Well thank you very much Mike.
It's a great pleasure to be here. I'd really
like to meet this John Preskill guy
he sounds fantastic.
Now my talk today is going to be really
about fundamental physics
but it's also to some degree about
technology,
quantum technology and we have
information technology today that all of
us find impressive
but we all recognize that that will be
replaced say by the end of this century
by new technology that we really can't
hope to imagine today.
but it's interesting just the same to
try to imagine future technologies
and I may not be the ideal person to do
that
because I'm not an engineer, I'm
theoretical physicist
and i can claim to be terribly
knowledgeable about
how computers work but I do know as a
physicist
that the crowning intellectual
achievement of the 20th century in my
view is the development of quantum
theory
and it's natural to wonder how the
emergence of quantum theory in the 20th
century is going to impact
21st century technology. Quantum theory
really isn't
a new subject anymore it's over 100
years old
but even so some of the deep ways in
which quantum and classical systems
differ from one another
we're just beginning to appreciate in
recent years and a lot of those differences
have to do with how information is
encoded and processed in these 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 we know that all
physical systems are really quantum
systems governed by
quantum physics and so information is
something that we can encode and store
in a quantum state and information
carried by quantum systems has some
notoriously
counter-intuitive properties that's why
physicist sometimes proudly speak of the
weirdness of quantum theory
and we cherish that weirdness and take
delight in it
but in recent years we're more often
taking seriously the idea that we might
be able to put the weirdest work
to exploit unusual properties of quantum
information that
would allow us to perform tasks that
wouldn't be possible if we'd lived in a
less weird, classical world
and that desire to put weirdness to work
is driving the emergence
of a field we call quantum information
science,
which gets a lot of its intellectual
vitality from three central ideas:
quantum entanglement, quantum computing, and quantum error correction and my goal in this
talk tonight is to
explain these ideas. So let's start at
the beginning we know than any amount of
classical, digital information can be
expressed in terms of units, bits of information
and we can envision a bit as an object
like a ball which can be either one of
two colours. Now I can take a bit and I can store it
for a while, I can put it inside a box
and then later on if I opened the box
again the color ball that I put in comes
out again so I can recover a bit
and read it and quantum information,
information carried
in the state of a quantum system can
also
be divided into units of quantum
information, what we call quantum bits or cubits for short
and for many purposes it can be
convenient to think of a cubit
as a colored objects stored inside a box
but where now, we can open the box
through either one of 
two complementary doors where those two
doors correspond to two different ways
in which we could prepare or measure this
state of our quibit
and I can put a ball in a quantum box
through either door number one or door
number two
and then later on when I open the same
door again
the color that I put in comes out again
just as though the information were
classical
but if I put information through door
number one and then I opened the
complementary door
then what comes out of the box is
completely random. We can't predict it all
it has probability 1/2 of being red and
probability 1/2 of
being green. So, if you want to read the
information that you put in the box you
have to open the box the right way and
if you do it the wrong way you'll damage the information
and one consequence of that you can
appreciate right away if you think about
copying quantum information. If I had a
quantum copy machine that would mean I
could put some information in door number
one of the qubit,
make a copy and then I could open door
number one on the original and the duplicate
and the color that I put in would come
out of both boxes
and similarly if I happened to have put
information in door number two with the
qubit and made a copy then I could
open door number two on the original and the duplicate
and the color that I put in would come
out to both boxes
but the thing is there's no such quantum
copy machine. It's not allowed
by the laws of physics we can't copy
unknown quantum states
and the reason is that to make the copy
the copying machine will have to probe
inside the box and it doesn't know ahead
of time what door I use so if it opens
the door that I use then it can copy the
information no problem just as though it
were a classical bed
but if it opens the wrong door, it will
damage the information.
There will never be any way to make a
high-fidelity copy.
So, although we might be able to clone a
sheep we can't clone a qubit.
Now there are a lot of different
physical realizations of a qubit that are possible
and I'll mention a few others later in
the talk but if you want something
concrete to think up for the time being
you can imagine a single photon, a
particle of light.
That photon has an electric field and
the electric field might be oriented
either horizontally or vertically
corresponding to the two colors that you
could see if you open door number one
of the box or we can consider its electric
field to be oriented either 45 degrees
to the left to the right
a vertical corresponding to the two
colors you could see if you open door
number two in the box
but for now I'd like to just think about
qubits in a more abstract way and not
worry about the particular physical
realization.
Now the really interesting differences
between quantum and classical systems
we can only appreciate if we consider
systems with more than one part.
So, let's imagine that we have two qubits
and they can be far apart from one another.
We could have won say at Caltech in
Pasadena
and one in the custody of my friend in
the Andromeda Galaxy
and this particular pair of qubits some time
ago when both the qubits where on Earth
was prepared in a particular state with
some interesting properties
namely I can open my box in Pasadena
through either
door number one or door number two and
either way what comes out of the box is
completely random
and can't be predicted and the same
thing is true for my friend in Andromeda.
So neither one of us by opening the box
acquires any information
but that's kinda funny because with two
boxes we should have been able to store
two bits of information
where could that information be hiding? The answer
for this particular state is that all
the information is actually in
correlations between what you find,
when you open a box in Pasadena, and you
open a box in Andromeda.
It turns out in this particular state
that if my friend and I both open door
number one we're always guaranteed to
see the same colour. It could be red or it
could be green but if we open the same
door it's the same
and that's also true if we both open door
number two.
We both see the same colour, probability
1/2 of being red or green but we're
guaranteed to see the same thing
and there are four perfectly distinguishable
ways in which
a quibit in Pasadena could be correlated
with a quibit
in Andromeda. We might see either the same colour
or different colours when we both
open door number one are we both open
door number 2
and I've chosen one of those four ways
that's two bits of information
which is stored in the boxes, but
what's unusual is that, that information
is completely inaccessible
locally. We can't get at any of that information by
looking at our quibit just in Pasadena or in
Andromeda. It is
shared by these two distantly separated
qubits
and that phenomenon that quantum
information can be inaccessible locally
and shared by distantly separated
systems is what we call quantum entanglement
and it's the really crucial way that
quantum information is different from
classical information.
Correlations are not necessarily a big
deal we encounter them all the time
in our daily lives usually my socks are
the same color
so you can look at one of my feet and you
know then without
having to look what color sock to expect
to find on my other
foot and it's kind of like that with
the boxes
if I wanna know what my friend is going
to find when he opens door number one
in Andromeda I can open door number one in
Pasadena
and if on the other hand I want to know
what he's going to find if he opens door
number 2
in Andromeda I can open door number two
in Pasadena
so it's almost the same thing and you might
think the boxes are really no different then the socks'
but in fact the boxes are not at all
like the socks' and the
essential difference is, there is just one
way to look at a sock
but we have these two complementary ways
to open a quantum box and that makes the
correlations among qubits
richer and a lot more interesting than
correlations in a classical system.
now this phenomenon of quantum
entanglement is not a new thing it was
first discussed by Einstein
and collaborators in a paper in 1935
and Einstein quantum entanglement was
very unsettling it seemed to indicate that
something is missing
from our current understanding of the
quantum description of nature, he thought.
And that paper elicited some
strong and interesting responses
including one that was particularly insightful
from Schrödinger, who said "it seems that
the best possible knowledgeable holders
not necessarily include the best
possible knowledge
of its parts." So what Schrödinger meant
was that even though we have this
completed description of that pair of
boxes that nature will allow we know
everything about how it was prepared. Even so,
we can predict what will happen when we
look at one of the boxes.
So, although the whole is definite the part
is random
and it was Schrödinger who suggested that
we use the word entangled to describe
this correlation, this quantum
relationship
between the two boxes and 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 experimenters mercy in
spite of his having no access to it."
What Schrödinger meant is, it seems rather strange that it's up to me to decide
by opening my box through door number
one
or door number two in Pasadena whether I
will know what will happen when my
friend opens his box in door number one
or door number 2. Now, Schrödinger understood
that this correlation doesn't allow us
to send a message immediately
from Pasadena to Andromeda because no
matter what I do to my box in Pasadena
when my friend opens his box through door
number one or number two he just finds a
random bit
and he doesn't know anything about what
I've done to my box. It's a correlation
which doesn't allow us to immediately communicate.
Now, this idea of quantum entanglement, the
theory of quantum entanglement didn't advance
very much for a long time for some
thirty years
until in the mid sixties we began to
think about quantum entanglement in a
somewhat different way
not just as something weird and
wonderful but as a resource that we can
potentially use to do things.
Bell in particular described
a game the two parties can play
Alice and Bob were playing their
cooperating with one another they're
both on the same side and trying to win
and under the rules of this game Alice
and Bob each receive inputs and they are
to produce outputs which are correlated in
a certain way that depends on the inputs that they recede
but the rules of the game say that Alice
and Bob are not allowed to communicate
with one another
between the time that they receive their
inputs and the time they produce
their outputs. They can use correlated
bits that might have been distributed to
them before the game began
but for this particular game if the
players use the best possible strategy
they will win
with the probability of success 75
percent if we average over the possible
inputs that they could receive
but Bell pointed out that if before the
game began we distributed to Alice and Bob
quantum correlations, entangled qubits
then they could play a better quantum
strategy
and win the game with a higher
probability of success.
So there's something, mainly winning the
game, that we can do with entanglement
that we couldn't do with just classical
correlations.
Experimentalists have been playing this game for
decades and they keep winning
with the higher probability of success
that Bell pointed out
is possible in quantum mechanics so
these
quantum correlations that are stronger
than classical ones really do seem to be part
of nature's design. Einstein had
derided quantum entanglement he call it
spooky action at a distance
this sounds even more derisive when 7 German
but it doesn't matter what I'm stein
thought
because nature is as experiment reveals
her to be
and we just have to learn to love her as
she is.
So, the boxes are not like the soxes,
you can win a game with a higher
probability of success if you have
quantum entanglement compared to if you
have classical correlation.
Is that really such a big deal? Is it a big yes?
Yes, it's a really big deal
and you can see, appreciate maybe a
little more deeply why it's a big deal.
If you think about systems with many
parts
imagine a book for example the book is a
hundred pages long
if it were classical book there would be
bits printed on every page
and if you read one of the 100 pages you
would know one percent of the content of the book.
And if you'd read another page you'd know
another one percent of the content of the book.
But suppose instead it's a quantum book
it's written in qubits,
not in bits and the pages are very
highly entangled with one another it's a
very highly entangled book
and then if you look at a single-page
you see only random
gibberish on that page there's no
information on a single page about the
content of the book or hardly any.
That's because nearly all the
information that distinguishes one
highly entangled book
from another is written not on the
individual pages but in the correlations
among the pages.
If you want to tell which entangled
quantum book you're reading
you have to make a collective
measurement or observation
on many pages at once that's
characteristic of quantum entanglement
and in fact you don't have to have very
many cubits just a few hundred or so
and if these qubits are in one typical
highly entangled state
and I wanted to completely characterize, write-down in terms of classical bits
all the correlations among these qubits
it would actually require writing down
more numbers than the number of atoms in
the visible universe.
So, it'll never be possible even
as a matter of principle to write such a
description down
that completely captures all the
correlations among the quibits
and that property of quantum
information that we can't hope to
express it
in any reasonable way in terms of
classical information
was intriguing to the physicist Richard
Feynman in particular
and it led Feynman in the early 1980s
to make the suggestion
that if we could build a computer that
operates on qubits instead of bits, a quantum computer
then it should be able to perform tasks
that we'd never be able to perform with
any conceivable
digital computer. What Feynman had in
mine is it if we can even hope to write
down using bits
the content of a few hundred qubits
then perhaps by
processing the qubits instead of bits, we
can perform a task that could never be emulated
with an ordinary classical computer and
around the time
Feynman was making this suggestion there
was an undergraduate student
at Caltech studying mathematics named
Peter Shor.
Peter Shor, like all Caltech sophomores
was required because it was part of the
core curriculum and still is
but next year will not be because we're
changing the core curriculum
but until this year every Caltech sophomore
had to learn quantum physics
including Peter Shor and I don't think
he ever took a more advanced
course on physics than that but like
many
Caltech sophomores, he remembered what he
learned about quantum mechanics and put
it to use
some years later to make a rather
amazing discovery.
An example of a problem that we think is
hard for classical computers is finding the prime
factors of a composite integer thats
many digits long
but what Shor said is that if we had a
quantum computer
that could operate on qubits instead of bits,
the factoring problem would be easy.
It wouldn't be much harder than
multiplying numbers together to find their product.
So, according to Shor, the boundary
between problems that are
hard and problems that are easy the
problems that
we'll never be able to solve in the
future even with advanced technology and
the problems that we can expect to solve eventually 
as technology advances
that boundary is different than it
otherwise would be
because we live in a quantum world
rather than a classical world.
A really amazing statement
and to give you an idea of what this means
about the hardest factoring problem that
we can solve with current technology is
factoring 193 digits.
It can be done by a network of
workstations collaborating over the Internet
in a few months and if we use the same
factoring algorithm that runs on that
hardware and the same hardware with the
same
clock speed to try to factor a 500 digit
number it would take longer than the age
of the universe. So,we don't expect that to happen for a
long while
but suppose we had a quantum computer we
have to suppose it cuz we don't have it yet,
which has the same clock speed as that
classical systemic. It can perform the same
number a fundamental operations
per second then we'd be able to factor
the 193 digit number in about a tenth of
a second and the 500 digit number in two
seconds.
So, the resources that you need to solve
the problem
scale in a fundamentally different way
for a quantum computer
than a classical computer that's what
Shor discovered.
Now, does anybody really care about whether
you can factor big numbers?
Actually, yeah, actually there are people who
care about this
because the difficulty the presumed
difficulty of factoring large numbers is
the basis for public-key cryptosystems
that are in widespread use today
which you use for example when you make
financial transactions
over the Internet. If in a few decades
quantum computers are widely
available we won't be able to use these
systems anymore, they won't be secure
and we'll have to protect our privacy
in other ways. Alternatives exist
but it's still not clear exactly how
we'll protect our privacy in a post-quantum
world where quantum computers
are readily available
but the more important point is that
Shor
drew our attention to a question about
computational problems.
There's an interesting class of problems
the ones which are hard for
classical computers but which can be
solved by quantum computers and we'd
like understand better what are the
problems in that class. It includes factoring
but what else is in there? Well in fact
quantum computers have
limitations and the problems for which
quantum computers can achieve very dramatic
speedups compared to classical computers
are special ones that have a structure
which is amenable to the power of quantum algorithms and in particular if we consider
problems for which in the worst case we
have no better method than a brute-force
search for the solution
then we only expect quantum computers to
speed up the solution moderately not
nearly as dramatically
as in the case of factoring. That's what
computer scientists call:
NP-complete problems. NP means that once
you find the solution it's easy to check
that the solution is correct an
NP-complete means the hardest problems
of that type, but it's also important to
emphasize that quantum computers can
solve problems that are not in NP.
That is the quantum computer can get the
answer but we can't easily check it with
the classical computer we could check it
with another quantum computer
and there's a large class of natural
problems
of that type which involves simulating
quantum systems to see
how they'll behave. That's a very natural
application for quantum computers
we can apply them to the chemistry of
large molecules, to the
properties of exotic quantum materials,
to the quantum field theories that we
used to study the fundamental particles and their
interactions.
In fact, there are computational methods
that are widely used by the particle physicist today
to predict for example, what will happen
when particles collide at very high
energy and an accelerator like the Large Hadron
Collider
and those methods are very useful but
the resources need to solve that problem
scale very badly
with things like the number of particles
that are produced in the collision and
the total energy
but with a quantum computer we would be
able to simulate such process ease
efficiently in fact the evidence is
growing
that we would be able to simulate any
quantum process that occurs in nature
efficiently if we had a
general-purpose, universal
quantum computer and that's certainly not
something that we can say about digital computers
where the resources scale very badly
when we tried to simulate quantum systems.
So quantum computers would be wonderful
to have.
So why don't we have them already, what's
the delay?
Well you see it's a really, really, really,
really hard to build them
and you might wonder whether there's some
fundamental obstacle
that will prevent this from ever
successfully realizing large-scale quantum computers.
One issue that comes to mind is the
problem errors. Quantum computers are very
susceptible to failure because
of noise that afflicts them.
Physicists sometimes like to speak,
sort of tongue in cheek, about the quantum
state a cat
which is in a superposition of its dead
and live state.
We never observe, in every day life, that type of superposition of macroscopically distinguishable states
of a large physical system and we
understand why not it's because
a real cat will immediately interact
with its surroundings and those
interactions will in effect measure the
cat and project it onto a state which is
completely dead or completely alive
and that phenomenon in which a large
quantum system which is imperfectly
isolated from its surroundings we call decoherence,
and decoherence is very important for
explaining
why for large systems in under ordinary
conditions
even though the underlying system is
quantum, it can be well described
by classical physics. Microscopic systems,
like individual atoms and so on which
can be well isolated from
other physical systems can exhibit
profoundly quantum behavior
but it's very difficult to see quantum
behavior in macroscopic systems
because they always interact with an
unseen environment.
Now, quantum computer won't be very much
like a cat probably
but it too will inevitably interact with
its environment at some level
and that can cause a quantum computer to
fail.
So, if we're going to successfully build
large-scale quantum computers we have to
find a way of fighting off the damaging
effects
of decoherence and other possible
sources of error.
Well, errors are a problem even in our
classical lives
everybody has bits that they cherish
and the trouble is they're always
dragons lurking around who try to
tamper with their bits
but in the classical world we know some
ways to fend off
the damage caused by the
Dragons. If I have a bit
that I want to be sure to save, I can
store some backup copies of the bit.
A dragon might come along and change the
colour of one of the balls,
but only one because he hasn't had time
to damage two of the balls and I can
employ a busy beaver who frequently
checks to see if the balls are the same
colour and when one is a different colour
from the others he repaints so all
three match again.
So my bit is preserved if the dragon is
only been able to damage one out of the three bits.
It was protected because we stored
redundantly
and we'd like to use that same principle,
that redundant storage
helps us protect information in the
quantum world
but there are subtleties as we've already
noted.
We can't copy unknown quantum state so
we can take the state of a quantum
computer and store a backup copy in case
the original
gets damaged and furthermore there are
more things that can go wrong with
quantum information than classical.
It may be that a dragon comes along and
opens a qubit through door number one in
changes the color the ball that would be
like a bit flip
that could occur in a classical system,
but on the other hand the dragon could
open the other door and change the color
the ball through that
complimentary way of looking at the
qubit and that also
would be bad so we have to protect
against both types. That second type
of error is what we call a phase error in
quantum information which really has no
classical analog. There's another way of
thinking about the phase errors,
it might be that the dragon doesn't open
door number two
but opens door number one and he doesn't flip the bit, he just
remembers the value of the bit or stores a
copy
of the value that he saw and that will
have the effect of changing
the color that we would see if we look
through door number 2. That's another
way that a phase error can arise
and because in most physical systems
it's easier to copy a bit
than flip a bit, these phase errors are
particularly pervasive
and hard to control in the quantum
systems that we'd like to use
for the hardware of a quantum computer.
So, really if we're going to resist decoherence
a key thing, and this is different from
trying to control errors in the classical world,
is that we have to prevent the
environment from finding out
anything about the state of the quantum
computer during the computation. It must
not store any record of what the quantum
computers is
doing during the computation. In fact, if
after we've successfully done a quantum computation
and then at the end we ask the quantum
computer: what did you just do?
It should always give the answer: I forget.
There shouldn't be any record left
behind of what the state of the quantum
computer
was during the processing except for
the final result at the end and it's fine for
that to be broadcast and you can tell
all your friends
but not the state in the middle of the
computation. If that were recorded the quantum computer
wouldn't work. So we have to find a way of encrypting the computation, of,
preventing any information about the
state of the computer from leaking out
into the environment while we're doing
the computation
and that's part of the reason that it's
so hard
but we've learned that it is possible to
fight off decoherence.
How? By exploiting quantum entanglement.
We can store the information that we
want to protect in the form of some
highly entangled state.
if I have one qubit that I want to
protect,
it doesn't work to store it in a block
of 3 like we were able to
protect the classical information but
there's a way of storing one qubits worth of information
in an entangled state of five cubits
and that state has the property that the
dragon can come along and do whatever he
wants to anyone at the five cubits
and no matter what he does he won't acquire
any information about the protected
state that's encoded in the block of five.
He can't acquire that information because
it doesn't reside in the individual qubits.
It's just like the 100 page book,
the information isn't on the individual
pages, the information is in the
correlations among the pages
and then we can ask the beaver to come
along and check how the quibits are
correlated with one another
he can tell if the dragon is done some
damage to the correlations but the beaver
also doesn't find out anything about the
encoded state
but he is able to correct the damage by
reversing what
the are beaver has done and so we can
redundantly encode quantum information
so as to protect it against error.
Now, one of the heroes of
the subject of quantum error correction is
Alexei Kitaev my colleague on the Caltech faculty. When I first met him in the 1990's, he was a 
scientists at the Landau Institute in
Moscow
and the day we first met was really
one of the most exciting days of my scientific life
because when Kitaev gave his
seminar and I made these notes,
I felt that I was hearing a really
transformative idea about quantum error correction.
What I learned from Kitaev is the
connection between
quantum error correction and topology.
Topology is the word that mathematicians
use
when they're describing properties of an object that remain invariant
if we smoothly deform the object without
ripping or tearing it and in the case
of doing a protected quantum
computation, we would like the way our quantum computer processes the protected data
to remain invariant if we deform
the computer by introducing some noise.
So, we would like to do quantum
processing with physical interactions
that have topological properties and physicists have known of such interactions for a long time.
We know for example that
an electron can be transported around a
magnetic flux tube
and its state will change in a way that
depends on the magnetic flux enclosed
in the tube. Even though the electron
never directly visited
the inside of the tube and that change
in its state remains
invariant if we deform the trajectory
of the electron. The only thing that
matters is that wound once around the flux tube.
So that's a topological interaction and
their,
at least as a mathematical possibility
of more complex topological interactions
for particles in two-dimensional systems
that we call "anyons."
These anyons have the property
that if I have a system of many particles
there are a huge number of quantum
states which are distinct
but which locally all look the same. You
can tell one of these states from another
by visiting the anyons one at a time
rather the
quantum information is spread out very
non-locally,
a collective property of the many anyons
and furthermore that information can be
processed
by performing exchanges in which the anyons swap positions and so we can imagine
operating a topological quantum computer, as Kitaev suggested
where we initialize the computer by
creating in some two-dimensional system many
pairs of anyons and then we process
information by performing a sequence of
exchanges of the anyons so that there
were lines and two plus one dimensional space-time
trace out a braid in space-time
and then we're ready to read out the
result of our computation we can bring
the anyons together, pairwise, and observe whether they annihilate one another or not.
So what's wonderful about doing the quantum
computation this way,
it's that the information at all times is
encoded in a highly non-local way.
So it's very hard for the environment to
acquire information about the state of
our quantum computer and therefore hard
to damage the state
so that if we do the computation
at low temperatures so there here aren't
uncontrolled anyons floating around
if we keep the anyons far apart from
one another except at the very beginning
of the computation and at the very end,
then as long as we execute the correct
Braid guaranteed to get
the right answer, it's a fault-tolerant
way of doing quantum computing.
Okay, that's how a theorist would
describe the idea of quantum computing
but what's the physical system in which
we can realize anyone?
Well there are several ideas about that.
Now I'll tell you about one of those which
also involves a suggestion made by Kitaev.
Kitaev pointed out that there are
conditions under which it's possible
to split an electron into two parts.
Specifically he said "imagine a wire
a one-dimensional wire, which is
superconducting it conducts electricity without resistance.
He pointed out that there are really two
types out superconducting wires the
garden-variety conventional type and
another type which he called the top a topological superconductor.
Now, if you have a finite segment of topological superconductor with conventional superconductor
on either side then if we add an extra
electron
to that segment that electron can in
effect dissolve and disappear
and in the process a change occurs in
what we call majorana fermions which are
localized at the two ends of that
segment of topological superconductor.
That change can't be observed locally it's
really a joint property of this
pair of majorana fermions. So there's a
way of storing information because
we could have either an even or odd number
of electrons in this segment of wire
and locally we can't really tell the
difference, it's a type of
non-local topological encoding of information.
Experiments have been done which seem to
suggest that this type of dissolving
of an electron added to a topological
superconductor occurs in
some materials that have really been
fabricated
but the evidence is still ambiguous and
more experiments will need to be done to
make that case conclusively
but suppose it's true how could we use
these
majorana fermions for information
processing
what we'd like to be able to exchange
them so that we can process the
information that they encode
and we can imagine doing that if we have
a network
of wires with T-junctions so that if I
wanted to exchange to majorana fermions
I could control the location of the
majorana fermions with some voltage gates
and park it around the corner, move the
majorana fermion that was originally on the right
over to the left and then unpark the
first one so I've accomplished an exchange
of these objects which really behave like
non abelian anyons
and many such operations done in
succession could be used
to build up, well some of the operations
that we need
for a quantum computer. So this type of
experiment with braiding
of majorana fermions hasn't even been
attempted yet
but we hope that in the next few years
it can be done
and if it is done it might be a step
towards an advanced
future technology but even apart for
that it'll be a real milestone
for physics demonstrating that a very
exotic type of
interaction, topological interaction can
be are induced by non-local effects in a solid state system.
Of course this might not be the way we
build the hardware of quantum computers
of the future there are a lot of other
approaches that are under development
and it's kind of timely to talk about, in particular,
the work of Dave Wineland since he was the
most recent recipient of the Nobel Prize
in physics which he shared with another
great
physicist, Serge Haroche. Wineland has been
one of the leaders in developing the
ion trap approach to quantum computing.
They developed the technology over years of effort
to trap charged atoms, ions with electromagnetic fields
hold them in the trap for a long time
and we can imagine that each one of the
ions is in either its lowest energy state, its ground state, or some very long-lived excited state.
So we can think of them as
two-level systems, balls that could be either
green or red qubits and since these are
individual atoms you might think well
it'll be hard to read them out
but actually that's not very hard
because we can illuminate ions with
laser light and if we choose the
frequency in the light
appropriately nothing happens if the ion
is in the green state,
but if the ion is in the red state it
will repeatedly absorb and remit the
light so it will glow visibly
and you can read out a series of zeros
and ones just by shining a laser on all the ions.
Of course we'd like to do more than read
out we have to process
the information in the ion trap by
performing entangling gates.
In a way that could be done is I could
pick out one ion in the trap
and address it with a pulsed laser,
choose the frequency and duration of that pulse appropriately and then
nothing would happen if that ion were
in its red state but if it's in the
green state it'll make a transition to the red state
and excite a vibrational mode of all the ions in the trap
and then we can pick out another ion in
the trap
and address it with the pulse laser, its
frequency and duration
can be chosen so that nothing will
happen if the ions are not vibrating but
if they are vibrating it will make a
transition from red to green
and the vibration will stop. So what
we've done is we picked out two
ions in this trap that and if the first one was in its red state nothing would have
happened and if it was in its green state,
both of the ions make a transition to the
other colour.
So if we started out in a superposition
of red and green for the first ion
and then we would have created a
quantum correlated state, an entangled
state have of the two ions.
So that's the type of operation that we
would repeatedly do
to perform a quantum computation in an
ion trap.
So at least that's a cartoon of how a
theorist sees an ion trap.
if you actually go and visit Dave Wineland's 
lab in Boulder, Colorado,
you might get a bit of a shock.
There's a lot of technical complexity
underlying that simple story that I just
told you
which may make you hesitant about the
prospects for scaling-up
ion trapped technology to very
large systems with many qubits in many operations.
Well, there are ideas about how do it
people are working on it. It is very, very,
very hard
and well we'll see whether it can be
done but meanwhile there are other
approaches to building
quantum hardware that are being developed.
Two significant ones are using superconducting circuits
and the magnetic field of a single-electron.
In the case of a superconducting
circuit, I have current which flows
without resistance in a superconducting wire
and for practical reasons this is not
really the best way to do it but for
purposes a visualization
we can imagine in coding a cubit by
having
the circulating current in a small loop
be either
clockwise or counterclockwise. What's
remarkable about that realization of a quibit
is that it really involves the collective motion of billions of electrons and yet it can be well controlled
and can remain in a coherent
superposition for a remarkably long time
at least if we design our
superconducting circuit a little bit
more cleverly
another physical realization is I can
consider a single-electron
which has magnetic field or magnetic
moment to spin
and that magnetic field, it's like a little magnet
and the North Pole can be either
pointing up or down corresponding to the
two states of a quibit and what's remarkable about
that realization of a quibit is that it's
just one electron
and yet, experimental physicists have gotten
pretty good at manipulating its state
and maintaining a coherent superposition
of the read and green state for a pretty
long time.
So there are a lot of different
approaches to building quantum hardware
that are under development and that's
good because we don't know
which of these, if any, is really going to
turn out to be the best approach
to building a scaleable device.
One of the, how well, no matter how we do
it
we are going to have to use quantum
error correction because the quantum
hardware is not going to be able to do
operations on qubits perfectly,
they will be noisy operations and
actually the best
idea we currently have for how to
control errors in a quantum computer is
no matter what kind of hardware we use
superconducting qubits or
electrons spins or ion traps, to an effect, simulate
the top a logical encoding that occurs in
something like a system of anyons no
matter how we do it we will want to spread
out the quantum information so that it's
stored in an entanglement
among many fundamental qubits in order
to protect it
and that will only work effectively if
our gates are accurate enough
we'd like the probability of an error per gate to be well below 1 percent and we'd like the noise
in the qubits to be weakly correlated
which correlations and the noise make it harder
to control the areas with quantum error correction.
Nowadays error rates are the order of one percent per gate
can be achieved in some of these system's. We'd like to
bring that down by a factor of ten or
so. That's really, really hard to do
but it doesn't seem impossible.
To give you an idea about the relative
state-of-the-art in quantum and classical
information processing: this an observation made by John Martinez, who is one of the leaders
in developing superconducting circuits
for quantum computing.
He said: suppose we want to factor a big
number, 2048. 
A number that would enable us to
break public key
protocols as they're currently being
used. Well, we can do that with the classical computer
we just need lots of parallelism.
How much parallelism? Well if we covered
one-quarter of the land area of North America
with a server farm, then we would be able
to do the computation in about 10 years.
Of course buying all those servers, it
would cost about a million trillion dollars.
We'd also have to consume a million terawatts of power which is about a hundred
thousand times the world's current
power output and the sad news is that we
would consume the world's supply of
fossil fuels in just one day and we have
to run the
program for ten years. Okay so, now
let's compare that
with quantum hardware today
well John Martinez can make a pretty
good quit for ten thousand dollars
or so he claims. If we want to solve this
factoring problem
we need something like 10,000
logical qubits which we process in our algorithm
but because we're gonna do quantum error correction we'll need more physical qubits
than that because we have to store the
information redundantly.
Maybe something like ten million
physical qubit so if we just scale
you know how much it cost him to do qubit
today we could get that for 100 billion dollars.
The great news is it would run in 16 hours and only consume 10 megawatts, sounds a lot better.
Well it's not quite as simple as that you know
even if you had a hundred billion
dollars you have a lot of problems to
solve in order to get
a very complex quantum system to be
well controlled. Big engineering problems
but at least it's something that we can
imagine becoming feasible in a few decades.
So the three questions about quantum
computing which I've touched on:
Why do we want to build one? Well one reason is we would like to be able to simulate any
quantum process that can occur in nature.
Can we build one? Well we don't know
of any reason in principle why we
can't but we'll have to use the
principles of quantum error correction to succeed.
How will we do it? Well, we don't exactly know
but there are a lot of different
promising approaches to building quantum
hardware, which are
making steady progress and I think just
addressing questions like these
already makes for a compelling research
agenda
but I'm not an engineer, I don't want to
just build a machine I'm a theoretical physicist.
So I get very interested in the
possibilities for
applying ideas about quantum computing,
about quantum information processing
which we developed in the last few years
to other areas of physics and
a lot of those applications to other
areas a physics have to do with what we
call the monogamy of entanglement.
Correlations in classical systems
are polygamous they can be shared many
ways
so if Adam and Betty both read the
newspaper
they have the same information they
become correlated with one another
but nothing prevents Charlie from
reading the paper too or everybody else in the room
and so everybody can join the party and
we're all equally correlated with each other.
The correlations are polygamous but
quantum correlations aren't like that.
They're harder to share so if Adam
and Betty are as fully entangled as
possible it means that Betty has used up
all of her ability to entangle
and she can't untangle it all with
Charlie.
If Betty wants to entangle with Charlie,
well she can be fully entangled with Charlie
but only by being completely unentangled
with Adam.
That's the monogamy of entanglement and
it's very frustrating because Betty
might want to entangle with both Adam and Charlie
but you'll always have to make a
compromise in order to entangle more
with Charlie she'll have to reduce her
entanglement with Adam
and that monogamy has many
consequences. It has consequences for
cryptography
because Adam and Betty can use their
shared entanglement
to generate a secret key which they can
use to
encode a private message and if they
have a way of checking that they really
are fully entangled with one another or
nearly so
say by showing that they can win Bells
game
then they know the charlie is completely
uncorrelated with them and doesn't know
anything about their key so it's safe to
use it
without any fear the Charlie can
eavesdrop on their communication
and that really is the main idea behind the conference that's taking place here at the IQC this week
on quantum cryptography it's very
important in the study of quantum matter
because if I have a system with many
atoms or many electrons
pairs of Adams are electrons may want
to entangle with one another
they can lower their energy
by entangling
but if an electron entangles strongly with
one of its neighbours, that will reduce its
ability to entangle with other electrons.
So the system of many electrons has to
find a way of relieving that frustration
to find its lowest energy state
and that means there are different types of
phases of matter which can be
characterized by the pattern of the
entanglement among
the particles and we're learning a lot
in the last few years
about how to characterize that many
particle entanglement
and classify it. Monogamy is even
important in the context of black hole physics.
I'll tell you a little bit about that.
Black holes have been greatly puzzling
for decades when we think about their
information processing capabilities and
the reason is
that Stephen Hawking discovered that
black holes
omit radiation because of quantum effects
and eventually completely evaporate and
disappear
and that leads one to wonder what
happens to the information that was
encoded in the collapsing matter
that claps together to form the black
hole.
If black holes are like other objects
which radiate thermally
then what should happen is that all the
information that was encoded in the system
gets radiated away, carried away by the radiation in some very highly scrambled form.
The information is still there but in a
form which is very non locally spread out
and hard to read but,
black holes are different from other
systems they have what we call an event horizon
and what that means is the geometry of
space time is very
deformed so I can draw this slice I've shown it in green,
which actually is a slice of constant
time. All of the clocks on that green
slice read the same time
but that slice actually intersects both
the collapsing body from which the black
hole formed
and the radiation which is omitted by
the black hole.
So if the information comes out in some
highly scrambled form
it means the information is really in
two places at once at the same time
that means quantum information has been
cloned, that's bad.
So, we seem to have a rather unpalatable
choice either the information is actually destroyed,
or if it comes out it seems like cloning
has occurred and that also violates
principles of quantum mechanics. Either
way it seems like we have
a revolution in physics and have to
replace quantum mechanics by something new.
Well, a possible way out of this quandary
we suggested a while back
called black hole complementarity and the
idea is that we shouldn't think
of the system inside the black hole and
the system outside the black hole
as two subsystems of one larger system,
we should think of them instead as two
different points of view
of the same system. So in other words
the information is only in one place but
the observers who are outside the black
hole see it in one form, in the form of
this highly scrambled information
but the observers who fall into the
black hole see the collapsing body.
It's just very hard to reconcile those two
points of view, there's a very complicated map
between what the observers inside and
outside see
but they're really seeing the same
system from two different points of view
and this idea black hole complementarity
seems to allow us
to simultaneously hold 3 reasonable
beliefs
that a black hole doesn't destroy
information, it just scrambles it up,
that an observer who falls into a black
hole doesn't see anything unusual happen
at least not right away eventually that
observer is going to reach the
singularity and get torn apart and
that's that's going to be very
unpleasant
but at the moment of entering the black
hole everything seems normal,
and an observer who stays outside the black
all sees nothing unusual just the
expected laws of physics
and what was pointed out last year by AMPS, is that there,
it doesn't seem to be possible for all
three of these reasonable statements to
be true it once
and they suggested that the one that we
should give up on is number two
that in fact an observer who enters a
black hole
doesn't sail through the horizon and
eventually get destroyed at the singularity,
but actually gets, who dies a very
sudden fiery death
right at the moment of entering the
black hole. They call that a firewall.
So why would they say something like
that? It's because of monogamy of entanglement,
because if these three reasonable things
are all true
we have these consequences that if we
consider radiation,
let's call it "Betty" which is just being
omitted today from a very old black hole
if information is coming out of the
black hole that means that
Betty should be very highly entangled
with Charlie,
that's radiation that was omitted from
the black hole a long time ago
but if an observer who crosses into the
black hole sees nothing unusual,
it should look like vacuum, there
shouldn't be many particles around
but the vacuum is actually a very highly
entangled state.
In a vacuum, there's a lot of
entanglement between just outside the horizon,
Betty and a system inside the horizon Adam.
So, this is bad news for Betty. She'd
like to entangle with Adam so that
nothing unusual happens with the horizon,
she'd like to entangle with Charlie so that
information can come out of a black hole
and she can't have it both ways.
We could say all right he doesn't entangle with Charlie that's the
alternative in which
information is lost when a black hole
evaporates
or she could decide not to entangle with
Adam, but that would mean to a freely
falling observer it doesn't look like
the vacuum at all. There are many highly
energetic particles around and that's
the firewall.
Well, I'm telling you about this because
actually this is an observation or a
puzzle that could have arisen
a long time ago but it only happened
last year because
physicists in many fields including
gravitational physics
are starting to think about physical
problems in more of an 
information processing language, which
brought to the forefront
this violation of the monogamy of
entanglement.
But, physics is a broad subject, there are
many exciting frontiers of physics today
we're exploring the short distance
fronteer,
trying to understand the fundamental
particles and their interactions at the
Large Hadron Collider and other
facilities,
we're exploring the long-distance frontier, the structure and evolution and origin of the universe
with more and more powerful telescopes
and sensitive instruments to measure the
Cosmic Microwave Background.
But, what I've tried to persuade you is that there's
another frontier
also very compelling and very exciting. A
frontier of complex quantum state, which we could call
the entanglement frontier. In the 21st
century, human civilization, for the first time will be able 
to, in a highly controllable way
prepare states of many particles that are
very profoundly entangled.
That's something we never done before
and we can't very well anticipate the consequences of it
because we don't have the ability with our feeble minds and the computers that we currently possess
to really predict how highly entangled
systems will behave
and so we can expect a lot of exciting
discoveries.
As Mike mentioned at Caltech, we have an
Institute for quantum information and matter
where we're trying to explore
this entanglement frontier across a
broad front and for many points of view,
both theoretically and experimentally
and you're doing that here in Waterloo
where the Institute for Quantum
Computing and Perimeter Institute, our
world leading institutions exploring the
entanglement frontier, making many profound and influential scientific contributions.
At the IQIM, we have a tagline: Nature is subtle.
That is a play on Einstein's famous pronouncement: Subtle is the Lord, but malicious He is not.
Once I was a genius, but even he
underestimated the subtlety of nature
when he
derisively dismissed quantum
entanglement calling it spooky action at a distance.
What we're trying to do now in quantum
information science
is to relish, explore, and exploit
that glorious subtlety of the quantum world
in all its facets and ramifications.
Thanks for listening to me tonight.
Many thanks for that wonderful, wonderful lecture. We can take a few questions
for professor Preskill related to his talk.
Yeah, hi. You seem to describe the black hole complementarity in terms of on the
is it on?
So you seems to
describe black hole complementarity in terms of
describing the state's of an
observer inside the event horizon and
outside the event horizon
at the same time. Now maybe I didn't totally
understand that explanation but that
seems a little strange to me.
What you mean by talking about observers
inside and outside the event horizon at the same time?
Well, so I, so the question is what did I
mean
when I spoke of black hole
complementarity when I said there are observers
inside and outside the black hole at the
same time.
That's what it looked like at least. So in fact
even before I got the black hole complementarity I'd
drew this green slice through the
space-time
and so what I meant by that is that,
that slice is actually space like.
Now any 2 points on that slice are spaced like
separated points
so we can choose our time coordinate so
that, that is
a surface of constant time. The important
thing is that there's a space like slice
and the information seems to be on that
slice at two places.
Sounds like cloning of quantum information.
What are we supposed to do about that?
And just a quick technical follow-up,
which, which coordinate system do you use to decide
that they are space like separated? Say it once more.
Is there some special coordinate system
where I can see this? Yeah, yeah in fact
so if you,
so I take it that you know a lot about
general relativity.
I know there's coordinate systems. Okay
well anyway, yeah, if you
if you use Kruskal coordinates, I can
draw the slice
I mean if you look at a Penrose diagram
which is you know the Kruskal coordinate
system and then conformally mapped
to make the causal structure clear, I need to draw a slice
across that diagram which looks
horizontal sort of manifestly all at the
same time and most of the
radiation omitted by the black all and
the collapsing body both
cross that slice, Thanks.
Making me run
Okay, so
you had the picture of the five
entangled qubits
and then the dragon that corrupted 1
of them. Yeah. And the beaver came and fixed it,
Right? How did the beaver know which one
to fix?
Right, so the question is when
I had one logical qubit stored in a
block of 5 physical qubits and the
dragon came along and damaged one of them,
nobody told the Beaver what the dragon
had done
or which qubit he had done it to, and
somehow
the beaver came running out and went
right to the correct qubit.
How did he know? Yeah, he
did something I didn't explicitly tell you about.
So, he made some clever collective
measurements
on the block with qubit measurements
which don't tell him anything
about the encoded information we don't
want him to find out anything about it
because that would damage it
but those measurements suffice to tell
him how the correlations among
qubits have been damage so that it can
be repaired
the important thing is that he does collect
some information
he has to know what the, which qubit the
dragon hit and what he did to it
but he doesn't collect any information
about the protected state
because that would be fatal.
So that's the difference between a
logical qubit and a physical qubit then?
Yeah, so when I speak of the logical qubit
I mean
the information that we're really
processing which is encoded
in a redundant way in a system of many
physical qubits
so that's the quantum generalization of when I took one
bit, a ball which is either red or green
and I stored it by having
three red balls or three green balls.
I had three physical bits storing just
one bit of information because they were
supposed to all be the same color
and in the quantum case though we store
the information using entangled states.
Given what you've said about how our
understanding of information and
the role it plays in quantum mechanics has
started to change how we see
other sciences for instance the nature of black holes,
could you speak a little bit about
how this is also changing maybe our
philosophical understanding of the
nature of reality and how we should be
thinking about things ontologically?
Now the question is
I spoke about how thinking about quantum
mechanics from an information
perspective is giving us new insights
into different
physical phenomenon but is it also
giving us
insights into the deep philosophical
problems about quantum reality.
Well, I'm probably not the best person to
ask this question
because I, I've never really
been convinced that there are any deep
philosophical problems about quantum
reality. However, some of my colleagues
who are very concerned about those
questions
have developed new approaches
to the interpretation of quantum mechanics,
which are very much informed by
quantum information processing ideas.
Are you able to quickly describe what makes a quantum computer so much faster than a classical computer?
Well, yeah I didn't tell you in a very direct way. What I,
I said several things so one thing I
said was, So the question was
could I explain already what it is that makes a
quantum computer so fast?
And so one thing I said was
that it seems to be hard in general to
simulate a quantum computer just using
classical bits that's what I meant when
I said if we wanted to
describe all the correlations among the qubits, we need a huge number
of classical bits. So we don't have any
succinct way of recording with classical bits,
the quantum state. So if I wanted to
simulate using classical
computers what's happening when I
process the
quantum state, we don't have any way to do
it which doesn't require
huge resources like a number of bits which is
exponential in the number of qubits and
I said one other thing
without explaining it very much. I said
that
there's a special class of problems that
quantum computers seem to be good at which have
the right structure and I didn't say
what I meant by that exactly
but in some cases I can put a
computational problem
in the form of, you know what are the
global properties of some
function for example the period of the
function. The period meaning,
you know how much I have to advance its
argument before it gives the same
answer again, okay? And if I'd tried to
answer questions like that
classically I'd have to compute the
function a huge number of times
but if you, for certain kinds of
questions you can
get the answer about the global
structure of the function by computing the function
a much smaller number of times and
that's really the key
in many in quantum algorithms to getting
a big speed up.
Okay, one last question then.
When you spoke about quantum error
correction, you said like
the system has to forget its information and
all we need is the endpoint and that's it.
So, does this imply that the
quantum computers will be memoryless,
like, we can't apply Von Neumann
architecture on quantum computers?
So the question is
I said that
in order for quantum computers to work
it has to forget what happened during
the computation
and does that mean that we can't have a
quantum computer which has
an architecture similar to the Von Neumann
architecture where I have
a central processing unit and a memory
and I shuttle information
back and forth. No, I didn't mean to imply
that
a quantum computer can have a memory and a processor.
What I meant was that when you
cycle through many steps of the
computation, of course
the state of the register,
the memory, and the CPU will be continually updated
and we don't at the end want to have
a record which says you know at time
step 1,049
the state was "x" So the current systems also don't do that, right?
Well, that's right but
so in the classical case the computer so
the question is of course
classical computers don't do that either
they don't normally store such a record
that's right but
if information leaks from the computer
into its environment
I mean you say that, yeah, the
computer didn't do that
but maybe the full physical system
consisting of the computer and its surroundings
does have some information stored in it. Maybe,
you know, different parts on the chip were
getting hot
at different time steps or something and
that heated up the air and
left an imprint in the air currents in
the room you know stuff like that
it's very hard to prevent some leakage
of information to the surroundings while
you're doing the computation
and its fine it doesn't matter it's okay
for all that information to be
recorded somewhere else. The computation
still works in the quantum case it wouldn't work.
They're in some very hard to read
format the information were available in the environment
of what the state had been and
intermediate stages the computation and
then the quantum computer would fail
that's what I meant. So maybe I'll
squeeze in one more question
with Einstein staring down upon us.
He died not a big fan of quantum theory,
thought something was still missing.
You're not going to ask me if he were alive today...
Exactly, that's exactly what i'm going to ask you
and if he maybe would have
become a fan, any idea where along the way he would have?
What would have changed his mind because a lot has happened since.
A lot has happened, and in particular, it's tempting
to wonder what Einstein would have made
about theorem
and whether that would have weakened his
deeply held belief that there's
something wrong with quantum mechanics
and that it has to be replaced by a more
complete theory.
I mean, obviously I don't know the answer
to that
but you know there are other very
smart people.
Oh, I don't think I wanna go there.
He might not have changed his mind let me
put it that way.
Well let's thank Professor Preskill again for this fascinating lecture.
