# “Quantum Computing and the Entanglement Frontier” John Preskill, CalTech

(ambient music) – Good evening, everyone. I’m Joel Moore, the interim chair of the

Berkeley Physics Department, and it is my great pleasure

to welcome you this evening to the annual J Robert

Oppenheimer Lecture. Since 1998, Berkeley Physics

has had the opportunity to bring truly world-renowned theoretical

physicists to campus to speak in honor of J Robert

Oppenheimer and his legacy. This lecture series occurs every spring, and it highlights trends, discoveries and groundbreaking research in theoretical physics, and it was made possible

through the generosity of Jane and Robert Wilson. Before introducing tonight’s lecturer, I would like to say a little bit about the Berkeley Physics

Department and some news, and say a little bit more about Oppenheimer and his legacy

and what he particularly means in the present time. To start with, Oppenheimer

was a theoretical physicist and created the first school

of theoretical physics in the US at Berkeley. He came to Berkeley one year after Ernest Lawrence, who was maybe the largest figure in Berkeley’s experimental

physics program, and between them, they turned Berkeley into one of the best departments

to do physics in the world. Oppenheimer’s achievements in physics, I would normally tell you a lot about. These include the

Born-Oppenheimer approximation for molecular weight functions and work on the theory of

electrons and positrons, the Oppenheimer-Phillips process infusion, and various other things. I would like to focus tonight on another aspect of

Oppenheimer’s career, which is what he did after he was at Berkeley. You may have heard that he

was the scientific leader of the Manhattan Project, the project to create the atomic bomb. And in that capacity, he was an incredible scientific manager. And normally, management is

not the most exciting thing to talk about. The particular point I would make is that Oppenheimer put together an unbelievable collection of talent. And this is not so much a scientific thing to me as it is being able to recognize very smart people and get them together and

then get out of the way, I think is Oppenheimer’s

great achievement. And one point I would like

to make about that talent is, some of it was born in the US, like Richard Feynman, for example, but a great deal of it was not. Much of it was immigrant, and, of that part, much

of that was refugee. And I think a great deal

of America’s leadership in post-war physics came

to that Manhattan Project, came from that Manhattan

Project generation. And that’s why if you try

to talk with physicists about politics, you’ll get

widely different opinions. Even with Oppenheimer, you

will get different opinions on, was Oppenheimer sufficiently

careful about security? Was the atomic bomb a

worthwhile exercise, and so on. Physicists are very

capable of disagreeing. You will very rarely hear a physicist say, in fact, never in my experience, that American physicists

have not benefited greatly from international collaboration and from people coming

from other countries, and I think that’s

probably worth remembering. So, Oppenheimer’s progress as the father, the founding father of the American School

of Theoretical Physics was to ask, what a talk was about, or what a piece of physics was about, what was learned by it, and what were the remaining

unsolved problems, and we continue to ask

those same questions, and that’s the theme of tonight’s lecture. So, as I mentioned, the

Oppenheimer Lecture we’ve had since 1998, and it’s become

a very nice tradition in our physics department, and there are new things

happening that I believe will last at least as well and become new traditions, and I wanted to call your

attention to a couple of those. One is, tonight is a night for theory, but we have created a

new experimental program at the undergraduate level, Physics 5, with a beautiful new laboratory that I think is going to make Berkeley, if it isn’t already,

the best place to learn experimental physics as an

undergraduate in the world. We have a new center for

quantum coherence science, which is actually very connected to the kind of work that

you’ll hear about tonight. It’s very much in the same theme, that certain fundamental ideas

of quantum mechanics unify a vast number of different

areas of physics. So that’s one of our main priorities in research at the moment. And then lastly, in order to link physics with the outside world in the same way that Oppenheimer did, we have a new industrial

partnership program, called Berkeley Physics Partners, or BP2, and I would be happy to talk with you about

any of these things, but I think, with that, let me move on to a little bit more about science and the Oppenheimer Lecture, and our distinguished guest

tonight, Professor Preskill. So, Oppenheimer lecturers,

since 1998, have included six Nobel laureates and distinguished figures from all areas of theoretical physics, ranging from astrophysics,

to condensed matter, to cosmology, to atomic and molecular physics. Tonight, we have an

unusually broad speaker in that Professor Preskill’s lecture on quantum computing and

the entanglement frontier will take us on a journey

into quantum entanglement and the various aspects of

physics that it unifies. So, Professor Preskill comes to us from the California

Institute of Technology, better known as Caltech. He is the Richard P Feynman professor of theoretical physics there, and he’s also director of The Institute for Quantum Information

and Matter at Caltech, and that institute, which has existed for quite some time now, I believe it started in 2000, was one of the first to

recognize that notions of quantum information are very powerful in linking the work of physicists

in different disciplines. Getting back to Professor Preskill, he received his PhD in

physics in 1980 from Harvard and moved rather quickly

to Caltech in 1983. He is a member of the National Academy. He is a two-time recipient of the Associated Students

of Caltech Teaching Award. He’s mentored more than 50 PhD students and more than 45 postdoctoral

scholars at Caltech, and many of those, a few of those are here, I believe, and many of those have

gone on to be leaders in their research areas. So if I had to pick a few

sentences to sort of summarize the theme of his research,

at least since 2000 or so, he’s especially intrigued

by the ways that our deepening understanding

of quantum information and quantum computing can be applied to other

fundamental issues in physics, such as the quantum

structure of space and time. Aside from his research papers, his celebrated lecture notes

from his Caltech course on quantum computation, which, by this time, includes

a great deal of things that I wouldn’t necessarily

call computation, they’ve exerted a profound influence on the development of the subject. And I would say that Caltech has become one of the leading centers

for theoretical research on quantum information

and quantum computing. Our own center for quantum

coherence science has a different emphasis in some ways, it’s based on what Berkeley leads in, but it’s fair to say that one of our intellectual progenitors in setting up this new center was what’s been done at Caltech. So, Preskill has been described as less weird than a quantum

computer and easier to understand. I agree with the second part, and the first, I’ll reserve

judgment until after the talk, but we are thrilled to

add Oppenheimer lecturer to his very long list of accolades. Please join me in welcoming

Professor John Preskill. (applause) – Thank you very much, Joel, for the beautiful introduction. And I’m deeply honored to be here to carry on the tradition of the Oppenheimer Lecture and to join the roster of great scientists who

have preceded me here. I’m going to be talking about quantum physics, but also about information. Everybody knows that

information technology has had a huge impact on our everyday lives, but we also recognize that

information technology that seems impressive to us

today is going to be surpassed in the future by new technology that we can’t really

expect to imagine today. It’s interesting just the same to speculate about future technologies, and I may not be the

ideal person to engage in that type of speculation. I’m not an engineer, I’m

a theoretical physicist and I can’t really claim to

be deeply knowledgeable about how computers really

work, but as a physicist, I do know that the crowning

intellectual achievement of the 20th century was the

development of quantum theory, and it’s natural for a

physicist to wonder how the development of quantum theory in the 20th century will impact 21st-century technology. Quantum theory is, of course,

an old subject by now, but some of the deep ways

in which quantum systems are different from classical systems we’ve only come to appreciate

relatively recently. And a lot of those differences have to do with the properties of information encoded in physical systems. To a physicist, information

is something we can encode and store in the state

of a physical system, like, for example, the pages of a book, but fundamentally, all physical systems are really quantum systems governed by quantum mechanics, and so information is something

that we can encode and store in a quantum state. And physicists have

appreciated, for a long time, that information carried

by quantum systems has some notoriously

counterintuitive properties. That’s why we like to

speak about the weirdness of quantum theory, and we relish that weirdness and find great enjoyment in it. But we’re also starting

to ask more seriously in recent years whether it’s possible to put the weirdness to work to exploit the unusual

properties of quantum information to perform tasks that wouldn’t be possible if this were a less weird classical world. And that desire to put

weirdness to work has driven the emergence of a field we call

quantum information science, which derives much of

its intellectual vitality from three central ideas, which are quantum entanglement,

quantum computing, and quantum error correction, and my goal in the talk is to introduce you to these ideas. I’d like to start at the beginning. We all know that any amount of

digital classical information can be expressed in terms

of indivisible units, bits of information, and we might think of a

bit as a physical object, like a ball, which can be

either one of two colors. Now if I want to, I can store a bit inside a box, and then later on, if I

want to recover the bit, I can open the box, and

the color that I put in comes out again, so I can

read the bit accurately. And when I speak of quantum

information, what I mean is information carried in a quantum system, and it, too, can be expressed in terms of indivisible units,

what we call quantum bits, or qubits for short. And for many purposes,

it’s useful or instructive to envision a qubit as an

object stored inside a box. Where we’re now, we have the

option of opening the box through two complementary doors, which correspond to two different ways in which we can prepare or observe the state of the qubit. And you can put information

in door number one of the box or door number two, and if, later on, you open that same door again,

the color ball that you put in comes out again, just as though the

information were classical. But if I put information into a qubit through door number one, for example, and then later on, I observe the qubit through door number two, observe it in the complementary way, then no one can predict what we’ll find. There’s a 50% probability

that the ball is red and 50% that it’s green. So if you want to read

quantum information, you have to do it the right way. If you do it the wrong way, then you will unavoidably

damage the information. And one consequence of

that we can appreciate, if we think about copying a quantum state. If I had a quantum copy machine, that would mean that if I happen to have put information through door

number one of our qubit, I can make a copy of the qubit, and then if I open the

original and the copy through door number one, then the color ball that I put in would come out of both boxes. And likewise, if I happen

to have put information in door number two of the original Qubit, once I build a copy, I

could open door number two on the original and the duplicate, and the color that I put in

would come out of both boxes. But, in fact, no such quantum

copying machine is possible. It’s not allowed by the laws of physics. We can’t make high-fidelity copies of unknown quantum states. And the reason why not is that in order to make the

copy, the copy machine has to probe inside the box, and if it guesses right and

uses the same door that I did, then it will be able

to copy the information just as though it were classical, but if it guesses wrong

and opens the wrong door, that will damage the information and there won’t be any way to build a high-fidelity copy. So although we might be

able to clone a sheep, we can’t clone a qubit. Now I’ve described qubits

in an abstract way, which I think is a useful

way to think about them, but a qubit always has

some physical realization, and I’ll give a few other examples later, but just so you’ll have something concrete to think about. We could consider, for example, the qubit to be a polarization state of a single particle of light, a photon. A photon has an electric

field, and if it’s oriented either horizontally or vertically, that corresponds to looking through door number one of the box, and if the polarization is tilted to the 45-degree rotated axes, that corresponds to door number two. So, for example, we could make a horizontally polarized

state of a single photon and observe it through the tilted axes, and what we would generate

is just a random bit. But the really interesting ways

in which quantum information is different from classical information we can only appreciate

if we consider states of more than one qubit. So let’s imagine we have two qubits, and they could be far

apart from one another. One at Caltech in Pasadena, the other in the custody of my friend in the Andromeda Galaxy. And some time ago, these two

qubits were both on earth and they interacted in a

certain way that prepared a correlated state of the two qubits which has some unusual properties. Namely, I can open my box in Pasadena through either door number

one or door number two, and either way, what I

find is just a random color with the 50% probability of

being either red or green, and the same thing is true

for my friend in Andromeda. He can open the box through

either door number one or door number two and just finds a random bit. So neither one of us finds any information in the boxes by opening a box in Pasadena or Andromeda, which seems kind of funny, because with two boxes,

we should have been able to store two bits of information. But where has that

information been hidden? The answer in this case is that all the information is actually encoded in the correlations between what happens when

you open the box in Pasadena and when you open it in Andromeda. Because it turns out, for this

particular correlated state of the two qubits, if I open door number

one, what I find might be red or green, but if

my friend in Andromeda also opens door number one for

that particular qubit pair, he’s guaranteed to find

the same color that I do. And the same thing is true if

we both open door number two. As long as we open the same door, we’re guaranteed to find the same color. And there are four perfectly

distinguishable ways in which a box in Pasadena

could be correlated with a box from Andromeda. We could see that the same

color or opposite colors when we both open door number one or both open door number two, and by choosing one of those four ways, we’ve encoded two bits of information in our pair of qubits. But what’s unusual in this

case is that that information is completely inaccessible locally, it’s a property stored non-locally, shared by the two

distantly separated qubits. And this property, that

information can be shared non-locally between

distantly separated objects is what we call quantum entanglement, and it’s the really important way in which quantum information is different from classical information. Correlations themselves

are nothing unusual. We encounter them all

the time in daily life. My socks are normally the same color. So if you look at my left

foot and observe my sock, then you know, without looking, what color you expect when

you look at my right foot. And it’s kind of like that

with the quantum boxes. If I want to know what my

friend is going to see when he opens door number one in Andromeda, I can open door number one

in Pasadena to find out. And if I want to know what

he’ll see when he opens door number two in Andromeda, then I can open door number

two in Pasadena to find out. So it might seem to you that

it’s really the same thing that the boxes are just like the soxes, but I claim that, in fact,

they’re fundamentally different. The boxes are not like the soxes, and the essence of the difference is there’s just one way to look at a sock, but because we have these

two complementary ways of observing the qubit, the correlations among qubits are richer and more interesting than the correlations among ordinary bits. This phenomenon of quantum

entanglement is an old subject. It was first explicitly discussed in a paper by Einstein,

Podolsky, and Rosen in 1935. And to Einstein, entanglement

was so unsettling as to indicate that something is missing from our current understanding of the quantum description of nature. And that paper elicited

some thoughtful responses, including a particularly

interesting one from Schrodinger. The way Schrodinger put it was, “The best possible knowledge of a whole “does not necessarily indicate

the best possible knowledge “of its parts.” What Schrodinger meant was

that even if we had the most complete description that the

laws of physics will allow of a pair of qubits, we’re still powerless to

predict what we’ll find when we open door number

one or door number two of one of those two qubits. And it was Schrodinger who suggested using the word entanglement to describe these unusual correlations. He also said, “It is rather discomforting “that the theory should

allow a system to be steered “or piloted into one or

the other type of state “at the experimenter’s mercy “in spite of his having no access to it.” And what Schrodinger

meant is it seems funny that it’s up to me to decide, by either opening door

number one or door number two in Pasadena, whether

I’ll know what my friend will find when he opens door

number one or door number two in Andromeda. But Schrodinger understood

that these correlations, though different from

ordinary correlations, don’t allow us to send

an instantaneous message from Pasadena to Andromeda. When my friend in Andromeda opens his box, he just finds a random bit, and the probability distribution governing what he finds is not affected by what I

choose to do in Pasadena. So no message is sent from

one party to the other. Now this theory of quantum

entanglement really didn’t advance very much

for the next 30 years, until the work of John Bell in the 1960s. And beginning with Bell,

we started to think about entanglement in

a rather different way, not just as something weird,

unsettling, and surprising, but as something potentially useful; a resource that we can

use to perform tasks that wouldn’t otherwise be possible. We don’t have to go into the details, but what Bell described can be thought of as a

game that two players play. Alice and Bob, it’s a cooperative game. Alice and Bob are on the same side. They’re trying to help each other win. And the way the game works is that Alice and Bob receive inputs, and their task is to

produce outputs which are correlated in a way that

depends on the inputs that they both receive. But under the rules of the game, Alice and Bob are not

allowed to communicate with one another between

when they receive the inputs and when they produce their outputs. And for this particular

version of the game, if Alice and Bob played

the best possible strategy, they’ll be able to win the game with a success probability of 75% if we average uniformly over the inputs that they could receive. But there’s also a quantum

version of this game, where the rules are exactly the same, except that, now, Alice

and Bob are allowed to use entangled pairs of qubits which have been distributed

to them before the game began. And with those short

qubits, they can play a better quantum strategy, which allows them to win the game with a higher success probability, about 85% rather than 75%. So they can use entanglement as a resource to perform a task winning the game better than they could using just classical correlations that they share. And experimental physicists

have been playing this game for decades now, and

winning with the higher probability of success,

which Bell pointed out, the laws of quantum mechanics will allow. So it seems that the

super strong correlations really are part of nature’s design. Einstein didn’t like quantum entanglement. He called it spooky action at a distance. This sounds even more derisive

when you say it in German. But it doesn’t even matter

what Einstein thinks. Nature is the way

experiments reveal her to be, and we should all learn

to love her as she is. So, boxes are not like soxes. Quantum correlations are

different from classical ones. You can use them to win a game with an 85% success probability instead

of a 75% success probability. Is that a really big deal? Yeah, it’s really a big deal. And we can appreciate

better why it’s a big deal if we think about more complex

systems with more qubits. We can think about quantum

entanglement this way. Imagine a book that’s 100 pages long. If this were an ordinary

book, written in bits, you could read the pages one at a time, and every time you read another page, you’ll know another 1% of

the content of the book, and after you’ve read all 100 pages, you know everything that’s in the book. But suppose it’s a quantum

book, written in qubits, and suppose the pages are highly

entangled with one another, then when you look at

the pages one at a time, all you see is random gibberish, revealing almost no

information that distinguishes one highly entangled book from another. And that’s because the

information in the quantum book is not written in the individual pages. It’s stored almost entirely

in the correlations among the pages. That’s quantum entanglement. And these correlations can be very complex and are hard to describe

in terms of classical bits. So, for a modest number of

qubits, just a few hundred, if I wanted to give a

complete description, in classical language,

of all the correlations among 300 qubits, I

would have to write down more bits than the number of

atoms in the visible universe. So it’ll never be possible,

even in principle, to write down that complete description of all the correlations. And that property of quantum information is very intriguing to the

physicist, Richard Feynman. They’d let him make the

suggestion in the early 1980s that if we could build

a computer that operates on qubits instead of

bits, a quantum computer, we’d be able to perform tasks that are beyond the reach of any

conceivable digital computer. Feynman’s idea was that

if we can’t even express, in terms of ordinary bits, the information content

of a few hundred qubits, then by processing the

qubits, we ought to be able to perform tasks that a digital computer would never be able to emulate. And at the time Feynman

was making this suggestion in the early 1980s, there was

an undergraduate at Caltech studying mathematics. Like all of our undergraduates,

he studied quantum physics as part of our core curriculum. And like most of our undergraduates, he retained what he learned and later put it to good use when he made a remarkable discovery. Shor thought about the problem

of finding the prime factors of a composite integer. This is a problem which we think is hard for classical computers, though there’s no

mathematical proof of that. And what Shor found is that if we had a quantum computer, the factoring problem would be easy. It wouldn’t be much

harder than multiplying two numbers together

to find their product. And when I heard about this in 1994 when Shor made the discovery, I was really awestruck, because what it means

is that the difference between hard and easy problems, the difference between problems that we’ll be able to solve some

day with advanced technologies and the problems that we’ll

never be able to solve because they’re just too hard, that that boundary between hard and easy is different than it otherwise would be because this is a quantum

world, not a classical world. And I thought that was one

of the most interesting ideas I had heard in my scientific life, and thinking about it eventually led me to change the direction of my own research from elementary particle

physics to quantum computing. Now does anybody care whether

factoring is a hard problem? Yeah, in fact, a lot of people care, because the security of the

protocols that we use everyday to protect our privacy when we

communicate over the internet are based on the presumed hardness of factoring and other similar

number theoretic problems. And in a few decades, when

everybody has a quantum computer, we won’t be able to protect our privacy using these protocols. We’ll have to do something else. Alternatives exist, but it’s still not exactly clear what will be the best

way to protect privacy in the coming post-quantum world. The important thing that we

learn from Shor and others is that there is an interesting

classification problem, classification of problems, that there are problems

that are hard classically and quantumly easy. Can’t be solved by

ordinary digital computers, could be solved if we

had quantum computers, and it becomes a compelling

research question to understand better what are the problems which are of such intermediate difficulty. And we’ve learned a lot of things about

that in the last 20 years, but I think the most

important thing we know, from a physicist’s point of

view, about quantum computers is that we think that we

can’t say this for sure, but with a quantum computer, we’d be able to simulate efficiently any

process that occurs in nature, which isn’t the case with digital computers, which are unable to simulate highly entangled systems. And that means with a quantum computer, we’d be able to explore

physics in new ways. For example, by simulating

strongly coupled field theories, we’d be able to compute the

properties of complex molecules, study exotic quantum materials, and study fundamental processes, like the formation and

evaporation of a black hole or the properties of the universe

right after the big bang. So a lot of people work

on developing applications for quantum computers

even though we don’t have large-scale quantum computers yet. One of them is my friend, Eddie Farhi, who, like me, is a lapsed

particle physicist, and when he wrote one of his

billion papers a few years ago, it inspired me to send him a poem, which read, in part, “We’re

very sorry, Eddie Farhi. “Your algorithm’s quantum. “Can’t run it on those mean machines “until we’ve actually got ’em.” And the poem goes on, but the point is that we have a lot of interesting ideas about what to do with quantum computers, but we don’t have quantum computers yet that can run those applications. So why not? What is it that’s taking so long? Well, it’s really hard to

make a quantum computer. And one of the difficulties is the phenomenon we call decoherence. Physicists like to imagine

a quantum state of a cat, which is simultaneously dead and alive. And we never observe,

in everyday experience, that type of superposition of macroscopically distinguishable

states of a system. And we understand the reason why not. It’s because no real cat

can be perfectly isolated from its surroundings. And the interactions with

the environment, in effect, immediately measure the cat, projecting it onto a state, which is either completely

dead or completely alive. That’s the phenomenon of decoherence, and decoherence helps us to understand why even though quantum physics holds sway at the microscopic scale, still, classical physics is quite adequate for describing most of the processes of our everyday experience. A quantum computer won’t be

otherwise much like a cat, but it, too, will be hard to perfectly isolate

from its surroundings. And interactions with

the environment can cause the quantum information

stored in a quantum computer to be damaged, and that will cause the

computation to fail. So if we’re going to operate a

large-scale quantum computer, we have to figure out how to protect it from the damaging effects of decoherence and other sources of error. Errors can be a problem, even in the classical world, we all

have bits that we cherish, but everywhere there

are dragons lurking, who take pleasure in damaging our

bits, flipping their color. We learn, in the classical world, some ways to protect our information. The important concept is

that we can redundantly encode the information so that

if it’s partially damaged, we can still recover the information. So if I want to store a bit,

which is one that I cherish, I can store backup copies of the bit, and then a dragon might

come along from time to time and change the color of one of the balls, but I can also ask a busy beaver to frequently check the balls, and whenever she sees that

one’s a different color from the other two, she repaints it so all three match again. So unless the dragon has had a chance to damage two out of the three balls, the information is well protected because of the redundant storage. Now we’d like to use the same idea that redundancy provides

protection for quantum states. But at first, there seem

to be difficulties because, as already discussed, we can’t

copy unknown quantum states. So I can’t, for example,

make a backup copy of the state of a quantum computer in the middle of a computation in case my original gets damaged. And furthermore, with

the quantum computer, there are more things that can go wrong with the information. It might be that a dragon opens

door number one of the box and flips the color of the

ball and then recloses the box. That would be like a bit flip that occurs for classical information. But instead, the dragon

could open door number two and change the color of the

ball and reclose the box. That’s what we call a

phase error on a qubit, and it really has no classical analog. We need to be able to protect

against both the bit flips and the phase errors to make sure our quantum

information is undamaged. There’s another way of thinking

about these phase errors, which is we might imagine that the dragon opens door number one, and instead of flipping the color of the ball, just observes the color and remembers it. It never had the effect

of changing the color, as observed through door number two. And in many physical settings, it’s easier for the environment to

remember the state of a qubit than to flip the qubit, and that makes phase errors

particularly pervasive in some physical settings. So the key thing is that if you look at quantum

information, you disturb it, and so if we want to

protect quantum information, we have to keep it almost perfectly isolated

from the environment. So there’s no leakage of information about the state of our quantum computer to the outside world. And that sounds impossible

because our hardware will never be perfect. So how can we perfectly isolate a quantum computer from the outside? But we learned, in principle, how to do it through the concept we call

quantum error correction, and the essential trick

is to use entanglement to protect the information. So if I have one qubit

that I want to protect, I can encode that one qubit of information in an entangled state of five qubits, which is chosen in such a way

that if the dragon comes along and observes or performs any action on one of the five boxes, that dragon doesn’t

acquire any information about what the encoded state is. Because the information doesn’t reside in that individual box, it’s a collective property

of the five qubits. It’s just like that 100-page book. When you look at one of

the qubits at a time, the information is completely hidden. And so it’s possible

then to ask the beaver, after the dragon has

acted on one of the boxes, to make some collective observations of the five qubits and restore the right kind of the entanglement. And, in the process, the

beaver doesn’t learn anything either about the protected encoded state, and so that state can be undamaged. So the basic idea of quantum

error correction is that we can use redundancy to

protect quantum states, but we have to do it the right way, and the right way to do it

is to encode the information in the form of entanglement

among many parts of the system. So just like that 100-page book, which reveals no information when

you look at one page at a time, the environment will interact locally with the parts of the

system one page at a time, and, in doing so, won’t be able to detect the encoded information or damage it. And we’ve also learned how to process information which is encoded

in this entangled form, and so operate a robust quantum computer, at least in principle. So, although we may never see a real cat in a superposition of

the dead and alive state, we should be able to prepare

an encoded state of a cat and maintain it in that

delicate superposition state for as long as we please. Well, we understood these principles of quantum error correction

about 20 years ago. We were very excited. And so my then-student, Daniel Gottesman, wrote a sonnet. And I’ll just read the beginning of it. “We cannot clone,

perforce; instead, we split “coherence to protect it from that wrong “that would destroy our valued quantum bit “and make our computation take too long.” And so on. The point is we were excited, because we had understood that, at least in principle, we could make a quantum computer resistant to the effects of noise and decoherence. Now another hero of this story is my Caltech colleague, Alexei Kitaev. The day when we met, which

was about 20 years ago, was one of the most exciting

days in my scientific life. When I heard his seminar

and took these notes, I thought that I was hearing, from Kitaev, ideas about quantum error correction which are potentially transformative. And what I learned from him

was the connection between quantum error correction and topology. Topology means the properties

of a mathematical object which remain invariant when

we smoothly deform the object without ripping or tearing it. And when we think of operating

a robust quantum computer, what we want is for the

protected information that’s being processed to remain invariant even as we deform the computer

by introducing some noise. So we would like to use interactions which take advantage of

topological principles for the purpose of information processing. And physicists now have such

topological interactions. For example, the Aharonov-Bohm effect. I can imagine transporting

a charged particle, like an electron, around

a magnetic flux tube. And then the quantum state

of that electron is modified in a way that depends

on the magnetic flux, which is enclosed in the

tube even though the electron never directly visits the region where the magnetic field is non-zero. And that change, that interaction

is a topological property. If we deform the trajectory of the electron, the effect of circling the

flux tube doesn’t change, the only thing that matters

is the topological property, the winding number of the electron around the flux tube. Now if we can engineer

two-dimensional systems, for example, in a layer separating two slabs of semiconductor, then there’s a very rich family of possible topological

interactions that can be realized. In these systems, if properly designed, we can have what we call anyons. And anyons have the interesting property that if I have a system of

many of these particles, that the quantum information

carried by the particles can be very complex, but when we visit the

particles one at a time, that information is completely invisible. Because it’s not a property

of the individual particles, but a collective property

of all the particles. And that’s just the type

of encoding of information that we want to protect against noise. That information will be well hidden from the influence of the environment. And furthermore, we can

process the information by performing exchanges of the particles in which they swap places. So we can imagine operating a topological quantum computer, which we would initialize by

in some two-dimensional medium, preparing pairs of anyons, then processing the

state of those anyons by successively exchanging pairs of particles so that their world lines in

two-plus-one-dimensional spacetime trace out the braid, and then we could read out a final result say by bringing the

particles together in pairs and observing whether the

pairs of particles annihilate and disappear or not. So what’s beautiful about this idea is that, in principle, we can do any computation we want this way, and the computation is

intrinsically resistant to decoherence if we keep

the temperature lower so we have no unwanted

anyons diffusing around, and if we keep the particles

far apart from one another, except at the very

beginning and the very end so there’s no unwanted exchange of charges between the particles, then as long as the world

lines execute the right braid, then we’ll do the right

computation and get the right answer. So I really like this idea, which led me to write a poem about it. And I won’t read you the whole thing, but part of it reads this way. Alexei exhibits a knack

for persuading that someday we’ll crunch quantum data by braiding, with quantum states hidden

where no one can see, protected from damage through topology. Anyon, anyon, where do you roam? Braid for a while before you go home. And there’s more to it than that, but the point is, it’s a really beautiful, exciting idea. But it’s a theorist’s dream, and it’s something that

we can really realize in hardware that can be built. Well, here, too, Kitaev

had a seminal idea, which is to use the principle that, under the right circumstances, we can divide an electron in half. That sounds ridiculous

because we know an electron is a fundamental elementary

particle and it’s indivisible, but in a highly entangled environment, in the right kind of

two-dimensional medium, electrons can split into pieces, and anyons can arise that way. Here’s one relatively simple setting in which that can happen, actually. In a one-dimensional wire, it’s possible for the wire

to be superconducting. That means it conducts electricity without any resistance. And there are two types of superconductor: what we might call the conventional type, and a more exotic type, called the topological superconductor. And at the boundary between the two types, there resides an object that we call a Majorana fermion. And now it’s possible

to add a single electron to this finite segment of

topological superconductor, and that electron will, in effect, dissolve and disappear. So we can’t tell whether

it’s been added or not. But in the process, the state

of these two Majorana fermions at the two end points of the

segment will have changed. But that change in the state

of the Majorana fermions is not locally visible; we can’t see it if we visit the endpoints of the

segment one at a time. It’s a collective property of the two. So that’s the type of non-local

encoding of information that we want to protect against

errors in a quantum system. And this type of Majorana fermion in a superconducting wire, well, we have some very

interesting evidence that it can be realized experimentally, more

experiments will be needed to make that case completely ironclad. Of course, we’d like to be

able to do more than just store information reliably, we’d like to be able to process it. And using quantum wires, one way to do that would be

to build a network of wires so that if I had two Majorana fermions, I would be able to change their positions, let’s say with voltage

gates underneath the sample, so that one Majorana

fermion could be parked around the corner, the other move from right to left, and then the first one unparked, and that would perform an exchange of the positions of the two particles, which would be a kind

of quantum operation, one step in a quantum computation which is protected from decoherence. That type of experiment

hasn’t been attempted yet, but I expect it will be in

the next couple of years, and when done successfully, that will not just be an interesting step towards a future technology,

but a real milestone in basic physics. Now I don’t want to give

the impression that this exotic topological

approach is the only way that we can build large-scale

quantum computers. No, that’s not at all the case. There are a number of ways

of building quantum hardware, which are currently being developed and are making impressive progress. I already mentioned one

way of encoding a qubit using the polarization

state of a single photon. There are a number of other ways. One is we could store our qubit in the state of a single atom, which could be, say, in either

its internal ground state or some long-lived metastable state corresponding to the

two states of the qubit. Or we could encode a qubit

in a single electron, which has a magnetic moment, or spin, which could be oriented either up or down. So these are two remarkable encodings, because in each case, we are encoding the information which is to be processed in a truly microscopic system, either a single atom or a single electron. Another possibility, though, is to use superconducting circuits, not the exotic topological type that I

just mentioned a minute ago, but conventional superconductors, where, although, in practice, there are better ways of doing things. You could imagine encoding a qubit by choosing a state in which this current in the circuit either circulates clockwise

or counterclockwise. That’s a remarkable encoding, too, because, in this case, the qubit involves the collective motion of billions of electrons, and yet, for information

processing purposes, it behaves like a single atom or electron and can be quite well-controlled. We’re not far away. I expect, in the next couple of years, we will have quantum computers with more than 50 qubits, and these will be systems

which are sufficiently complex that we can’t simulate

them with digital computers that exist today. So this will be in the onset of the age of quantum supremacy, in which quantum systems

are performing tasks that go beyond what we can

achieve in the classical world. And I think we should

view that as the opening of a new frontier in

the physical sciences, what we could call the

complexity frontier, or entanglement frontier. This is different from the frontier we explore in particle

physics at short distances, or in cosmology at long distances, but, like those, very

fundamental and exciting, and, like those, in order to make advances, we

need more and more powerful instruments. We are now in the process of developing

and perfecting the ability to prepare and precisely control highly entangled states of many particles, which go beyond what we can simulate. We don’t have the theoretical tools to predict very well the behavior of these systems, and that’s going to open new

opportunities for discovery. What are the things that

we’ll be able to do with a quantum computer, which we hope we’ll have

in a couple of years, with 50 to 100 qubits? Well, maybe one of the most

important things is we’ll use these smaller quantum computers to learn how to make rather

big quantum computers, in particular, by testing and perfecting our procedures for doing

quantum error correction. But we’ll also be able to run, at relatively small scales, new

kinds of algorithms, which will already surpass what we

can do with digital computers, study certain quantum simulation problems, for example, to investigate

quantum chaos in new ways, or to simulate complex

molecules going beyond what we can do classically. But once we have quantum

computers that we can try out and play around with, I expect we’ll discover a number of new applications

which we haven’t anticipated. Now how far off is it that we’ll have scalable quantum computers that can, for example, break the RSA

public-key cryptosystem? Oh, that’s farther away, perhaps decades. You know, I said earlier that

you can’t solve this problem using digital computers, but that’s not strictly true, it’s just a question of resources. So if you wanted to break RSA

as it’s typically used today, it’s possible, but you would have to cover about a quarter of the land area of North America with a server farm, and then you’d be able to

solve the problem in about 10 years, but the catch is that, with

existing computing technology, the power consumption would burn up the world’s supply of fossil

fuels in just one day. So, from that perspective, the quantum computer looks pretty good. If we just took the technology

we have today and sort of brute force scaled it up, it’s not quite as simple as it sounds, but suppose we did that, and this estimate was done

by John Martinis, who’s a experimentalist who works

in superconducting qubits, well, in order to have

sufficient redundancy to do error correction,

we’d probably need about 10-million physical qubits, and then we’d be able to

run the algorithm that factors a number and breaks

RSA in less than a day, and the power we would

need is just 10 megawatts. The thing is, at the current cost of making a very good qubit, it would cost 10s of billions of dollars. So, the cost is gonna have

to come down, and it will. So there are three questions

about quantum computers that I’ve been emphasizing. One is, what will we do

with quantum computers? Why build one? And I think the best

answer we have to that is that, with a quantum computer, we’d be able to simulate, we think, any process that occurs in nature, which we can’t do with

digital computers, which are unable to simulate

highly entangled systems. Can we really build one? Well, we know of no

insurmountable obstacles to doing so now that we

understand the principles of quantum error correction. And how will we do it? Well, as I’ve emphasized, there

are a number of approaches to building quantum hardware that are under development and

making good progress. And it’s important to continue

those different paths because different quantum technologies may find different applications, and we don’t really know which technology will ultimately have the best

prospects for scalability to large devices. What I really find interesting is the ways in which our

ideas about quantum computing are giving us new approaches to some of the other

fundamental problems in physics, particularly quantum

condensed matter physics, and also elementary particle physics. There’s been a surge of

interest in recent years among the community of people who work on quantum field theory

and quantum gravity in quantum information concepts. These people feel that

quantum information ideas are highly relevant and useful for addressing the problems

that they’re interested in. And in a way, that’s not so surprising, because the quantum gravity

community has been struggling for 40 years with a very deep puzzle, whose origin really has to

do with quantum entanglement, specifically, the quantum entanglement between the inside and the

outside of a black hole. A black hole is a wonderful object, and one of the seminal papers

on the subject, by the way, was by J Robert Oppenheimer. It’s an extremely simple object. It’s composed of nothing but warped spacetime geometry. Its defining property

is its event horizon. If you are foolish enough

to cross the event horizon and enter a black hole, you’ll be unable to return

to the outside or even communicate with your

friend who stays outside. But the inside and the

outside of a black hole can be and will be

entangled with one another, and Stephen Hawking

understood in the 1970s that, as a result, a black hole will emit radiation due to quantum effects and eventually radiate away

all its mass and disappears. And that creates a

puzzle, because we can ask about what happened to

any information that fell into a black hole

during its lifetime. It’s a foundational principle

of quantum mechanics that information is not destroyed, though it can be scrambled up

into a form that’s exceedingly hard to read. So, we’re faced with an unpleasant choice. If we lose information inside a black hole and then the black hole disappears, if that information is lost

from the universe forever, then we have to recast the

foundations of quantum theory. On the other hand, if that

information manages to escape from the interior of the black hole, that means we have to

rethink the foundations of general relativity. And after 40 years, we still don’t have a clear and completely

satisfactory resolution of this puzzle. What we can say about it, the best thing we can say about it is that we understood the resolution, to a large degree but not completely, in a particular setting, what we call AdS-CFT duality, and this is a description of

quantum gravity in the case where the vacuum energy is negative and the curvature of

spacetime is negative. And in that setting, we have two complementary ways of

describing the same physics. In a way, this correspondence allows us to put a black hole inside a tin can. The walls of the can are what we call CFT, for conformal field theory, and that’s just an ordinary

quantum theory without gravity. And in the interior, we have gravitation, geometry, and

quantum fluctuations of geometry, and a process in which a black hole forms and evaporates completely has a complementary

description in terms of just the field theory on boundary. And on the boundary,

there’s no black hole, there’s no gravity, there’s no place for information to hide, and so it seems manifest, that the process can be described without any loss of information. So at least in this case, the one where we understand

quantum gravity the best, it seems clear that a

black hole does not destroy quantum information. But even so, we’re left without

a satisfactory understanding of how the information manages to escape, and, in fact, it’s not so

clear how this boundary description encodes the experience of someone who falls through

the black hole event horizon and enters the black hole interior. So, to make further progress, we should try to deepen our understanding of this correspondence, which is a subject of much ongoing work. So let me say a little

bit more about that. Here, for ease of visualization,

I’ve indicated the boundary is one-dimensional, a circle, and the bulk geometry as

two spacial dimensions. So, here in this cut through the bulk, in order to indicate

the negative curvature, I’ve used the Poincare disc description, each one of these colored

regions actually has the same geometrical size, but they

appear to be smaller and smaller as we get closer to the boundary in order to capture

the negative curvature. And the idea the

correspondence is there are two exactly equivalent descriptions

of the same physics, one on the boundary and one in the bulk, and there’s a very complex dictionary, which is only partially understood, which maps the states and

observables of the bulk theory to the corresponding

states and observables of the boundary theory. But what has become increasingly clearer in the last few years is that this geometry in

the bulk can be viewed as an emergent property of

the quantum entanglement on the boundary. What evidence do we have

pointing in that direction? I’ll tell you a few things that indicate that

geometry can be thought of as emergent from entanglement. Well, one is what we call

holographic entanglement entropy, which was discovered 10 years ago now by Ryu and Takayanagi. Well, they asked the following question. Suppose we consider some

state to find on the boundary, and we’re interested in a connected region on the boundary,

and we’d like to know how entangled that region is with

the complementary region. And they pointed out that there’s an answer to this question which

is geometrical in the bulk. We can quantify

entanglement using entropy, which is a measure of how

much information is missing from this region, A,

because it’s encoded in the form of entanglement with

the complementary region, and that entropy can be expressed in suitable units as the area of the minimal surface in the bulk which separates boundary region A from the complementary

region on the boundary. And those units in which we

express the area are just the same units that we use to express the entropy of the black

hole in terms of the area of its event horizon. So, we can think of where

these minimal surfaces lie, which encodes the geometry of the bulk as corresponding to

properties of the entanglement on the boundary. Now here’s another example. We can imagine a boundary theory which has

some holographic dual, has some higher dimensional

gravitational interpretation, and we consider two such theories and ask what happens when we

entangle those two systems with one another. And the answer is that the bulk geometry corresponding

to that pair of systems will have a wormhole

which connects together the two asymptotic regions

on the left and the right. And when there’s no entanglement between the two systems, then

there will be no wormhole connecting them. So this relationship between

connectedness of space and entanglement was elevated by Maldacena and

Susskind a few years ago to a general principle,

which they ingeniously called ER equals EPR. EPR means Einstein, Podolsky, and Rosen, who first discussed quantum entanglement in that 1935 paper I mentioned, and ER refers to Einstein and

Rosen, who, in that same year, wrote the first paper discussing wormholes in general relativity. Now, if you had a quantum

computer or, by some other means, you tried to remove the entanglement between distant regions of space, the effect of that, according to this ER equals EPR principle, would be that the space would

break up into fragments. So, there’s a sense in which entanglement provides the glue

that holds space together. Now, this wormhole can’t be used to travel quickly from one region of space to another. It’s not a traversable wormhole. This corresponds with the

property of quantum entanglement that we can’t use entanglement to send an instantaneous message from one party to another. What happens is the wormhole is dynamical; it grows too quickly for anyone to pass from one end to the other. So you might think, “If a

wormhole isn’t traversable, “that’s not really very much fun.” But actually, it’s a lot of fun. Because we can imagine

two lovers, Alice and Bob, who live in different galaxies and long for each other’s company, but it’s completely impractical to travel from one galaxy to another. But let’s say Alice and

Bob had the foresight to prepare many entangled

pairs of particles, and Alice took one member of each pair, and Bob took the other

member of each pair, then Alice could take her particles and gravitationally collapse

them to make a black hole, and Bob could do the same. And those two black

holes would be entangled with one another, and that means they would

be connected by a wormhole. Now Alice wouldn’t be able

to jump into her black hole and emerge from Bob’s, but Alice and Bob could both

jump into their black holes, and then they’d be able to

meet inside their own hole and have a fulfilling

relationship for a while, but ultimately, they’d

be destined to arrive at the singularity inside the black hole and be torn asunder. So it turns out to be a tragic love story. Now, another thing that’s become apparent in just

the last couple of years is that there’s a connection between this dictionary, between the bulk and boundary theory and quantum error correction, that if I consider some local operator deep inside the bulk geometry, the corresponding operator on the boundary is a very non-local operator, it’s just the kind of mapping

from local to non-local that we need to protect quantum

information from damage, just the kind that occurs in a quantum error-correcting code. And so the bulk geometry deep in the bulk is actually very robustly encoded so that if some damage

occurs on the boundary, that bulk geometry won’t be much affected. So I’m hopeful that this insight can be taken further. It’s really a remarkable illustration of the unity of physics. We develop the idea of

quantum error correction because we want it to keep

quantum computers from crashing, and we wound up with a

different perspective on the geometry of quantum spacetime. So far, we’ve understood this

within the context of this… Well, partially understood

it within the context of this AdS-CFT duality, but we’d like to broaden our understanding beyond the context of

Anti-de Sitter space, because Anti-de Sitter space isn’t the real case that we want to solve. Anti-de Sitter space, the thing that we

understand reasonably well, that’s the case where the

vacuum energy is negative and the curvature of

spacetime is negative, but it just so happens

that we live in a universe where our vacuum energy is positive and curvature is positive,

what we call de Sitter space. It’s much easier to do quantum mechanics in Anti-de Sitter space

because there’s a boundary, and we can make reference to the boundary when we want to discuss the

observables of the theory. De Sitter space doesn’t have a boundary, and that makes it much

harder to understand quantum physics in that setting. But we’re going to have to learn

how to do quantum mechanics in de Sitter space because

that’s where we live, and I’m confident we’ll figure it out eventually, but it’s hard. Last year, Robbert Dijkgraaf, the director of The

Institute for Advanced Study, spoke at a Caltech event, and he showed this slide

near the end of his talk, and I was quite struck by it, because he was trying to

illustrate how the different ideas of theoretical

physics are connected, and he put quantum information right in the center of things. I don’t think he would have

done that a few years earlier. This idea that quantum information

is a unifying principle of physics has really

only started to take hold in the last couple of years. But unlike Dijkgraaf, I would cross out the word, theoretical, because quantum information

is an experimental subject, and if it’s true, as we

increasingly have reason to believe, that we can think of the

geometry of spacetime as an emergent property

of quantum entanglement in some underlying system, then we should be able to get insights into quantum gravity by

doing laboratory experiments. So I anticipate that, in the coming decades, we will gain deep insights into the

quantum structure of spacetime by doing laboratory experiments with highly entangled quantum systems that, on the tabletop, in a laboratory at a place like Berkeley, will be able to, in effect, to create spacetimes

that didn’t exist before and explore their properties

and learn new things. But whether that prediction

comes to pass or not, I think we can be highly confident that we’ll find many

surprises and discoveries as we explore the entanglement frontier. Thanks a lot for listening. (applause) – [Joel] Thank you, Professor Preskill. We normally allow a few

minutes for questions at the end of Oppenheimer lectures, and we try to have a mix

of questions from both professional physicists

and amateur physicists. And if you managed to follow the talk, then you’re already an

amateur physicist at least. So, please, any sort of question. – [Audience Member] How do you feel now about the bet you made with

Stephen Hawking in 1997? – Now the question was about a bet. This will be the opening line

in my obituary, I’m afraid. I won a couple of bets

with Stephen Hawking, and, in particular, on one of those bets, concern the question of information and whether it can escape

from black holes or gets permanently destroyed. Hawking and also our friend, Kip Thorne, took the position that black

holes destroy information, and then my side of the

bet was that black holes actually just scramble up information into a form that’s hard to read. And Stephen has recanted,

but he believed very deeply at the time that black holes destroy information, and it was

a bit of a shock to me when he conceded this bet in 2004. It was a rather dramatic occasion. We were at a conference in Ireland, in a big convention hall in Dublin, and somehow the word was leaked

out that Stephen was gonna make a big announcement, and so there were 100 people from the press and various amateur physicists. Michael Flatley, the Lord of the Dance, it turns out that

general relativity is his hobby, he was there. So Stephen gave a technical talk, and then at the end, he

presented me with my prize, which was a baseball encyclopedia from which you can withdraw information. He knows I’m a baseball fan. This was very hard to get in Ireland because you can’t get a

baseball encyclopedia in Dublin, so we had to have it shipped overnight. How do I feel about it? Well, I was surprised that

he conceded because I think we still don’t have a

satisfactory understanding of the problem and he would

have been well within his rights if he had decided to hold out longer until the question is

definitively settled. And I still think I

took the right position, and now Stephen agrees with that. Kip does not, he has not conceded. But I don’t think we really have a 100% convincing argument that information escapes

from black holes, even today. – [Joel] Thank you. – [Audience Member] Can you describe the hardware that will replace the transistor chip in

the quantum computer? In other words, I’m interested

in what the hardware is gonna look like. – So the question is, what

will the hardware look like in a quantum computer? Well, I mean, we have

quantum computers now, but they’re small, and so I think you’re really

asking about the scalable quantum computers of the

future, where we might have millions of physical qubits. So the honest answer

is, I don’t know exactly what the hardware is going to look like. Actually, here at Berkeley,

in the Siddiqi Group, they’re doing terrific work on quantum computing hardware

with superconducting circuits, and they can show you a device that has 10 qubits in it, which is based on superconducting technology. We can imagine scaling

up devices like that to millions of physical qubits, though it’s going to be very challenging. Another approach, which, in the long run, I think

has a lot of promise, is using, as I mentioned,

electron spins as qubits. That technology is lagging

behind at this stage, but it’s something that is perhaps especially compatible with the silicon classical technology that we have now. And I also mentioned these

topological approaches, where it’s even less clear what

the hardware is going to look like, but I did sort of a

cartoon version of it in my drawing of a quantum wire. – [Audience Member] A lot

of these questions will be answered by experimentation,

experimental physics. What kind of experimentation? What does that look like? Or is it the same answer

as the last question? – Well, so, what I had in mind is that we have understood, to some degree, that it’s possible for a quantum system which doesn’t involve gravitation at all to behave like a system that has gravity, and that’s what this story of the AdS-CFT correspondence is about. So, the example we’ve

been able to understand is a very special one. It has lots of symmetry,

it has special features. But I think the phenomenon of a highly entangled system behaving like a gravitational

system is a more general one. But we don’t have the mathematical tools to

understand it in other contexts. So, what we’ll need to be

able to do experimentally, I think, is build systems in which there are many particles which all interact with one another in a typical system

that’s easier to realize. The strength and the interactions

between the particles depends on how distantly

separated they are, and it falls off with distance, but I think the kind of system

that we would need is one with many particles or degrees of freedom which all have strong

interactions with one another. And in such systems, then we’d be able to drive them and make measurements of the way the different

parts of the system are correlated with one another, and the task would be then to see if those correlations have an interpretation in terms of some kind

of gravitational system. – [Audience Member] We

can’t really understand quantum entangled states. So we would have a computer, and we would take classical

information, put it into a quantum computer,

wait a while, and take a classical solution out

that we can understand. Just curious how you

get it in and out, and I guess the contradiction

between the number of states inside the computer versus

the very simple states that we can comprehend,

put it in, and take it out. – Alright, so the question is, how do we get information into and out of a quantum computer? As the question anticipated, the information that we put in

and we take out is classical. The processing that occurs

can’t be done classically, but is done in a quantum device. It’s the task of the designer

of quantum algorithms to understand how to do

that quantum processing, but the initialization

and the reading out are easier to describe. So, if I have many qubits, I mean, in my cartoon analogy, the

preparation would just consist of putting a lot of balls in door number

one of a lot of qubits, and then a lot of quantum

processing goes on, which can’t be described classically, and in the end, we open all

the boxes one at a time. So, the preparation

would just be preparation of one qubit at a time. Like, let’s say it’s a bunch

of electron spins and we prepare them so that they’re

all pointing, spin up, and then we do the quantum processing, and, at the end, we just

observe the spins one at a time and see whether they’re

pointing up or down, or, in my analogy, open the

box to see if the ball is red or green. So, the process of

initializing and reading out is not so exotic. The art of designing a quantum algorithm is to

figure out how to make use of the quantum entanglement

at intermediate stages to speed up the solution

to a suitable problem. – [Audience Member] Is there a chance that quantum computing will extend

the validity of Moore’s law into a longer extent of time? – So, the question was about Moore’s law and whether quantum computing

will extend Moore’s Law further into the future. Of course, Moore’s Law is the miracle that we’ve all been living in for 50 years or so. We’ve seen exponential improvement in the performance of integrated circuits. Although we’ve reached a

stage now where it’s getting harder and harder to

increase the clock speed, and a lot of the improvement

is coming from increasing parallelism of classical systems, and it’s an amazing story, and I think a very instructive

one for quantum technology. If you go back to the 1960s, when Moore and others were thinking about the prospects for improving

integrated circuits in the future, you know, they couldn’t

imagine things like an iPhone. It was just far beyond what the technology was

pointing to at the time. And, in the case of quantum technology, I think we’re in a similar situation. We are now starting to

interact with information in a completely different

way from anything that happened before, and we don’t know where

that’s going to take us. We have a few ideas of how we

will apply quantum computers. Undoubtedly, we haven’t

thought of the most important applications that are going

to arise in the future. So, I think my answer

to the question is that we’ve seen, in recent history, and even longer term history, that physics can drive the economic expansion of the world, that the technologies that come

out of physics eventually have a big, big impact on

the way we live our lives. We’ve certainly seen that with the basic physics in the 20th century of understanding semiconductors, which led to integrated circuits, quantum physics of lasers,

which we make use of in many ways today. But that 20th century

physics, that was the physics of, if you like, single

particle quantum mechanics. And now we’re getting a grasp on a new quantum revolution: the

properties of many particles, and I think that could well drive economic development in the 21st century. Nobody really knows, and so I don’t have a precise prediction about the quantum Moore’s Law. And I think we can expect that these new technologies are going to take us to remarkable places

that we haven’t yet imagined. – [Audience Member] In quantum mechanics, electrons are indistinguishable. Are qubits also indistinguishable? – Now the question was about indistinguishable

particles, that we know that electrons, for example,

are indistinguishable, and does that apply to qubits as well? It need not. I mean, it’s possible for the qubits to be distinguishable. For example, in these superconducting circuit realizations of a qubit, each qubit is actually

an engineered device. They’re not all identical. And so there’s no notion

of indistinguishability among the qubits that doesn’t

impair the quantum computer’s ability to perform its special magic. In the case of the anyons I described, they can be viewed as a rather exotic type of

indistinguishable particle, and that’s why it makes sense

to process the information by exchanging the particles. That affects the information that’s encoded

in the many-particle system. When the anyons change places, the… When you look at them one at a

time, they all look the same. – [Audience Member] Do you

subscribe to any particular interpretation of quantum mechanics? – The question is, do I… It’s a question for me personally? Do I subscribe to any particular interpretation of quantum mechanics? I’m an Everettian. I like the idea. Sometimes people call it the

many worlds interpretation, though I’m not very fond of that name. But I think the essence

of that point of view is that there’s really just one way for things to change in the world. Technically, quantum states

can change by evolving in a way which doesn’t create

or destroy information, that is unitary evolution, and that’s the only

thing that ever happens. That measurement is not a

fundamentally different process. This is a subject that people

can get emotional about. A disadvantage, you might

say, of that point of view is that in order to understand why, when I observe a quantum system,

I see one definite outcome, I have to include myself

in the description, because what really happens is that there’s more than one possible outcome, and I become correlated with the state of the

system I’m observing. And some people think this

is a very extravagant thing, in that we have to keep track

of all the possible outcomes by including the observer in the system. But I prefer that to

introducing measurement as some kind of new fundamental process. However, I think, you know, everybody’s entitled, to a certain degree, to their own interpretation

of quantum mechanics if they prefer. Different interpretations

can give rise to different insights and can help to

generate different ideas. I mean, I think, to me, the

question of interpretation is most interesting to the degree that it raises questions about what the alternative to

quantum mechanics might be. Maybe quantum mechanics will fail, and some people expect quantum

mechanics to break down in some stage because of the issues of interpretation. I’m not sure whether that’s true. But I think thinking about

interpretations can be useful, particularly if it suggests new ways in which

we can test quantum theory and look for deviations from it. – [Joel] One last question in the back. (audience member questioning) – So, I think the question was, technology is very dependent

on advances in materials, and what can we say about how advances in materials will

impact quantum technology? Was that more or less the question? (audience member speaking) Yeah, well, there are materials issues in all of the things that I mentioned. There have been tremendous improvements, for example, in the performance

of superconducting qubits going back 15 years, and many of those improvements

have to do with using superior materials to make the Josephson junctions,

which are the essential ingredient in the

superconducting circuits that makes them control the

ball and behave quantumly. These topological quantum computing ideas, computing with anyons, that’s very much a materials issue, though it’s been a great challenge to synthesize materials and

to fabricate devices that bring together all the physical

ingredients that we need to make topological quantum

computing work better. And spins and semiconductors,

same thing, that materials issues are

currently a huge impediment, and improvements in the materials will surely

lead to improved technology. – [Joel] I think, with that,

we should call it a night. Before we go, let’s

thank Professor Preskill for a beautiful and stimulating

Oppenheimer Lecture. (drum beat)