for
that particular qubit pair,
he's guaranteed to find
the same color that I do.
And the same thing is true if
we both open door number two.
As long as we open the same door,
we're guaranteed to find the same color.
And there are four perfectly
distinguishable ways
in which a box in Pasadena
could be correlated
with a box from Andromeda.
We could see that the same
color or opposite colors
when we both open door number one
or both open door number two,
and by choosing one of those four ways,
we've encoded two bits of information
in our pair of qubits.
But what's unusual in this
case is that that information
is completely inaccessible locally,
it's a property stored non-locally,
shared by the two
distantly separated qubits.
And this property, that
information can be shared
non-locally between
distantly separated objects
is what we call quantum entanglement,
and it's the really important way
in which quantum information
is different from classical information.
Correlations themselves
are nothing unusual.
We encounter them all
the time in daily life.
My socks are normally the same color.
So if you look at my left
foot and observe my sock,
then you know, without looking,
what color you expect when
you look at my right foot.
And it's kind of like that
with the quantum boxes.
If I want to know what my
friend is going to see when
he opens door number one in Andromeda,
I can open door number one
in Pasadena to find out.
And if I want to know what
he'll see when he opens
door number two in Andromeda,
then I can open door number
two in Pasadena to find out.
So it might seem to you that
it's really the same thing
that the boxes are just like the soxes,
but I claim that, in fact,
they're fundamentally different.
The boxes are not like the soxes,
and the essence of the difference is
there's just one way to look at a sock,
but because we have these
two complementary ways
of observing the qubit,
the correlations among qubits are richer
and more interesting
than the correlations among ordinary bits.
This phenomenon of quantum
entanglement is an old subject.
It was first explicitly discussed
in a paper by Einstein,
Podolsky, and Rosen in 1935.
And to Einstein, entanglement
was so unsettling
as to indicate that something is missing
from our current understanding
of the quantum description of nature.
And that paper elicited
some thoughtful responses,
including a particularly
interesting one from Schrodinger.
The way Schrodinger put it was,
"The best possible knowledge of a whole
"does not necessarily indicate
the best possible knowledge
"of its parts."
What Schrodinger meant was
that even if we had the most
complete description that the
laws of physics will allow
of a pair of qubits,
we're still powerless to
predict what we'll find
when we open door number
one or door number two
of one of those two qubits.
And it was Schrodinger who suggested
using the word entanglement
to describe these unusual correlations.
He also said, "It is rather 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."
And what Schrodinger
meant is it seems funny
that it's up to me to decide,
by either opening door
number one or door number two
in Pasadena, whether
I'll know what my friend
will find when he opens door
number one or door number two
in Andromeda.
But Schrodinger understood
that these correlations,
though different from
ordinary correlations,
don't allow us to send
an instantaneous message
from Pasadena to Andromeda.
When my friend in Andromeda opens his box,
he just finds a random bit,
and the probability distribution
governing what he finds
is not affected by what I
choose to do in Pasadena.
So no message is sent from
one party to the other.
Now this theory of quantum
entanglement really
didn't advance very much
for the next 30 years,
until the work of John Bell in the 1960s.
And beginning with Bell,
we started to think
about entanglement in
a rather different way,
not just as something weird,
unsettling, and surprising,
but as something potentially useful;
a resource that we can
use to perform tasks
that wouldn't otherwise be possible.
We don't have to go into the details,
but what Bell described
can be thought of as a
game that two players play.
Alice and Bob, it's a cooperative game.
Alice and Bob are on the same side.
They're trying to help each other win.
And the way the game works
is that Alice and Bob receive inputs,
and their task is to
produce outputs which are
correlated in a way that
depends on the inputs
that they both receive.
But under the rules of the game,
Alice and Bob are not
allowed to communicate
with one another between
when they receive the inputs
and when they produce their outputs.
And for this particular
version of the game,
if Alice and Bob played
the best possible strategy,
they'll be able to win the game with a
success probability of 75%
if we average uniformly over the inputs
that they could receive.
But there's also a quantum
version of this game,
where the rules are exactly the same,
except that, now, Alice
and Bob are allowed
to use entangled pairs of qubits
which have been distributed
to them before the game began.
And with those short
qubits, they can play a
better quantum strategy,
which allows them to win the game
with a higher success probability,
about 85% rather than 75%.
So they can use entanglement as a resource
to perform a task winning the game
better than they could using just
classical correlations that they share.
And experimental physicists
have been playing this game
for decades now, and
winning with the higher
probability of success,
which Bell pointed out,
the laws of quantum mechanics will allow.
So it seems that the
super strong correlations
really are part of nature's design.
Einstein didn't like quantum entanglement.
He called it spooky action at a distance.
This sounds even more derisive
when you say it in German.
But it doesn't even matter
what Einstein thinks.
Nature is the way
experiments reveal her to be,
and we should all learn
to love her as she is.
So, boxes are not like soxes.
Quantum correlations are
different from classical ones.
You can use them to win a game with an 85%
success probability instead
of a 75% success probability.
Is that a really big deal?
Yeah, it's really a big deal.
And we can appreciate
better why it's a big deal
if we think about more complex
systems with more qubits.
We can think about quantum
entanglement this way.
Imagine a book that's 100 pages long.
If this were an ordinary
book, written in bits,
you could read the pages one at a time,
and every time you read another page,
you'll know another 1% of
the content of the book,
and after you've read all 100 pages,
you know everything that's in the book.
But suppose it's a quantum
book, written in qubits,
and suppose the pages are highly
entangled with one another,
then when you look at
the pages one at a time,
all you see is random gibberish,
revealing almost no
information that distinguishes
one highly entangled book from another.
And that's because the
information in the quantum book
is not written in the individual pages.
It's stored almost entirely
in the correlations
among the pages.
That's quantum entanglement.
And these correlations can be very complex
and are hard to describe
in terms of classical bits.
So, for a modest number of
qubits, just a few hundred,
if I wanted to give a
complete description,
in classical language,
of all the correlations
among 300 qubits, I
would have to write down
more bits than the number of
atoms in the visible universe.
So it'll never be possible,
even in principle,
to write down that complete description
of all the correlations.
And that property of quantum information
is very intriguing to the
physicist, Richard Feynman.
They'd let him make the
suggestion in the early 1980s
that if we could build
a computer that operates
on qubits instead of
bits, a quantum computer,
we'd be able to perform tasks that are
beyond the reach of any
conceivable digital computer.
Feynman's idea was that
if we can't even express,
in terms of ordinary bits,
the information content
of a few hundred qubits,
then by processing the
qubits, we ought to be able
to perform tasks that a digital computer
would never be able to emulate.
And at the time Feynman
was making this suggestion
in the early 1980s, there was
an undergraduate at Caltech
studying mathematics.
Like all of our undergraduates,
he studied quantum physics
as part of our core curriculum.
And like most of our undergraduates,
he retained what he learned
and later put it to good use
when he made a remarkable discovery.
Shor thought about the problem
of finding the prime factors
of a composite integer.
This is a problem which we think is hard
for classical computers,
though there's no
mathematical proof of that.
And what Shor found is that
if we had a quantum computer,
the factoring problem would be easy.
It wouldn't be much
harder than multiplying
two numbers together
to find their product.
And when I heard about this
in 1994 when Shor made the discovery,
I was really awestruck,
because what it means
is that the difference
between hard and easy problems,
the difference between problems that
we'll be able to solve some
day with advanced technologies
and the problems that we'll
never be able to solve
because they're just too hard,
that that boundary between hard and easy
is different than it otherwise would be
because this is a quantum
world, not a classical world.
And I thought that was one
of the most interesting ideas
I had heard in my scientific life,
and thinking about it eventually led me
to change the direction of my own research
from elementary particle
physics to quantum computing.
Now does anybody care whether
factoring is a hard problem?
Yeah, in fact, a lot of people care,
because the security of the
protocols that we use everyday
to protect our privacy when we
communicate over the internet
are based on the presumed hardness of
factoring and other similar
number theoretic problems.
And in a few decades, when
everybody has a quantum computer,
we won't be able to protect our privacy
using these protocols.
We'll have to do something else.
Alternatives exist,
but it's still not exactly clear
what will be the best
way to protect privacy
in the coming post-quantum world.
The important thing that we
learn from Shor and others
is that there is an interesting
classification problem,
classification of problems,
that there are problems
that are hard classically
and quantumly easy.
Can't be solved by
ordinary digital computers,
could be solved if we
had quantum computers,
and it becomes a compelling
research question
to understand better
what are the problems which are
of such intermediate difficulty.
And we've learned
a lot of things about
that in the last 20 years,
but I think the most
important thing we know,
from a physicist's point of
view, about quantum computers
is that we think that we
can't say this for sure,
but with a quantum computer, we'd be able
to simulate efficiently any
process that occurs in nature,
which isn't the case
with digital computers, which are unable
to simulate highly entangled systems.
And that means with a quantum computer,
we'd be able to explore
physics in new ways.
For example, by simulating
strongly coupled field theories,
we'd be able to compute the
properties of complex molecules,
study exotic quantum materials,
and study fundamental processes,
like the formation and
evaporation of a black hole
or the properties of the universe
right after the big bang.
So a lot of people work
on developing applications
for quantum computers
even though we don't have
large-scale quantum computers yet.
One of them is my friend, Eddie Farhi,
who, like me, is a lapsed
particle physicist,
and when he wrote one of his
billion papers a few years ago,
it inspired me to send him a poem,
which read, in part, "We're
very sorry, Eddie Farhi.
"Your algorithm's quantum.
"Can't run it on those mean machines
"until we've actually got 'em."
And the poem goes on, but the point is
that we have a lot of interesting ideas
about what to do with quantum computers,
but we don't have quantum computers yet
that can run those applications.
So why not?
What is it that's taking so long?
Well, it's really hard to
make a quantum computer.
And one of the difficulties
is the phenomenon we call decoherence.
Physicists like to imagine
a quantum state of a cat,
which is simultaneously dead and alive.
And we never observe,
in everyday experience,
that type of superposition
of macroscopically distinguishable
states of a system.
And we understand the reason why not.
It's because no real cat
can be perfectly isolated
from its surroundings.
And the interactions with
the environment, in effect,
immediately measure the cat,
projecting it onto a state,
which is either completely
dead or completely alive.
That's the phenomenon of decoherence,
and decoherence helps us to understand why
even though quantum physics holds sway
at the microscopic scale,
still, classical physics is quite adequate
for describing most of the processes
of our everyday experience.
A quantum computer won't be
otherwise much like a cat,
but it, too, will be hard
to perfectly isolate
from its surroundings.
And interactions with
the environment can cause
the quantum information
stored in a quantum computer
to be damaged,
and that will cause the
computation to fail.
So if we're going to operate a
large-scale quantum computer,
we have to figure out how to protect it
from the damaging effects of decoherence
and other sources of error.
Errors can be a problem, even in the
classical world, we all
have bits that we cherish,
but everywhere there
are dragons lurking, who
take pleasure in damaging our
bits, flipping their color.
We learn, in the classical world,
some ways to protect our information.
The important concept is
that we can redundantly
encode the information so that
if it's partially damaged,
we can still recover the information.
So if I want to store a bit,
which is one that I cherish,
I can store backup copies of the bit,
and then a dragon might
come along from time to time
and change the color of one of the balls,
but I can also ask a busy beaver
to frequently check the balls,
and whenever she sees that
one's a different color
from the other two, she repaints it
so all three match again.
So unless the dragon has had a chance
to damage two out of the three balls,
the information is well protected
because of the redundant storage.
Now we'd like to use the same idea
that redundancy provides
protection for quantum states.
But at first, there seem
to be difficulties because,
as already discussed, we can't
copy unknown quantum states.
So I can't, for example,
make a backup copy
of the state of a quantum computer
in the middle of a computation
in case my original gets damaged.
And furthermore, with
the quantum computer,
there are more things that can go wrong
with the information.
It might be that a dragon opens
door number one of the box
and flips the color of the
ball and then recloses the box.
That would be like a bit flip
that occurs for classical information.
But instead, the dragon
could open door number two
and change the color of the
ball and reclose the box.
That's what we call a
phase error on a qubit,
and it really has no classical analog.
We need to be able to protect
against both the bit flips
and the phase errors
to make sure our quantum
information is undamaged.
There's another way of thinking
about these phase errors,
which is we might imagine that the dragon
opens door number one, and instead
of flipping the color of the ball,
just observes the color and remembers it.
It never had the effect
of changing the color,
as observed through door number two.
And in many physical settings, it's easier
for the environment to
remember the state of a qubit
than to flip the qubit,
and that makes phase errors
particularly pervasive
in some physical settings.
So the key thing is that
if you look at quantum
information, you disturb it,
and so if we want to
protect quantum information,
we have to keep it
almost perfectly isolated
from the environment.
So there's no leakage of information
about the state of our quantum computer
to the outside world.
And that sounds impossible
because our hardware
will never be perfect.
So how can we perfectly isolate
a quantum computer from the outside?
But we learned, in principle, how to do it
through the concept we call
quantum error correction,
and the essential trick
is to use entanglement
to protect the information.
So if I have one qubit
that I want to protect,
I can encode that one qubit of information
in an entangled state of five qubits,
which is chosen in such a way
that if the dragon comes along
and observes or performs any action
on one of the five boxes,
that dragon doesn't
acquire any information
about what the encoded state is.
Because the information doesn't reside
in that individual box,
it's a collective property
of the five qubits.
It's just like that 100-page book.
When you look at one of
the qubits at a time,
the information is completely hidden.
And so it's possible
then to ask the beaver,
after the dragon has
acted on one of the boxes,
to make some collective observations of
the five qubits and restore the right kind
of the entanglement.
And, in the process, the
beaver doesn't learn anything
either about the protected encoded state,
and so that state can be undamaged.
So the basic idea of quantum
error correction is that
we can use redundancy to
protect quantum states,
but we have to do it the right way,
and the right way to do it
is to encode the information
in the form of entanglement
among many parts of the system.
So just like that 100-page book, which
reveals no information when
you look at one page at a time,
the environment will interact locally
with the parts of the
system one page at a time,
and, in doing so, won't be able to detect
the encoded information or damage it.
And we've also learned how to process
information which is encoded
in this entangled form,
and so operate a robust quantum computer,
at least in principle.
So, although we may never see a real cat
in a superposition of
the dead and alive state,
we should be able to prepare
an encoded state of a cat
and maintain it in that
delicate superposition state
for as long as we please.
Well, we understood these principles
of quantum error correction
about 20 years ago.
We were very excited.
And so my then-student, Daniel Gottesman,
wrote a sonnet.
And I'll just read the beginning of it.
"We cannot clone,
perforce; instead, we split
"coherence to protect it from that wrong
"that would destroy our valued quantum bit
"and make our computation take too long."
And so on.
The point is we were excited,
because we had understood
that, at least in principle,
we could make a quantum computer resistant
to the effects of noise and decoherence.
Now another hero of this story
is my Caltech colleague, Alexei Kitaev.
The day when we met, which
was about 20 years ago,
was one of the most exciting
days in my scientific life.
When I heard his seminar
and took these notes,
I thought that I was hearing, from Kitaev,
ideas about quantum error correction
which are potentially transformative.
And what I learned from him
was the connection between
quantum error correction and topology.
Topology means the properties
of a mathematical object
which remain invariant when
we smoothly deform the object
without ripping or tearing it.
And when we think of operating
a robust quantum computer,
what we want is for the
protected information
that's being processed to remain invariant
even as we deform the computer
by introducing some noise.
So we would like to use interactions
which take advantage of
topological principles
for the purpose of information processing.
And physicists now have such
topological interactions.
For example, the Aharonov-Bohm effect.
I can imagine transporting
a charged particle,
like an electron, around
a magnetic flux tube.
And then the quantum state
of that electron is modified
in a way that depends
on the magnetic flux,
which is enclosed in the
tube even though the electron
never directly visits the region
where the magnetic field is non-zero.
And that change, that interaction
is a topological property.
If we deform the trajectory
of the electron,
the effect of circling the
flux tube doesn't change,
the only thing that matters
is the topological property,
the winding number of the electron
around the flux tube.
Now if we can engineer
two-dimensional systems,
for example, in a layer
separating two slabs of semiconductor,
then there's a very rich family
of possible topological
interactions that can be realized.
In these systems, if properly designed,
we can have what we call anyons.
And anyons have the interesting property
that if I have a system of
many of these particles,
that the quantum information
carried by the particles
can be very complex,
but when we visit the
particles one at a time,
that information is completely invisible.
Because it's not a property
of the individual particles,
but a collective property
of all the particles.
And that's just the type
of encoding of information
that we want to protect against noise.
That information will be well hidden
from the influence of the environment.
And furthermore, we can
process the information
by performing exchanges of the particles
in which they swap places.
So we can imagine operating a
topological quantum computer,
which we would initialize by
in some two-dimensional medium,
preparing pairs of anyons,
then processing the
state of those anyons by
successively exchanging pairs of particles
so that their
world lines in
two-plus-one-dimensional spacetime
trace out the braid,
and then we could read out a final result
say by bringing the
particles together in pairs
and observing whether the
pairs of particles annihilate
and disappear or not.
So what's beautiful about this idea
is that, in principle, we can do
any computation we want this way,
and the computation is
intrinsically resistant
to decoherence if we keep
the temperature lower
so we have no unwanted
anyons diffusing around,
and if we keep the particles
far apart from one another,
except at the very
beginning and the very end
so there's no unwanted exchange of
charges between the particles,
then as long as the world
lines execute the right braid,
then we'll do the right
computation and get
the right answer.
So I really like this idea,
which led me to write a poem about it.
And I won't read you the whole thing,
but part of it reads this way.
Alexei exhibits a knack
for persuading that someday
we'll crunch quantum data by braiding,
with quantum states hidden
where no one can see,
protected from damage through topology.
Anyon, anyon, where do you roam?
Braid for a while before you go home.
And there's more to it than that,
but the point is,
it's a really beautiful, exciting idea.
But it's a theorist's dream,
and it's something that
we can really realize
in hardware that can be built.
Well, here, too, Kitaev
had a seminal idea,
which is to use the principle
that, under the right circumstances,
we can divide an electron in half.
That sounds ridiculous
because we know an electron is
a fundamental elementary
particle and it's indivisible,
but in a highly entangled environment,
in the right kind of
two-dimensional medium,
electrons can split into pieces,
and anyons can arise that way.
Here's one relatively simple setting
in which that can happen, actually.
In a one-dimensional wire,
it's possible for the wire
to be superconducting.
That means it conducts electricity
without any resistance.
And there are two types of superconductor:
what we might call the conventional type,
and a more exotic type,
called the topological superconductor.
And at the boundary between the two types,
there resides an object
that we call a Majorana fermion.
And now it's possible
to add a single electron
to this finite segment of
topological superconductor,
and that electron will,
in effect, dissolve and disappear.
So we can't tell whether
it's been added or not.
But in the process, the state
of these two Majorana fermions
at the two end points of the
segment will have changed.
But that change in the state
of the Majorana fermions
is not locally visible;
we can't see it if we visit
the endpoints of the
segment one at a time.
It's a collective property of the two.
So that's the type of non-local
encoding of information
that we want to protect against
errors in a quantum system.
And this type of Majorana fermion
in a superconducting wire,
well, we have some very
interesting evidence that it can be
realized experimentally, more
experiments will be needed
to make that case completely ironclad.
Of course, we'd like to be
able to do more than just
store information reliably,
we'd like to be able to process it.
And using quantum wires,
one way to do that would be
to build a network of wires
so that if I had two Majorana fermions,
I would be able to change their positions,
let's say with voltage
gates underneath the sample,
so that one Majorana
fermion could be parked
around the corner,
the other move from right to left,
and then the first one unparked,
and that would perform an exchange
of the positions of the two particles,
which would be a kind
of quantum operation,
one step in a quantum computation
which is protected from decoherence.
That type of experiment
hasn't been attempted yet,
but I expect it will be in
the next couple of years,
and when done successfully,
that will not just be an interesting step
towards a future technology,
but a real milestone
in basic physics.
Now I don't want to give
the impression that this
exotic topological
approach is the only way
that we can build large-scale
quantum computers.
No, that's not at all the case.
There are a number of ways
of building quantum hardware,
which are currently being developed
and are making impressive progress.
I already mentioned one
way of encoding a qubit
using the polarization
state of a single photon.
There are a number of other ways.
One is we could store our qubit
in the state of a single atom, which
could be, say, in either
its internal ground state
or some long-lived metastable state
corresponding to the
two states of the qubit.
Or we could encode a qubit
in a single electron,
which has a magnetic moment, or spin,
which could be oriented either up or down.
So these are two remarkable encodings,
because in each case, we are encoding
the information which is to be processed
in a truly microscopic system,
either a single atom or a single electron.
Another possibility, though, is
to use superconducting circuits,
not the exotic
topological type that I
just mentioned a minute ago,
but conventional superconductors,
where, although, in practice,
there are better ways of doing things.
You could imagine encoding a qubit
by choosing a state in which this
current in the circuit
either circulates clockwise
or counterclockwise.
That's a remarkable encoding, too,
because, in this case,
the qubit involves the collective motion
of billions of electrons,
and yet, for information
processing purposes,
it behaves like a single atom or electron
and can be quite well-controlled.
We're not far away.
I expect, in the next couple of years,
we will have quantum computers
with more than 50 qubits,
and these will be systems
which are sufficiently complex
that we can't simulate
them with digital computers
that exist today.
So this will be in the onset of the age of
quantum supremacy,
in which quantum systems
are performing tasks
that go beyond what we can
achieve in the classical world.
And I think we should
view that as the opening
of a new frontier in
the physical sciences,
what we could call the
complexity frontier,
or entanglement frontier.
This is different from the frontier we
explore in particle
physics at short distances,
or in cosmology at long distances,
but, like those, very
fundamental and exciting,
and, like those,
in order to make advances, we
need more and more powerful
instruments.
We are now
in the process of developing
and perfecting the ability
to prepare and precisely control
highly entangled states of many particles,
which go beyond what we can simulate.
We don't have the
theoretical tools to predict very well
the behavior of these systems,
and that's going to open new
opportunities for discovery.
What are the things that
we'll be able to do with a
quantum computer,
which we hope we'll have
in a couple of years,
with 50 to 100 qubits?
Well, maybe one of the most
important things is we'll use
these smaller quantum computers
to learn how to make rather
big quantum computers,
in particular, by testing and perfecting
our procedures for doing
quantum error correction.
But we'll also be able to run, at
relatively small scales, new
kinds of algorithms, which
will already surpass what we
can do with digital computers,
study certain quantum simulation problems,
for example, to investigate
quantum chaos in new ways,
or to simulate complex
molecules going beyond
what we can do classically.
But once we have quantum
computers that we can
try out and play around with,
I expect we'll discover
a number of new applications
which we haven't anticipated.
Now how far off is it that we'll have
scalable quantum computers that can,
for example, break the RSA
public-key cryptosystem?
Oh, that's farther away,
perhaps decades.
You know, I said earlier that
you can't solve this problem
using digital computers,
but that's not strictly true,
it's just a question of resources.
So if you wanted to break RSA
as it's typically used today,
it's possible, but you would have to cover
about a quarter of the land area of
North America with a server farm,
and then you'd be able to
solve the problem in about
10 years,
but the catch is that, with
existing computing technology,
the power consumption would burn up
the world's supply of fossil
fuels in just one day.
So, from that perspective,
the quantum computer looks pretty good.
If we just took the technology
we have today and sort of
brute force scaled it up, it's
not quite as simple as it sounds,
but suppose we did that,
and this estimate was done
by John Martinis, who's a
experimentalist who works
in superconducting qubits,
well, in order to have
sufficient redundancy
to do error correction,
we'd probably need about
10-million physical qubits,
and then we'd be able to
run the algorithm that
factors a number and breaks
RSA in less than a day,
and the power we would
need is just 10 megawatts.
The thing is, at the current cost of
making a very good qubit,
it would cost 10s of billions of dollars.
So, the cost is gonna have
to come down, and it will.
So there are three questions
about quantum computers
that I've been emphasizing.
One is, what will we do
with quantum computers?
Why build one?
And I think the best
answer we have to that
is that, with a quantum computer,
we'd be able to simulate, we think,
any process that occurs in nature,
which we can't do with
digital computers, which are
unable to simulate
highly entangled systems.
Can we really build one?
Well, we know of no
insurmountable obstacles
to doing so now that we
understand the principles
of quantum error correction.
And how will we do it?
Well, as I've emphasized, there
are a number of approaches
to building quantum hardware that are
under development and
making good progress.
And it's important to continue
those different paths because
different quantum technologies may find
different applications,
and we don't really know which technology
will ultimately have the best
prospects for scalability
to large devices.
What I really find interesting
is the ways in which our
ideas about quantum computing
are giving us new approaches
to some of the other
fundamental problems in physics,
particularly quantum
condensed matter physics,
and also elementary particle physics.
There's been a surge of
interest in recent years
among the community of people who work
on quantum field theory
and quantum gravity
in quantum information concepts.
These people feel that
quantum information ideas
are highly relevant and useful
for addressing the problems
that they're interested in.
And in a way, that's not so surprising,
because the quantum gravity
community has been struggling
for 40 years with a very deep puzzle,
whose origin really has to
do with quantum entanglement,
specifically, the quantum entanglement
between the inside and the
outside of a black hole.
A black hole is a wonderful object,
and one of the seminal papers
on the subject, by the way,
was by J Robert Oppenheimer.
It's an extremely simple object.
It's composed of nothing but warped
spacetime geometry.
Its defining property
is its event horizon.
If you are foolish enough
to cross the event horizon
and enter a black hole,
you'll be unable to return
to the outside or even
communicate with your
friend who stays outside.
But the inside and the
outside of a black hole
can be and will be
entangled with one another,
and Stephen Hawking
understood in the 1970s
that, as a result,
a black hole will emit
radiation due to quantum effects
and eventually radiate away
all its mass and disappears.
And that creates a
puzzle, because we can ask
about what happened to
any information that
fell into a black hole
during its lifetime.
It's a foundational principle
of quantum mechanics
that information is not destroyed,
though it can be scrambled up
into a form that's exceedingly
hard to read.
So, we're faced with an unpleasant choice.
If we lose information inside a black hole
and then the black hole disappears,
if that information is lost
from the universe forever,
then we have to recast the
foundations of quantum theory.
On the other hand, if that
information manages to escape
from the interior of the black hole,
that means we have to
rethink the foundations
of general relativity.
And after 40 years, we still don't have
a clear and completely
satisfactory resolution
of this puzzle.
What we can say about it,
the best thing we can say about it
is that we understood the resolution,
to a large degree but not completely,
in a particular setting,
what we call AdS-CFT duality,
and this is a description of
quantum gravity in the case
where the vacuum energy is negative
and the curvature of
spacetime is negative.
And in that setting, we have
two complementary ways of
describing the same physics.
In a way, this correspondence allows us
to put a black hole inside a tin can.
The walls of the can are what we call CFT,
for conformal field theory,
and that's just an ordinary
quantum theory without gravity.
And in the interior, we have
gravitation, geometry, and
quantum fluctuations of geometry,
and a process in which a black hole
forms and evaporates completely
has a complementary
description in terms of
just the field theory on boundary.
And on the boundary,
there's no black hole,
there's no gravity, there's no place
for information to hide,
and so it seems manifest,
that the process can be described
without any loss of information.
So at least in this case,
the one where we understand
quantum gravity the best,
it seems clear that a
black hole does not destroy
quantum information.
But even so, we're left without
a satisfactory understanding
of how the information manages to escape,
and, in fact, it's not so
clear how this boundary
description encodes the experience of
someone who falls through
the black hole event horizon
and enters the black hole interior.
So, to make further progress,
we should try to deepen our understanding
of this correspondence, which is a
subject of much ongoing work.
So let me say a little
bit more about that.
Here, for ease of visualization,
I've indicated the
boundary is one-dimensional, a circle,
and the bulk geometry as
two spacial dimensions.
So, here in this cut through
the bulk, in order to indicate
the negative curvature,
I've used the Poincare disc description,
each one of these colored
regions actually has the same
geometrical size, but they
appear to be smaller and smaller
as we get closer to the boundary
in order to capture
the negative curvature.
And the idea the
correspondence is there are two
exactly equivalent descriptions
of the same physics,
one on the boundary and one in the bulk,
and there's a very complex dictionary,
which is only partially understood,
which maps the states and
observables of the bulk theory
to the corresponding
states and observables
of the boundary theory.
But what has become increasingly
clearer in the last few years
is that this geometry in
the bulk can be viewed
as an emergent property of
the quantum entanglement
on the boundary.
What evidence do we have
pointing in that direction?
I'll tell you a few things
that indicate that
geometry can be thought of
as emergent from entanglement.
Well, one is what we call
holographic entanglement entropy,
which was discovered 10 years ago now
by Ryu and Takayanagi.
Well, they asked the following question.
Suppose we consider some
state to find on the boundary,
and we're interested in a connected
region on the boundary,
and we'd like to know how
entangled that region is with
the complementary region.
And they pointed out that there's an
answer to this question which
is geometrical in the bulk.
We can quantify
entanglement using entropy,
which is a measure of how
much information is missing
from this region, A,
because it's encoded in the
form of entanglement with
the complementary region,
and that entropy can be expressed
in suitable units as the area
of the minimal surface in the bulk
which separates boundary region A
from the complementary
region on the boundary.
And those units in which we
express the area are just the
same units that we use to express the
entropy of the black
hole in terms of the area
of its event horizon.
So, we can think of where
these minimal surfaces lie,
which encodes the geometry of the bulk
as corresponding to
properties of the entanglement
on the boundary.
Now here's another example.
We can imagine a
boundary theory which has
some holographic dual,
has some higher dimensional
gravitational interpretation,
and we consider two such theories
and ask what happens when we
entangle those two systems
with one another.
And the answer is that the
bulk geometry corresponding
to that pair of systems
will have a wormhole
which connects together
the two asymptotic regions
on the left and the right.
And when there's no entanglement
between the two systems, then
there will be no wormhole
connecting them.
So this relationship between
connectedness of space
and entanglement was
elevated by Maldacena and
Susskind a few years ago
to a general principle,
which they ingeniously called
ER equals EPR.
EPR means Einstein, Podolsky, and Rosen,
who first discussed quantum entanglement
in that 1935 paper I mentioned,
and ER refers to Einstein and
Rosen, who, in that same year,
wrote the first paper discussing wormholes
in general relativity.
Now, if you had a quantum
computer or, by some other means,
you tried to remove the entanglement
between distant regions of space,
the effect of that, according to this
ER equals EPR principle,
would be that the space would
break up into fragments.
So, there's a sense in which
entanglement provides the glue
that holds space together.
Now, this wormhole
can't be used to travel quickly
from one region of space to another.
It's not a traversable wormhole.
This corresponds with the
property of quantum entanglement
that we can't use entanglement
to send an instantaneous message
from one party to another.
What happens is the wormhole is dynamical;
it grows too quickly for anyone to pass
from one end to the other.
So you might think, "If a
wormhole isn't traversable,
"that's not really very much fun."
But actually, it's a lot of fun.
Because we can imagine
two lovers, Alice and Bob,
who live in different galaxies
and long for each other's company,
but it's completely impractical to travel
from one galaxy to another.
But let's say Alice and
Bob had the foresight
to prepare many entangled
pairs of particles, and
Alice took one member of each pair,
and Bob took the other
member of each pair,
then Alice could take her particles
and gravitationally collapse
them to make a black hole,
and Bob could do the same.
And those two black
holes would be entangled
with one another,
and that means they would
be connected by a wormhole.
Now Alice wouldn't be able
to jump into her black hole
and emerge from Bob's,
but Alice and Bob could both
jump into their black holes,
and then they'd be able to
meet inside their own hole
and have a fulfilling
relationship for a while,
but ultimately, they'd
be destined to arrive
at the singularity inside the black hole
and be torn asunder.
So it turns out to be a tragic love story.
Now, another thing that's
become apparent in just
the last couple of years
is that there's a connection
between this dictionary,
between the bulk and boundary theory
and quantum error correction,
that if I consider some local operator
deep inside the bulk geometry,
the corresponding operator on the boundary
is a very non-local operator,
it's just the kind of mapping
from local to non-local
that we need to protect quantum
information from damage,
just the kind that occurs
in a quantum error-correcting code.
And so the bulk geometry deep in the bulk
is actually very robustly encoded
so that if some damage
occurs on the boundary,
that bulk geometry won't be much affected.
So I'm hopeful that this insight
can be taken further.
It's really a remarkable illustration
of the unity of physics.
We develop the idea of
quantum error correction
because we want it to keep
quantum computers from crashing,
and we wound up with a
different perspective
on the geometry of quantum spacetime.
So far, we've understood this
within the context of this...
Well, partially understood
it within the context of this
AdS-CFT duality,
but we'd like to broaden our understanding
beyond the context of
Anti-de Sitter space,
because Anti-de Sitter space isn't
the real case that we want to solve.
Anti-de Sitter space,
the thing that we
understand reasonably well,
that's the case where the
vacuum energy is negative
and the curvature of
spacetime is negative,
but it just so happens
that we live in a universe
where our vacuum energy is positive
and curvature is positive,
what we call de Sitter space.
It's much easier to do quantum mechanics
in Anti-de Sitter space
because there's a boundary,
and we can make reference to the boundary
when we want to discuss the
observables of the theory.
De Sitter space doesn't have a boundary,
and that makes it much
harder to understand
quantum physics in that setting.
But we're going to have to learn
how to do quantum mechanics
in de Sitter space because
that's where we live,
and I'm confident we'll figure it out
eventually, but it's hard.
Last year, Robbert Dijkgraaf,
the director of The
Institute for Advanced Study,
spoke at a Caltech event,
and he showed this slide
near the end of his talk,
and I was quite struck by it,
because he was trying to
illustrate how the different
ideas of theoretical
physics are connected,
and he put quantum information right
in the center of things.
I don't think he would have
done that a few years earlier.
This idea that quantum information
is a unifying principle
of physics has really
only started to take hold
in the last couple of years.
But unlike Dijkgraaf, I would
cross out the word, theoretical,
because quantum information
is an experimental subject,
and if it's true, as we
increasingly have reason to believe,
that we can think of the
geometry of spacetime
as an emergent property
of quantum entanglement
in some underlying system,
then we should be able to get insights
into quantum gravity by
doing laboratory experiments.
So I anticipate that,
in the coming decades, we will
gain deep insights into the
quantum structure of spacetime
by doing laboratory experiments
with highly entangled quantum systems
that, on the tabletop,
in a laboratory at a place like Berkeley,
will be able to, in effect,
to create spacetimes
that didn't exist before
and explore their properties
and learn new things.
But whether that prediction
comes to pass or not,
I think we can be highly confident
that we'll find many
surprises and discoveries
as we explore the entanglement frontier.
Thanks a lot for listening.
(applause)
- [Joel] Thank you, Professor Preskill.
We normally allow a few
minutes for questions
at the end of Oppenheimer lectures,
and we try to have a mix
of questions from both
professional physicists
and amateur physicists.
And if you managed to follow the talk,
then you're already an
amateur physicist at least.
So, please, any sort of question.
- [Audience Member] How do you feel now
about the bet you made with
Stephen Hawking in 1997?
- Now the question was about a bet.
This will be the opening line
in my obituary, I'm afraid.
I won a couple of bets
with Stephen Hawking,
and, in particular, on one of those bets,
concern the question of information
and whether it can escape
from black holes or gets
permanently destroyed.
Hawking and also our friend, Kip Thorne,
took the position that black
holes destroy information,
and then my side of the
bet was that black holes
actually just scramble up information
into a form that's hard to read.
And Stephen has recanted,
but he believed very deeply
at the time that black holes destroy
information, and it was
a bit of a shock to me
when he conceded this bet in 2004.
It was a rather dramatic occasion.
We were at a conference in Ireland,
in a big convention hall in Dublin,
and somehow the word was leaked
out that Stephen was gonna
make a big announcement, and so there were
100 people from the press and
various amateur physicists.
Michael Flatley, the Lord of the Dance,
it turns out that
general relativity is his
hobby, he was there.
So Stephen gave a technical talk,
and then at the end, he
presented me with my prize,
which was a baseball encyclopedia
from which you can withdraw information.
He knows I'm a baseball fan.
This was very hard to get in Ireland
because you can't get a
baseball encyclopedia in Dublin,
so we had to have it shipped overnight.
How do I feel about it?
Well, I was surprised that
he conceded because I think
we still don't have a
satisfactory understanding
of the problem and he would
have been well within his rights
if he had decided to hold out longer
until the question is
definitively settled.
And I still think I
took the right position,
and now Stephen agrees with that.
Kip does not, he has not conceded.
But I don't think we really
have a 100% convincing argument
that information escapes
from black holes, even today.
- [Joel] Thank you.
- [Audience Member] Can you describe
the hardware that will replace
the transistor chip in
the quantum computer?
In other words, I'm interested
in what the hardware
is gonna look like.
- So the question is, what
will the hardware look like
in a quantum computer?
Well, I mean, we have
quantum computers now,
but they're small,
and so I think you're really
asking about the scalable
quantum computers of the
future, where we might have
millions of physical qubits.
So the honest answer
is, I don't know exactly
what the hardware is going to look like.
Actually, here at Berkeley,
in the Siddiqi Group,
they're doing terrific work
on quantum computing hardware
with superconducting circuits,
and they can show you a device that has
10 qubits in it, which is
based on superconducting technology.
We can imagine scaling
up devices like that
to millions of physical qubits,
though it's going to be very challenging.
Another approach, which,
in the long run, I think
has a lot of promise,
is using, as I mentioned,
electron spins as qubits.
That technology is lagging
behind at this stage,
but it's something that is perhaps
especially compatible with the silicon
classical technology that we have now.
And I also mentioned these
topological approaches, where
it's even less clear what
the hardware is going
to look like,
but I did sort of a
cartoon version of it in my
drawing of a quantum wire.
- [Audience Member] A lot
of these questions will be
answered by experimentation,
experimental physics.
What kind of experimentation?
What does that look like?
Or is it the same answer
as the last question?
- Well, so, what I had in mind is that
we have understood, to some degree,
that it's possible for a quantum system
which doesn't involve gravitation at all
to behave like a system that has gravity,
and that's what this story of
the AdS-CFT correspondence is about.
So, the example we've
been able to understand
is a very special one.
It has lots of symmetry,
it has special features.
But I think the phenomenon of
a highly entangled system
behaving like a gravitational
system is a more general one.
But we don't have the
mathematical tools to
understand it in other contexts.
So, what we'll need to be
able to do experimentally,
I think, is build systems
in which there are many particles
which all interact with one another
in a typical system
that's easier to realize.
The strength and the interactions
between the particles
depends on how distantly
separated they are,
and it falls off with distance,
but I think the kind of system
that we would need is one
with many particles or degrees of freedom
which all have strong
interactions with one another.
And in such systems, then we'd be able to
drive them and make measurements
of the way the different
parts of the system are
correlated with one another,
and the task would be then to see if those
correlations have an interpretation
in terms of some kind
of gravitational system.
- [Audience Member] We
can't really understand
quantum entangled states.
So we would have a computer,
and we would take classical
information, put it into
a quantum computer,
wait a while, and take a
classical solution out
that we can understand.
Just curious how you
get it in and out, and
I guess the contradiction
between the number of states
inside the computer versus
the very simple states
that we can comprehend,
put it in, and take it out.
- Alright, so the question is,
how do we get information into
and out of a quantum computer?
As the question anticipated,
the information that we put in
and we take out is classical.
The processing that occurs
can't be done classically, but
is done in a quantum device.
It's the task of the designer
of quantum algorithms
to understand how to do
that quantum processing,
but the initialization
and the reading out are
easier to describe.
So, if I have many qubits, I mean, in my
cartoon analogy, the
preparation would just consist
of putting a lot of
balls in door number
one of a lot of qubits,
and then a lot of quantum
processing goes on,
which can't be described classically,
and in the end, we open all
the boxes one at a time.
So, the preparation
would just be preparation
of one qubit at a time.
Like, let's say it's a bunch
of electron spins and we
prepare them so that they're
all pointing, spin up,
and then we do the quantum processing,
and, at the end, we just
observe the spins one at a time
and see whether they're
pointing up or down,
or, in my analogy, open the
box to see if the ball is
red or green.
So, the process of
initializing and reading out
is not so exotic.
The art of designing a
quantum algorithm is to
figure out how to make use
of the quantum entanglement
at intermediate stages
to speed up the solution
to a suitable problem.
- [Audience Member] Is there a chance that
quantum computing will extend
the validity of Moore's law
into a longer extent of time?
- So, the question was about Moore's law
and whether quantum computing
will extend Moore's Law
further into the future.
Of course, Moore's Law is
the miracle that we've all been living in
for 50 years or so.
We've seen exponential improvement
in the performance of integrated circuits.
Although we've reached a
stage now where it's getting
harder and harder to
increase the clock speed,
and a lot of the improvement
is coming from increasing
parallelism of classical systems,
and it's an amazing story,
and I think a very instructive
one for quantum technology.
If you go back to the 1960s, when
Moore and others were thinking about the
prospects for improving
integrated circuits in the future,
you know, they couldn't
imagine things like
an iPhone.
It was just far beyond what
the technology was
pointing to at the time.
And, in the case of quantum technology,
I think we're in a similar situation.
We are now starting to
interact with information
in a completely different
way from anything that
happened before,
and we don't know where
that's going to take us.
We have a few ideas of how we
will apply quantum computers.
Undoubtedly, we haven't
thought of the most important
applications that are going
to arise in the future.
So, I think my answer
to the question is that
we've seen, in recent history,
and even longer term history,
that physics can drive the
economic expansion of the world, that
the technologies that come
out of physics eventually
have a big, big impact on
the way we live our lives.
We've certainly seen that with
the basic physics in the 20th century
of understanding semiconductors,
which led to integrated circuits,
quantum physics of lasers,
which we make use of
in many ways today.
But that 20th century
physics, that was the
physics of, if you like, single
particle quantum mechanics.
And now we're getting a grasp on
a new quantum revolution: the
properties of many particles,
and I think that could well drive
economic development in the 21st century.
Nobody really knows,
and so I don't have
a precise prediction about
the quantum Moore's Law.
And I think we can expect that
these new technologies are going to
take us to remarkable places
that we haven't yet imagined.
- [Audience Member] In quantum mechanics,
electrons are indistinguishable.
Are qubits also indistinguishable?
- Now the question was about
indistinguishable
particles, that we know that
electrons, for example,
are indistinguishable,
and does that apply to qubits as well?
It need not.
I mean, it's possible
for the qubits to be distinguishable.
For example, in these superconducting
circuit realizations of a qubit,
each qubit is actually
an engineered device.
They're not all identical.
And so there's no notion
of indistinguishability
among the qubits that doesn't
impair the quantum computer's
ability to perform its special magic.
In the case of the anyons I described,
they can be viewed as
a rather exotic type of
indistinguishable particle,
and that's why it makes sense
to process the information
by exchanging the particles.
That affects the
information that's encoded
in the many-particle system.
When the anyons change places, the...
When you look at them one at a
time, they all look the same.
- [Audience Member] Do you
subscribe to any particular
interpretation of quantum mechanics?
- The question is, do I...
It's a question for me personally?
Do I subscribe to any particular
interpretation of quantum mechanics?
I'm an Everettian.
I like the idea.
Sometimes people call it the
many worlds interpretation,
though I'm not very fond of that name.
But I think the essence
of that point of view
is that there's really just one
way for things to change in the world.
Technically, quantum states
can change by evolving
in a way which doesn't create
or destroy information,
that is unitary evolution,
and that's the only
thing that ever happens.
That measurement is not a
fundamentally different process.
This is a subject that people
can get emotional about.
A disadvantage, you might
say, of that point of view
is that in order to understand why, when I
observe a quantum system,
I see one definite outcome,
I have to include myself
in the description,
because what really happens is that
there's more than one possible outcome,
and I become correlated
with the state of the
system I'm observing.
And some people think this
is a very extravagant thing,
in that we have to keep track
of all the possible outcomes
by including the observer in the system.
But I prefer that to
introducing measurement
as some kind of new fundamental process.
However, I think, you know,
everybody's entitled, to a certain degree,
to their own interpretation
of quantum mechanics
if they prefer.
Different interpretations
can give rise to different
insights and can help to
generate different ideas.
I mean, I think, to me, the
question of interpretation
is most interesting
to the degree that it raises questions
about what the alternative to
quantum mechanics might be.
Maybe quantum mechanics will fail,
and some people expect quantum
mechanics to break down
in some stage because of the
issues of interpretation.
I'm not sure whether that's true.
But I think thinking about
interpretations can be
useful, particularly if it
suggests new ways in which
we can test quantum theory
and look for deviations from it.
- [Joel] One last question in the back.
(audience member questioning)
- So, I think the question was,
technology is very dependent
on advances in materials,
and what can we say about how
advances in materials will
impact quantum technology?
Was that more or less the question?
(audience member speaking)
Yeah, well,
there are materials issues
in all of the things that I mentioned.
There have been tremendous improvements,
for example, in the performance
of superconducting qubits
going back 15 years,
and many of those improvements
have to do with using
superior materials to
make the Josephson junctions,
which are the essential
ingredient in the
superconducting circuits that
makes them control the
ball and behave quantumly.
These topological quantum computing ideas,
computing with anyons,
that's very much a materials issue,
though it's been a great challenge to
synthesize materials and
to fabricate devices that
bring together all the physical
ingredients that we need
to make topological quantum
computing work better.
And spins and semiconductors,
same thing, that
materials issues are
currently a huge impediment,
and improvements
in the materials will surely
lead to improved technology.
- [Joel] I think, with that,
we should call it a night.
Before we go, let's
thank Professor Preskill
for a beautiful and stimulating
Oppenheimer Lecture.
(drum beat)
