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.

FUCK YOU!!!!

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.

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.

Photosynthesis is known to benefit from quantum effects.

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]

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.

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!"

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

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 ðŸ˜€

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."

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

Hartman and those fucking glasses… Every time lol

Slides please!

Damn, nature is so complex.

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 lolï»¿

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.