John Preskill: Quantum Computing and the Entanglement Frontier

John Preskill: Quantum Computing and the Entanglement Frontier


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

15 thoughts to “John Preskill: Quantum Computing and the Entanglement Frontier”

  1. A hunderd billion dollars is affordable by the NSA and that means any crypto is already broken and nobody should not listen to Bruce Schneier because he might be a sellout.

  2. That is ignorant thinking, trust the math of cryptography. Math doesn't lie.

    NSA absolutely has used their muscle to implement backdoors (see RSA) but that does not mean they have broken all encryption by any means.

  3. D-Wave produced similar videos but I liked the entanglement frontier technology,Quantum cryptography part etc.QKD or Quantum key distribution can be used here to detect long distance Quantum cryptography [email protected]

  4. Dear genius, what the math says is that that the NSA can afford a quantum computer today and that a quantum computer can break very long codes.

  5. The first person to encode a quantum program to answer the question of the universe to be 42 should be rewarded one huge cookie!
    "But how was it computed?"
    "You will never know, for if you look at the computation then you are ruining it!"

  6. Such a great talk, really appreciate it. Lots of bad resources about Q computation, this helped me understand much better.

  7. This limerick has been driving me mad all morning. Partly because the physics makes my brain decohere. But mostly because I can't get the bloody thing to scan properly 😀

    Decoherent Limerick

    There was a pissed quantum computer
    whose qubits got fuzzy to cohere.
    When they asked "Are you sure
    that that's the answer?"
    it said "Yes, but don't ask how I got here."

  8. @ time  1:04 -06  out side np …..  would that include weather, and other chaotic systems?  Could you check a Quantum computer with different runs of the same problem, aka statistical  averaging?

  9. The famous E=mc2 equation basically says mass is energy and energy is mass so why are people surprised or confused about young's double slit experiment ? Thats where a single photon or atom behaves like an energy wave and creates an interference pattern, but everyone accepts Einstein's equation of e=mc2, so why is it that people can't accept, or see when mass scaled down to it's truly fundamental state is energy, but guess what? This is what string theory says exactly that beyond the atomic level is ubber tiny vibrating string or circle shaped energy, even today people have failed to see how to prove string theory, the big hurdle is since its soo small how can we see it? Well we can't directly see it, but!!! We can see it's effects,it's shadows, or its fingerprints, how? Well soo far scientists have trying to use the large (lhc) hydron collider to prove or disprove it, but I say it's already been proven, how? I say look at Young's two slit experiment and keep Einstein's equation of E=mc2 in mind, and you realize "hey doesn't it seem like the single atom or photon act like a wave?" What also makes waves? Energy!!! Bingo!!! The interference pattern will emerge like it was made by energy waves because in essence it is energy, look at it like this the smaller you go the closer you get to the division or definition btwn energy or mass or you can look at it as a countinous bridge btwn the two. So exactly what happens on how the interference pattern is created by one single atom sent through at a time? Since an atom at that level is now crossing or has crossed the threshold btwn beeing effected by classical physics or energy waves physics, it will now follow and act like energy waves basically it's creating a standing vibration energy wave,and when it travels those waves travel along with it wherever it goes in spacial demension of energy, because energy is everywhere unless you can cool to absolute zero which i now believe the energy limit or void of it then just maybe it wont create or ride on energy waves, but getting to absolute zero is impossible as of now, hence when it travels through the two slits it creates two waves and they clash and even cancel some of one another out, and thus you get the interference pattern……. So in conclusion String Theory is proven, and this will explain everything aka Dark matter, Dark energy, and quantum physics which is now basically from what ive seen is gone since it only is one slice of the effects of string theory, and what scienctists have only done before for to explain quantum mechanics is basically calculating the probability or the shadow of string theory in young's two slit experiment. The last piece of the puzzle put into place or rather the pieces put together at last we can finally realize the big picture… Did I blow anyone's mind? Nobel prize people i await my acceptance of the award lol

  10. Just a load of bragging. The reality is that quantum computing is illogical nonsense. These con-artists are just sucking up tax payers money to play with expensive toys.

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