The following is a conversation with Scott Aaronson,

a professor at UT Austin,

director of its Quantum Information Center,

and previously a professor at MIT.

His research interests center

around the capabilities and limits of quantum computers

and computational complexity theory more generally.

He is an excellent writer

and one of my favorite communicators

of computer science in the world.

We only had about an hour and a half of this conversation,

so I decided to focus on quantum computing.

But I can see us talking again in the future

on this podcast at some point

about computational complexity theory

and all the complexity classes that Scott catalogs

in his amazing Complexity Zoo Wiki.

As a quick aside,

based on questions and comments I've received,

my goal with these conversations

is to try to be in the background without ego

and do three things.

One, let the guests shine

and try to discover together

the most beautiful insights in their work

and in their mind.

Two, try to play devil's advocate

just enough to provide a creative tension

in exploring ideas through conversation.

And three, to ask very basic questions

about terminology, about concepts, about ideas.

Many of the topics we talk about in the podcast

I've been studying for years

as a grad student, as a researcher,

and generally as a curious human who loves to read.

But frankly, I see myself in these conversations

as the main character

for one of my favorite novels by Dostoevsky

called The Idiot.

I enjoy playing dumb.

Clearly, it comes naturally.

But the basic questions

don't come from my ignorance of the subject

but from an instinct that the fundamentals are simple.

And if we linger on them

from almost a naive perspective,

we can draw an insightful thread

from computer science to neuroscience

to physics to philosophy

and to artificial intelligence.

This is the Artificial Intelligence Podcast.

If you enjoy it, subscribe on YouTube,

give it five stars on Apple Podcast,

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at Lex Friedman, spelled F R I D M A N.

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And now, here's my conversation with Scott Aaronson.

I sometimes get criticism from a listener here and there

that while having a conversation

with a world class mathematician, physicist,

neurobiologist, aerospace engineer,

or a theoretical computer scientist like yourself,

I waste time by asking philosophical questions

about free will, consciousness, mortality, love,

nature of truth, super intelligence,

whether time travel is possible,

whether space time is emergent and fundamental,

even the crazier questions like whether aliens exist,

what their language might look like,

what their math might look like,

whether math is invented or discovered,

and of course, whether we live in a simulation or not.

So I try.

Out with it.

Out with it.

I try to dance back and forth from the deep technical

to the philosophical, so I've done that quite a bit.

So you're a world class computer scientist,

and yet you've written about this very point,

the philosophy is important for experts

in any technical discipline,

though they somehow seem to avoid this.

So I thought it'd be really interesting

to talk to you about this point.

Why should we computer scientists, mathematicians,

physicists care about philosophy, do you think?

Well, I would reframe the question a little bit.

I mean, philosophy almost by definition

is the subject that's concerned with the biggest questions

that you could possibly ask, right?

So the ones you mentioned, right?

Are we living in a simulation?

Are we alone in the universe?

How should we even think about such questions?

Is the future determined,

and what do we even mean by it being determined?

Why are we alive at the time we are

and not at some other time?

And when you sort of contemplate

the enormity of those questions,

I think you could ask,

well, then why be concerned with anything else, right?

Why not spend your whole life on those questions?

I think in some sense,

that is the right way to phrase the question.

And actually, what we learned, I mean, throughout history,

but really starting with the scientific revolution

with Galileo and so on,

is that there is a good reason to focus

on narrower questions, more technical,

mathematical or empirical questions.

And that is that you can actually make progress on them,

and you can actually often answer them.

And sometimes they actually tell you something

about the philosophical questions

that sort of maybe motivated your curiosity as a child.

They don't necessarily resolve the philosophical questions,

but sometimes they reframe

your whole understanding of them, right?

And so for me, philosophy is just the thing

that you have in the background from the very beginning

that you want to, these are sort of the reasons

why you went into intellectual life in the first place,

at least the reasons why I did, right?

But math and science are tools that we have

for actually making progress.

And hopefully even changing our understanding

of these philosophical questions,

sometimes even more than philosophy itself does.

Why do you think computer scientists avoid these questions?

We'll run away from them a little bit,

at least in a technical scientific discourse.

Well, I'm not sure if they do so

more than any other scientists do.

I mean, Alan Turing was famously interested

and his most famous, one of his two most famous papers

was in a philosophy journal mind.

It was the one where he proposed the Turing test.

He took a Wittgenstein's course at Cambridge,

argued with him.

I just recently learned that little bit

and it's actually fascinating.

I was trying to look for resources

in trying to understand where the sources of disagreement

and debates between Wittgenstein and Turing were.

That's interesting that these two minds

have somehow met in the arc of history.

Yeah, well, the transcript of the course,

which was in 1939, right,

is one of the more fascinating documents that I've ever read

because Wittgenstein is trying to say,

well, all of these formal systems

are just complete irrelevancies, right?

If a formal system is irrelevant, who cares?

Why does that matter in real life, right?

And Turing is saying, well, look,

if you use an inconsistent formal system to design a bridge,

the bridge may collapse, right?

And so Turing, in some sense, is thinking decades ahead,

you know, I think, of where Wittgenstein is,

to where the formal systems are actually going to be used

in computers, right, to actually do things in the world.

You know, and it's interesting that Turing

actually dropped the course halfway through.

Why?

Because he had to go to Bletchley Park

and work on something of more immediate importance.

That's fascinating.

Take a step from philosophy to actual,

like the biggest possible step to actual engineering

with actual real impact.

Yeah, and I would say more generally, right,

a lot of scientists are interested in philosophy,

but they're also busy, right?

And they have a lot on their plate,

and there are a lot of sort of very concrete questions

that are already not answered,

but look like they might be answerable, right?

And so then you could say, well, then why break your brain

over these metaphysically unanswerable questions

when there were all of these answerable ones instead?

So I think, you know, for me,

I enjoy talking about philosophy.

I even go to philosophy conferences sometimes,

such as the FQXI conferences.

I enjoy interacting with philosophers.

I would not want to be a professional philosopher

because I like being in a field where I feel like,

you know, if I get too confused

about the sort of eternal questions,

then I can actually make progress on something.

Can you maybe link on that for just a little longer?

What do you think is the difference?

So like the corollary of the criticism

that I mentioned previously,

that why ask the philosophical questions

of the mathematician is if you want

to ask philosophical questions,

then invite a real philosopher on and ask them.

So what's the difference between the way

a computer scientist or mathematician

ponders a philosophical question

and a philosopher ponders a philosophical question?

Well, I mean, a lot of it just depends

on the individual, right?

It's hard to make generalizations about entire fields,

but, you know, I think if we tried to,

if we tried to stereotype, you know,

we would say that scientists very often

will be less careful in their use of words.

You know, I mean, philosophers are really experts

in sort of, you know, like when I talk to them,

they will just pounce if I, you know,

use the wrong phrase for something.

Experts is a very nice word.

You could say sticklers.

Sticklers, yeah, yeah, yeah, or, you know,

they will sort of interrogate my word choices,

let's say, to a much greater extent

than scientists would, right?

And scientists, you know, will often,

if you ask them about a philosophical problem,

like the hard problem of consciousness

or free will or whatever,

they will try to relate it back to, you know,

recent research, you know, research about neurobiology

or, you know, the best of all is research

that they personally are involved with, right?

And, you know, of course they will want to talk about that,

you know, and it is what they will think of, you know,

and of course you could have an argument

that maybe, you know, it's all interesting as it goes,

but maybe none of it touches the philosophical question,

right?

But, you know, but maybe, you know, a science,

you know, at least it, as I said,

it does tell us concrete things.

And, you know, even if like a deep dive into neurobiology

will not answer the hard problem of consciousness,

you know, maybe it can take us about as far as we can get

toward, you know, expanding our minds about it,

you know, toward thinking about it in a different way.

Well, I mean, I think neurobiology can do that,

but, you know, with these profound philosophical questions,

I mean, also art and literature do that, right?

They're all different ways

of trying to approach these questions that, you know,

we don't, for which we don't even know really

what an answer would look like,

but, and yet somehow we can't help,

but keep returning to the questions.

And you have a kind of mathematical,

beautiful mathematical way of discussing this

with the idea of Q prime.

Oh, right.

You write that usually the only way to make progress

on the big questions, like the philosophical questions

we're talking about now is to pick off smaller sub questions.

Ideally sub questions that you can attack

using math, empirical observation, or both.

You define the idea of a Q prime.

So given an unanswerable philosophical riddle Q,

replace it with a merely, in quotes, scientific

or mathematical question Q prime,

which captures part of what people have wanted to know

when they first asked Q.

Then with luck, one solves Q prime.

So you described some examples of such Q prime sub questions

in your long essay titled,

Why Philosophers Should Care About Computational Complexity.

So you catalog the various Q primes

on which you think theoretical computer science

has made progress.

Can you mention a few favorites, if any pop to mind,

or do you remember some?

Well, yeah.

So, I mean, I would say some of the most famous examples

in history of that sort of replacement were,

I mean, to go back to Alan Turing, right?

What he did in his computing machinery

and intelligence paper was exactly,

he explicitly started with the question,

can machines think?

And then he said, sorry,

I think that question is too meaningless,

but here's a different question.

Could you program a computer

so that you couldn't tell the difference

between it and a human, right?

And yeah.

So in the very first few sentences,

he in fact just formulates the Q prime question.

He does precisely that.

Or we could look at Gödel, right?

Where you had these philosophers arguing for centuries

about the limits of mathematical reasoning, right?

The limits of formal systems.

And then by the early 20th century,

logicians, starting with Frege, Russell,

and then most spectacularly Gödel,

managed to reframe those questions as,

look, we have these formal systems.

They have these definite rules.

Are there questions that we can phrase

within the rules of these systems

that are not provable within the rules of the systems?

And can we prove that fact, right?

And so that would be another example.

You know, I had this essay called

The Ghost in the Quantum Turing Machine.

That was one of the crazier things I've written,

but I tried to do something,

or to advocate doing something similar there for free will,

where instead of talking about is free will real,

where we get hung up on the meaning of,

what exactly do we mean by freedom?

And can you have, can you be,

or do we mean compatibilist free will,

libertarian free will?

What do these things mean?

You know, I suggested just asking the question,

how well in principle, consistently with the laws of physics,

could a person's behavior be predicted?

You know, without, so let's say,

destroying the person's brain, you know,

taking it apart in the process of trying to predict them.

And, you know, and that actually,

asking that question gets you into all sorts of meaty

and interesting issues, you know, issues of,

what is the computational substrate of the brain?

You know, or can you understand the brain, you know,

just at the sort of level of the neurons, you know,

at sort of the abstraction of a neural network,

or do you need to go deeper to the, you know,

molecular level and ultimately even to the quantum level?

Right, and of course,

that would put limits on predictability if you did.

So you need to reduce,

you need to reduce the mind to a computational device,

like formalize it so then you can make predictions

about what, you know, whether you could predict the behavior

of the system. Well, if you were trying

to predict a person, yeah, then presumably,

you would need some model of their brain, right?

And now the question becomes one of,

how accurate can such a model become?

Can you make a model that will be accurate enough

to really seriously threaten people's sense of free will?

You know, not just metaphysically, but like really,

I have written in this envelope

what you were going to say next.

Is accuracy the right term here?

So it's also a level of abstraction has to be right.

So if you're accurate at the, somehow at the quantum level,

that may not be convincing to us at the human level.

Well, right, but the question is what accuracy

at the sort of level of the underlying mechanisms

do you need in order to predict the behavior, right?

At the end of the day, the test is just,

can you, you know, foresee what the person is going to do?

Right, I am, you know, and in discussions of free will,

you know, it seems like both sides wanna, you know,

very quickly dismiss that question as irrelevant.

Well, to me, it's totally relevant.

Okay, because, you know, if someone says,

oh, well, you know, a Laplace demon

that knew the complete state of the universe,

you know, could predict everything you're going to do,

therefore you don't have free will.

You know, it doesn't trouble me that much because,

well, you know, I've never met such a demon, right?

You know, and we, you know, we even have some reasons

to think, you know, maybe, you know,

it could not exist as part of our world,

you know, it's only an abstraction, a thought experiment.

On the other hand, if someone said,

well, you know, I have this brain scanning machine,

you know, you step into it and then, you know,

every paper that you will ever write, it will write,

you know, every thought that you will have, you know,

even right now about the machine itself, it will foresee.

You know, well, if you can actually demonstrate that,

then I think, you know, that sort of threatens

my internal sense of having free will

in a much more visceral way.

You know, but now you notice that we're asking

a much more empirical question.

We're asking, is such a machine possible or isn't it?

We're asking, if it's not possible,

then what in the laws of physics

or what about the behavior of the brain,

you know, prevents it from existing?

So if you could philosophize a little bit

within this empirical question,

where do you think would enter the,

by which mechanism would enter the possibility

that we can't predict the outcome?

So there would be something

that would be akin to a free will.

Yeah, well, you could say the sort of obvious possibility,

which was, you know, recognized by Eddington

and many others about as soon as quantum mechanics

was discovered in the 1920s, was that if,

you know, let's say a sodium ion channel,

you know, in the brain, right?

You know, its behavior is chaotic, right?

It's sort of, it's governed by these

Hodgley–Huckskin equations in neuroscience, right?

Which are differential equations

that have a stochastic component, right?

Now, where does, you know, and this ultimately governs,

let's say whether a neuron will fire or not fire, right?

So that's the basic chemical process

or electrical process by which signals

are sent in the brain.

Exactly, exactly.

And, you know, and so you could ask,

well, where does the randomness in the process,

you know, that neuroscientists,

or what neuroscientists would treat as randomness,

where does it come from?

You know, ultimately it's thermal noise, right?

Where does thermal noise come from?

But ultimately, you know,

there were some quantum mechanical events

at the molecular level

that are getting sort of chaotically amplified

by, you know, a sort of butterfly effect.

And so, you know, even if you knew

the complete quantum state of someone's brain,

you know, at best you could predict the probabilities

that they would do one thing or do another thing, right?

I think that part is actually relatively uncontroversial,

right?

The controversial question is whether any of it matters

for the sort of philosophical questions that we care about.

Because you could say, if all it's doing

is just injecting some randomness

into an otherwise completely mechanistic process,

well, then who cares, right?

And more concretely, if you could build a machine

that, you know, could just calculate

even just the probabilities

of all of the possible things that you would do, right?

And, you know, of all the things that said

you had a 10% chance of doing,

you did exactly a 10th of them, you know,

and so on and so on.

And that somehow also takes away the feeling of free will.

Exactly.

I mean, to me, it seems essentially just as bad

as if the machine deterministically predicted you.

It seems, you know, hardly different from that.

So then, but a more subtle question

is could you even learn enough

about someone's brain to do that, okay?

Because, you know, another central fact

about quantum mechanics is that making a measurement

on a quantum state is an inherently destructive operation.

Okay, so, you know, if I want to measure the, you know,

position of a particle, right?

It was, well, before I measured,

it had a superposition over many different positions.

As soon as I measure, I localize it, right?

So now I know the position,

but I've also fundamentally changed the state.

And so you could say, well, maybe in trying to build

a model of someone's brain that was accurate enough

to actually, you know, make, let's say,

even well calibrated probabilistic predictions

of their future behavior,

maybe you would have to make measurements

that were just so accurate

that you would just fundamentally alter their brain, okay?

Or maybe not, maybe you only, you know,

it would suffice to just make some nanorobots

that just measured some sort of much larger scale,

you know, macroscopic behavior, like, you know,

what is this neuron doing?

What is that neuron doing?

Maybe that would be enough.

See, but now, you know, what I claim is that

we're now asking a question, you know,

in which, you know, it is possible to envision

what progress on it would look like.

Yeah, but just as you said,

that question may be slightly detached

from the philosophical question in the sense

if consciousness somehow has a role

to the experience of free will.

Because ultimately, when we're talking about free will,

we're also talking about not just the predictability

of our actions, but somehow the experience

of that predictability.

Yeah, well, I mean, a lot of philosophical questions

ultimately, like, feedback to the hard problem

of consciousness, you know,

and as much as you can try to sort of talk around it

or not, right?

And, you know, and there is a reason

why people try to talk around it,

which is that, you know,

Democritus talked about the hard problem of consciousness,

you know, in 400 BC in terms that would be

totally recognizable to us today, right?

And it's really not clear if there's been progress since

or what progress could possibly consist of.

Is there a Q prime type of subquestion

that could help us get at consciousness?

It's something about consciousness.

Well, I mean, well, I mean, there is the whole question

of, you know, of AI, right?

Of, you know, can you build a human level

or superhuman level AI?

And, you know, can it work in a completely different

substrate from the brain?

I mean, you know, and of course,

that was Alan Turing's point.

And, you know, and even if that was done,

it's, you know, maybe people would still argue

about the hard problem of consciousness, right?

And yet, you know, my claim is a little different.

My claim is that in a world where, you know,

there were, you know, human level AIs

or we'd been even overtaken by such AIs,

the entire discussion of the hard problem of consciousness

would have a different character, right?

It would take place in different terms in such a world,

even if we hadn't answered the question.

And my claim about free will would be similar, right?

That if this prediction machine that I was talking about

could actually be built, well, now the entire discussion

of the, you know, of free will is sort of transformed

by that, you know, even if in some sense

the metaphysical question hasn't been answered.

Yeah, exactly, it transforms it fundamentally

because say that machine does tell you

that it can predict perfectly

and yet there is this deep experience of free will

and then that changes the question completely.

And it starts actually getting to the question

of the AGI, the touring questions

of the demonstration of free will,

the demonstration of intelligence,

the demonstration of consciousness,

does that equal consciousness, intelligence and free will?

But see, Alex, if every time I was contemplating a decision,

you know, this machine had printed out an envelope,

you know, where I could open it

and see that it knew my decision,

I think that actually would change

my subjective experience of making decisions, right?

I mean, it would.

Does knowledge change your subjective experience?

Well, you know, I mean, the knowledge

that this machine had predicted everything I would do,

I mean, it might drive me completely insane, right?

But at any rate, it would change my experience

to act, you know, to not just discuss such a machine

as a thought experiment, but to actually see it.

Yeah.

I mean, you know, you could say at that point,

you know, you could say, you know,

why not simply call this machine

a second instantiation of me and be done with it, right?

What, you know, why even privilege the original me

over this perfect duplicate that exists in the machine?

Yeah, or there could be a religious experience with it too.

It's kind of what God throughout the generations

is supposed to have.

That God kind of represents that perfect machine,

is able to, I guess, actually,

well, I don't even know what are the religious

interpretations of free will.

So if God knows perfectly everything in religion,

in the various religions,

where does free will fit into that?

Do you know?

That has been one of the big things that theologians

have argued about for thousands of years.

Yeah.

You know, I am not a theologian,

so maybe I shouldn't go there.

So there's not a clear answer in a book like...

I mean, this is, you know, the Calvinists debated this,

the, you know, this has been, you know,

I mean, different religious movements

have taken different positions on that question,

but that is how they think about it.

You know, meanwhile, you know,

a large part of sort of what animates,

you know, theoretical computer science,

you could say is, you know, we're asking sort of,

what are the ultimate limits of, you know,

what you can know or, you know, calculate or figure out

by, you know, entities that you can actually build

in the physical world, right?

And if I were trying to explain it to a theologian,

maybe I would say, you know, we are studying, you know,

to what extent, you know,

gods can be made manifest in the physical world.

I'm not sure my colleagues would like that.

So let's talk about quantum computers for a second.

Yeah, sure, sure.

As you've said, quantum computing,

at least in the 1990s, was a profound story

at the intersection of computer science,

physics, engineering, math, and philosophy.

So there's this broad and deep aspect to quantum computing

that represents more than just the quantum computer.

But can we start at the very basics?

What is quantum computing?

Yeah, so it's a proposal for a new type of computation,

or let's say a new way to harness nature to do computation

that is based on the principles of quantum mechanics.

Okay, now the principles of quantum mechanics

have been in place since 1926.

You know, they haven't changed.

You know, what's new is, you know, how we wanna use them.

Okay, so what does quantum mechanics say about the world?

You know, the physicists, I think, over the generations,

you know, convinced people

that that is an unbelievably complicated question

and, you know, just give up on trying to understand it.

I can let you in, not being a physicist,

I can let you in on a secret,

which is that it becomes a lot simpler

if you do what we do in quantum information theory

and sort of take the physics out of it.

So the way that we think about quantum mechanics

is sort of as a generalization

of the rules of probability themselves.

So, you know, you might say there was a 30% chance

that it was going to snow today or something.

You would never say that there was a negative 30% chance,

right, that would be nonsense.

Much less would you say that there was, you know,

an I% chance, you know, square root of minus 1% chance.

Now, the central discovery

that sort of quantum mechanics made

is that fundamentally the world is described by,

or, you know, the sort of, let's say the possibilities

for, you know, what a system could be doing

are described using numbers called amplitudes, okay,

which are like probabilities in some ways,

but they are not probabilities.

They can be positive.

For one thing, they can be positive or negative.

In fact, they can even be complex numbers.

Okay, and if you've heard of a quantum superposition,

this just means some state of affairs

where you assign an amplitude,

one of these complex numbers,

to every possible configuration

that you could see a system in on measuring it.

So for example, you might say that an electron

has some amplitude for being here

and some other amplitude for being there, right?

Now, if you look to see where it is,

you will localize it, right?

You will sort of force the amplitudes

to be converted into probabilities.

That happens by taking their squared absolute value, okay,

and then, you know, you can say

either the electron will be here or it will be there.

And, you know, knowing the amplitudes,

you can predict at least the probabilities

that you'll see each possible outcome, okay?

But while a system is isolated

from the whole rest of the universe,

the rest of its environment,

the amplitudes can change in time

by rules that are different

from the normal rules of probability

and that are, you know, alien to our everyday experience.

So anytime anyone ever tells you anything

about the weirdness of the quantum world,

you know, or assuming that they're not lying to you, right,

they are telling you, you know,

yet another consequence of nature

being described by these amplitudes.

So most famously, what amplitudes can do

is that they can interfere with each other, okay?

So in the famous double slit experiment,

what happens is that you shoot a particle,

like an electron, let's say,

at a screen with two slits in it,

and you find that there are, you know, on a second screen,

now there are certain places

where that electron will never end up,

you know, after it passes through the first screen.

And yet, if I close off one of the slits,

then the electron can appear in that place, okay?

So by decreasing the number of paths

that the electron could take to get somewhere,

you can increase the chance that it gets there, okay?

Now, how is that possible?

Well, it's because, you know, as we would say now,

the electron has a superposition state, okay?

It has some amplitude for reaching this point

by going through the first slit.

It has some other amplitude for reaching it

by going through the second slit.

But now, if one amplitude is positive

and the other one is negative,

then, you know, I have to add them all up, right?

I have to add the amplitudes for every path

that the electron could have taken to reach this point.

And those amplitudes,

if they're pointing in different directions,

they can cancel each other out.

That would mean the total amplitude is zero

and the thing never happens at all.

I close off one of the possibilities,

then the amplitude is positive or it's negative,

and now the thing can happen.

Okay, so that is sort of the one trick of quantum mechanics.

And now I can tell you what a quantum computer is.

Okay, a quantum computer is a computer

that tries to exploit, you know, exactly these phenomena,

superposition, amplitudes, and interference,

in order to solve certain problems much faster

than we know how to solve them otherwise.

So the basic building block of a quantum computer

is what we call a quantum bit or a qubit.

That just means a bit that has some amplitude for being zero

and some other amplitude for being one.

So it's a superposition of zero and one states, right?

But now the key point is that if I've got,

let's say, a thousand qubits,

the rules of quantum mechanics are completely unequivocal

that I do not just need one ampli...

You know, I don't just need amplitudes for each qubit separately.

Okay, in general, I need an amplitude

for every possible setting of all thousand of those bits, okay?

So that what that means is two to the one thousand power amplitudes.

Okay, if I had to write those down,

or let's say in the memory of a conventional computer,

if I had to write down two to the one thousand complex numbers,

that would not fit within the entire observable universe.

Okay, and yet, you know, quantum mechanics is unequivocal

that if these qubits can all interact with each other,

and in some sense, I need two to the one thousand parameters,

you know, amplitudes to describe what is going on.

Now, you know, now I can tell, you know, where all the popular articles,

you know, about quantum computing go off the rails

is that they say, you know, they sort of say what I just said,

and then they say, oh, so the way a quantum computer works

is just by trying every possible answer in parallel.

You know, that sounds too good to be true,

and unfortunately, it kind of is too good to be true.

The problem is I could make a superposition

over every possible answer to my problem, you know,

even if there are two to the one thousand of them, right?

I can easily do that.

The trouble is for a computer to be useful,

you've got to, at some point, you've got to look at it

and see an output, right?

And if I just measure a superposition over every possible answer,

then the rules of quantum mechanics tell me

that all I'll see will be a random answer.

You know, if I just wanted a random answer,

well, I could have picked one myself with a lot less trouble, right?

So the entire trick with quantum computing,

with every algorithm for a quantum computer,

is that you try to choreograph a pattern

of interference of amplitudes,

and you try to do it so that for each wrong answer,

some of the paths leading to that wrong answer

have positive amplitudes and others have negative amplitudes.

So on the whole, they cancel each other out, okay?

Whereas all the paths leading to the right answer

should reinforce each other, you know, should have amplitudes

pointing the same direction.

So the design of algorithms in the space

is the choreography of the interferences.

Precisely. That's precisely what it is.

Can we take a brief step back?

And you mentioned information.

Yes.

So in which part of this beautiful picture

that you've painted is information contained?

Oh, well, information is at the core of everything

that we've been talking about, right?

I mean, the bit is, you know, the basic unit of information

since, you know, Claude Shannon's paper in 1948.

You know, and, you know, of course, you know,

people had the concept even before that, you know,

he popularized the name, right?

But I mean...

But a bit is zero or one.

That's right.

So that's a basic element of information.

That's right.

And what we would say is that the basic unit

of quantum information is the qubit,

is, you know, the object, any object

that can be maintained in this, or manipulated,

in a superposition of zero and one states.

Now, you know, sometimes people ask, well,

but what is a qubit physically, right?

And there are all these different, you know,

proposals that are being pursued in parallel

for how you implement qubits.

There is, you know, superconducting quantum computing

that was in the news recently

because of Google's quantum supremacy experiment, right?

Where you would have some little coils

where a current can flow through them

in two different energy states,

one representing a zero, another representing a one.

And if you cool these coils

to just slightly above absolute zero,

like a hundredth of a degree, then they superconduct.

And then the current can actually be

in a superposition of the two different states.

So that's one kind of qubit.

Another kind would be, you know,

just an individual atomic nucleus, right?

It has a spin.

It could be spinning clockwise.

It could be spinning counterclockwise,

or it could be in a superposition of the two spin states.

That is another qubit.

But see, just like in the classical world, right?

You could be a virtuoso programmer

without having any idea of what a transistor is, right?

Or how the bits are physically represented inside the machine,

even that the machine uses electricity, right?

You just care about the logic.

It's sort of the same with quantum computing, right?

Qubits could be realized by many,

many different quantum systems.

And yet all of those systems will lead to the same logic,

you know, the logic of qubits and how, you know,

how you measure them, how you change them over time.

And so, you know, the subject of, you know,

how qubits behave and what you can do with qubits,

that is quantum information.

So just to linger on that.

Sure.

So the physical design implementation of a qubit

does not interfere with the,

that next level of abstraction that you can program over it.

So it truly is, the idea of it is, okay.

Well, to be honest with you,

today they do interfere with each other.

That's because all the quantum computers

we can build today are very noisy, right?

And so sort of the, you know,

the qubits are very far from perfect.

And so the lower level sort of does affect the higher levels.

And we sort of have to think about all of them at once.

Okay, but eventually where we hope to get

is to what are called error corrected quantum computers,

where the qubits really do behave

like perfect abstract qubits for as long as we want them to.

And in that future, you know,

a future that we can already sort of prove theorems about

or think about today.

But in that future, the logic of it

really does become decoupled from the hardware.

So if noise is currently like the biggest problem

for quantum computing,

and then the dream is error correcting quantum computers,

can you just maybe describe what does it mean

for there to be noise in the system?

Absolutely, so yeah, so the problem

is even a little more specific than noise.

So the fundamental problem,

if you're trying to actually build a quantum computer,

you know, of any appreciable size,

is something called decoherence.

Okay, and this was recognized from the very beginning,

you know, when people first started thinking about this

in the 1990s.

Now, what decoherence means

is sort of the unwanted interaction

between, you know, your qubits,

you know, the state of your quantum computer

and the external environment.

Okay, and why is that such a problem?

Well, I talked before about how, you know,

when you measure a quantum system,

so let's say if I measure a qubit

that's in a superposition of zero and one states

to ask it, you know, are you zero or are you one?

Well, now I force it to make up its mind, right?

And now, probabilistically, it chooses one or the other

and now, you know, it's no longer a superposition,

there's no longer amplitudes,

there's just, there's some probability that I get a zero

and there's some that I get a one.

And now, the trouble is that it doesn't have to be me

who's looking, okay?

Or in fact, it doesn't have to be any conscious entity.

Any kind of interaction with the external world

that leaks out the information

about whether this qubit was a zero or a one,

sort of that causes the zerowness

or the oneness of the qubit to be recorded

in, you know, the radiation in the room,

in the molecules of the air,

in the wires that are connected to my device,

any of that, as soon as the information leaks out,

it is as if that qubit has been measured, okay?

It is, you know, the state has now collapsed.

You know, another way to say it

is that it's become entangled with its environment, okay?

But, you know, from the perspective of someone

who's just looking at this qubit,

it is as though it has lost its quantum state.

And so, what this means is that

if I want to do a quantum computation,

I have to keep the qubits sort of fanatically

well isolated from their environment.

But then at the same time,

they can't be perfectly isolated

because I need to tell them what to do.

I need to make them interact with each other,

for one thing, and not only that,

but in a precisely choreographed way, okay?

And, you know, that is such a staggering problem, right?

How do I isolate these qubits from the whole universe

but then also tell them exactly what to do?

I mean, you know, there were distinguished physicists

and computer scientists in the 90s who said,

this is fundamentally impossible, you know?

The laws of physics will just never let you control qubits

to the degree of accuracy that you're talking about.

Now, what changed the views of most of us

was a profound discovery in the mid to late 90s

which was called the theory of quantum error correction

and quantum fault tolerance, okay?

And the upshot of that theory is that

if I want to build a reliable quantum computer

and scale it up to, you know, an arbitrary number

of as many qubits as I want, you know,

and doing as much on them as I want,

I do not actually have to get the qubits

perfectly isolated from their environment.

It is enough to get them really, really, really well isolated, okay?

And even if every qubit is sort of leaking,

you know, its state into the environment at some rate,

as long as that rate is low enough, okay,

I can sort of encode the information that I care about

in very clever ways across the collective states

of multiple qubits, okay?

In such a way that even if, you know,

a small percentage of my qubits leak,

well, I'm constantly monitoring them

to see if that leak happened.

I can detect it and I can correct it.

I can recover the information I care about

from the remaining qubits, okay?

And so, you know, you can build a reliable quantum computer

even out of unreliable parts, right?

Now, in some sense, you know,

that discovery is what set the engineering agenda

for quantum computing research

from the 1990s until the present, okay?

The goal has been, you know,

engineer qubits that are not perfectly reliable

but reliable enough that you can then use

these error correcting codes

to have them simulate qubits

that are even more reliable than they are, right?

The error correction becomes a net win

rather than a net loss, right?

And then once you reach that sort of crossover point,

then, you know, your simulated qubits

could in turn simulate qubits

that are even more reliable and so on

until you've just, you know, effectively,

you have arbitrarily reliable qubits.

So long story short,

we are not at that breakeven point yet.

We're a hell of a lot closer than we were

when people started doing this in the 90s,

like orders of magnitude closer.

But the key ingredient there

is the more qubits, the better because...

Ah, well, the more qubits,

the larger the computation you can do, right?

I mean, qubits are what constitute

the memory of your quantum computer, right?

But also for the, sorry,

for the error correcting mechanism.

Ah, yes.

So the way I would say it

is that error correction imposes an overhead

in the number of qubits.

And that is actually one of the biggest practical problems

with building a scalable quantum computer.

If you look at the error correcting codes,

at least the ones that we know about today,

and you look at, you know,

what would it take to actually use a quantum computer

to, you know, hack your credit card number,

which is, you know,

maybe, you know, the most famous application

people talk about, right?

Let's say to factor huge numbers

and thereby break the RSA cryptosystem.

Well, what that would take

would be thousands of, several thousand logical qubits.

But now with the known error correcting codes,

each of those logical qubits

would need to be encoded itself

using thousands of physical qubits.

So at that point,

you're talking about millions of physical qubits.

And in some sense,

that is the reason why quantum computers

are not breaking cryptography already.

It's because of these immense overheads involved.

So that overhead is additive or multiplicative?

Well, it's multiplicative.

I mean, it's like you take the number

of logical qubits that you need

in your abstract quantum circuit,

you multiply it by a thousand or so.

So, you know, there's a lot of work

on, you know, inventing better,

trying to invent better error correcting codes.

Okay, that is the situation right now.

In the meantime, we are now in,

what the physicist John Preskill called

the noisy intermediate scale quantum or NISQ era.

And this is the era,

you can think of it as sort of like the vacuum,

you know, we're now entering the very early

vacuum tube era of quantum computers.

The quantum computer analog of the transistor

has not been invented yet, right?

That would be like true error correction, right?

Where, you know, we are not or something else

that would achieve the same effect, right?

We are not there yet.

But where we are now,

let's say as of a few months ago,

you know, as of Google's announcement

of quantum supremacy,

you know, we are now finally at the point

where even with a non error corrected quantum computer,

with, you know, these noisy devices,

we can do something that is hard

for classical computers to simulate, okay?

So we can eke out some advantage.

Now, will we in this noisy era

be able to do something beyond

what a classical computer can do

that is also useful to someone?

That we still don't know.

People are going to be racing over the next decade

to try to do that.

By people, I mean, Google, IBM,

you know, a bunch of startup companies.

And research labs.

Yeah, and research labs and governments.

And yeah.

You just mentioned a million things.

Well, I'll backtrack for a second.

Yeah, sure, sure.

So we're in these vacuum tube days.

Yeah, just entering them.

And just entering, wow.

Okay, so how do we escape the vacuum?

So how do we get to,

how do we get to where we are now with the CPU?

Is this a fundamental engineering challenge?

Is there breakthroughs on the physics side

that are needed on the computer science side?

Or is it a financial issue

where much larger just sheer investment

and excitement is needed?

So, you know, those are excellent questions.

My guess might, well, no, no.

My guess would be all of the above.

I mean, my guess, you know,

I mean, you could say fundamentally

it is an engineering issue, right?

The theory has been in place since the 90s.

You know, at least, you know, this is what,

you know, error correction would look like.

You know, we do not have the hardware

that is at that level.

But at the same time, you know,

so you could just, you know, try to power through,

you know, maybe even like, you know,

if someone spent a trillion dollars

on some quantum computing Manhattan project, right?

Then conceivably they could just, you know,

build an error corrected quantum computer

as it was envisioned back in the 90s, right?

I think the more plausible thing to happen

is that there will be further theoretical breakthroughs

and there will be further insights

that will cut down the cost of doing this.

So let's take a brief step to the philosophical.

I just recently talked to Jim Keller

who's sort of like the famed architect

in the microprocessor world.

And he's been told for decades,

every year that the Moore's law is going to die this year.

And he tries to argue that the Moore's law

is still alive and well,

and it'll be alive for quite a long time to come.

How long?

How long did he say?

Well, the main point is it's still alive,

but he thinks there's still a thousand X improvement

just on shrinking the transition that's possible.

Whatever.

The point is that the exponential growth we see

is actually a huge number of these S curves,

just constant breakthroughs.

At the philosophical level,

why do you think we as descendants of apes

were able to just keep coming up

with these new breakthroughs on the CPU side

is this something unique to this particular endeavor

or will it be possible to replicate

in the quantum computer space?

Okay.

All right.

There was a lot there,

but to break off something,

I mean, I think we are in an extremely special period

of human history, right?

I mean, it is, you could say,

obviously special in many ways, right?

There are way more people alive

than there have been

and the whole future of the planet

is in question in a way that it hasn't been

for the rest of human history.

But in particular, we are in the era

where we finally figured out

how to build universal machines,

you could say, the things that we call computers,

machines that you program to simulate the behavior

of whatever machine you want.

And once you've sort of crossed this threshold

of universality, you've built,

you could say, touring,

you've instantiated touring machines

in the physical world.

Well, then the main questions are ones of numbers.

They are ones of how much memory can you access?

How fast does it run?

How many parallel processors?

At least until quantum computing.

Quantum computing is the one thing

that changes what I just said, right?

But as long as it's classical computing,

then it's all questions of numbers.

And you could say at a theoretical level,

the computers that we have today

are the same as the ones in the 50s.

They're just millions of times faster

and with millions of times more memory.

And I think there's been an immense economic pressure

to get more and more transistors,

get them smaller and smaller,

add more and more cores.

And in some sense, a huge fraction

of all of the technological progress

that there is in all of civilization

has gotten concentrated just more narrowly

into just those problems, right?

And so it has been one of the biggest success stories

in the history of technology, right?

There's, I mean, it is, I am as amazed by it

as anyone else is, right?

But at the same time, we also know that it,

and I really do mean we know

that it cannot continue indefinitely, okay?

Because you will reach fundamental limits

on how small you can possibly make a processor.

And if you want a real proof

that would justify my use of the word,

we know that Moore's law has to end.

I mean, ultimately you will reach the limits

imposed by quantum gravity.

If you tried to build a computer

that operated at 10 to the 43 Hertz,

so did 10 to the 43 operations per second,

that computer would use so much energy

that it would simply collapse through a black hole, okay?

So in reality, we're going to reach the limits

long before that, but that is a sufficient proof.

That there's a limit.

Yes, yes.

But it would be interesting to try to understand

the mechanism, the economic pressure that you said,

just like the Cold War was a pressure on getting us,

getting us, because my us is both the Soviet Union

and the United States, but getting us,

the two countries to get to hurry up,

to get to space, to the moon,

there seems to be that same kind of economic pressure

that somehow created a chain of engineering breakthroughs

that resulted in the Moore's law.

And it'd be nice to replicate.

Yeah, well, I mean, some people are sort of,

get depressed about the fact

that technological progress may seem to have slowed down

in many, many realms outside of computing, right?

And there was this whole thing of we wanted flying cars

and we only got Twitter instead, right?

Yeah, good old Peter Thiel, yeah.

Yeah, yeah, yeah, right, right, right.

So then jumping to another really interesting topic

that you mentioned, so Google announced with their work

in the paper in Nature with quantum supremacy.

Yes.

Can you describe, again, back to the basic,

what is perhaps not so basic, what is quantum supremacy?

Absolutely, so quantum supremacy is a term

that was coined by, again, by John Preskill in 2012.

Not everyone likes the name, but it sort of stuck.

We don't, we sort of haven't found a better alternative.

It's technically quantum computational supremacy.

Yeah, yeah, supremacy, that's right, that's right.

But the basic idea is actually one that goes all the way back

to the beginnings of quantum computing

when Richard Feynman and David Deutsch, people like that,

were talking about it in the early 80s.

And quantum supremacy just refers to sort of the point

in history when you can first use a quantum computer

to do some well defined task much faster

than any known algorithm running on any of the classical computers

that are available, okay?

So notice that I did not say a useful task, okay?

It could be something completely artificial,

but it's important that the task be well defined.

So in other words, it is something that has right and wrong answers

that are knowable independently of this device, right?

And we can then run the device, see if it gets the right answer or not.

Can you clarify a small point?

You said much faster than a classical implementation.

What about sort of what about the space with where the class,

there's no, there's not, it doesn't even exist,

a classical algorithm to show the power?

So maybe I should clarify.

Everything that a quantum computer can do,

a classical computer can also eventually do, okay?

And the reason why we know that is that a classical computer

could always, you know, if it had no limits of time and memory,

it could always just store the entire quantum state,

you know, of your, you know, of the quantum,

store a list of all the amplitudes,

you know, in the state of the quantum computer,

and then just, you know, do some linear algebra

to just update that state, right?

And so anything that quantum computers can do

can also be done by classical computers,

albeit exponentially slower in some cases.

So quantum computers don't go into some magical place

outside of Alan Turing's definition of computation.

Precisely.

They do not solve the halting problem.

They cannot solve anything that is uncomputable

in Alan Turing's sense.

What we think they do change

is what is efficiently computable, okay?

And, you know, since the 1960s, you know,

the word efficiently, you know,

as well has been a central word in computer science,

but it's sort of a code word for something technical,

which is basically with polynomial scaling, you know,

that as you get to larger and larger inputs,

you would like an algorithm that uses an amount of time

that scales only like the size of the input

raised to some power

and not exponentially with the size of the input, right?

Yeah, so I do hope we get to talk again

because one of the many topics

that there's probably several hours worth of conversation on

is complexity,

which we probably won't even get a chance to touch today,

but you briefly mentioned it,

but let's maybe try to continue.

So you said the definition of quantum supremacy

is basically achieving a place

where much faster on a formal,

that quantum computer is much faster

on a formal well defined problem

that is or isn't useful.

Yeah, yeah, yeah, right, right.

And I would say that we really want three things, right?

We want, first of all,

the quantum computer to be much faster

just in the literal sense of like number of seconds,

you know, it's a solving this, you know,

well defined, you know, problem.

Secondly, we want it to be sort of, you know,

for a problem where we really believe

that a quantum computer has better scaling behavior, right?

So it's not just an incidental, you know,

matter of hardware,

but it's that, you know,

as you went to larger and larger inputs,

you know, the classical scaling would be exponential

and the scaling for the quantum algorithm

would only be polynomial.

And then thirdly, we want the first thing,

the actual observed speed up

to only be explainable in terms of the scaling behavior, right?

So, you know, I want, you know,

a real world, you know, a real problem to get solved,

let's say by a quantum computer with 50 qubits or so,

and for no one to be able to explain that in any way

other than, well, you know, this computer involved a quantum state

with two to the 50th power amplitudes.

And, you know, a classical simulation,

at least any that we know today,

would require keeping track of two to the 50th numbers.

And this is the reason why it was faster.

So the intuition is that then if you demonstrate on 50 qubits,

then once you get to 100 qubits,

then it'll be even much more faster.

Precisely, precisely.

Yeah, and, you know, and quantum supremacy

does not require error correction, right?

We don't, you know, we don't have, you could say,

true scalability yet or true, you know, error correction yet.

But you could say quantum supremacy is already enough by itself

to refute the skeptics who said a quantum computer

will never outperform a classical computer for anything.

But one, how do you demonstrate quantum supremacy?

And two, what's up with these news articles

I'm reading that Google did so?

Yeah, all right, well, great, great questions,

because now you get into actually, you know,

a lot of the work that I've, you know,

I and my students have been doing for the last decade,

which was precisely about how do you demonstrate

quantum supremacy using technologies that, you know,

we thought would be available in the near future.

And so one of the main things that we realized around 2011,

and this was me and my student, Alex Arkhipov at MIT at the time,

and independently of some others,

including Bremner, Joseph, and Shepherd, okay?

And the realization that we came to was that

if you just want to prove that a quantum computer is faster,

you know, and not do something useful with it,

then there are huge advantages to sort of switching

your attention from problems like factoring numbers

that have a single right answer

to what we call sampling problems.

So these are problems where the goal is just to output

a sample from some probability distribution,

let's say over strings of 50 bits, right?

So there are, you know, many, many,

many possible valid outputs.

You know, your computer will probably never even produce

the same output twice, you know,

if it's running as, even, you know,

assuming it's running perfectly, okay?

But the key is that some outputs are supposed

to be likelier than other ones.

So, sorry, to clarify, is there a set of outputs

that are valid and set they're not,

or is it more that the distribution

of a particular kind of output is more,

is like there's a specific distribution

of a particular kind of output?

Yeah, there's a specific distribution

that you're trying to hit, right?

Or, you know, that you're trying to sample from.

Now, there are a lot of questions about this,

you know, how do you do that, right?

Now, how you do it, you know,

it turns out that with a quantum computer,

even with the noisy quantum computers

that we have now, that we have today,

what you can do is basically just apply

a randomly chosen sequence of operations, right?

So we, you know, in some of the, you know,

that part is almost trivial, right?

We just sort of get the qubits to interact

in some random way,

although a sort of precisely specified random way

so we can repeat the exact same random sequence

of interactions again and get another sample

from that same distribution.

And what this does is it basically,

well, it creates a lot of garbage,

but, you know, very specific garbage, right?

So, you know, of all of the,

so we're gonna talk about Google's device

that were 53 qubits there, okay?

And so there were two to the 53 power possible outputs.

Now, for some of those outputs,

you know, there was a little bit more

destructive interference in their amplitude, okay?

So their amplitudes were a little bit smaller.

And for others, there was a little more

constructive interference.

You know, the amplitudes were a little bit

more aligned with each other, you know,

and so those were a little bit likelier, okay?

All of the outputs are exponentially unlikely,

but some are, let's say, two times or three times,

you know, unlikelier than others, okay?

And so you can define, you know,

this sequence of operations that gives rise

to this probability distribution.

Okay, now the next question would be,

well, how do you, you know,

even if you're sampling from it,

how do you verify that, right?

How do you know?

And so my students and I,

and also the people at Google

were doing the experiment,

came up with statistical tests

that you can apply to the outputs

in order to try to verify, you know,

what is, you know, that at least

that some hard problem is being solved.

The test that Google ended up using

was something that they called

the linear cross entropy benchmark, okay?

And it's basically, you know,

so the drawback of this test

is that it requires, like,

it requires you to do a two to the 53 time calculation

with your classical computer, okay?

So it's very expensive to do the test

on a classical computer.

The good news is...

How big of a number is two to the 53?

It's about nine quadrillion, okay?

That doesn't help.

Well, you know,

it's, you want it in like scientific notation.

No, no, no, what I mean is...

Yeah, it is just...

It's impossible to run on a...

Yeah, so we will come back to that.

It is just barely possible to run,

we think, on the largest supercomputer

that currently exists on Earth,

which is called Summit at Oak Ridge National Lab, okay?

Great, this is exciting.

That's the short answer.

So ironically, for this type of experiment,

we don't want 100 qubits, okay?

Because with 100 qubits, even if it works,

we don't know how to verify the results, okay?

So we want, you know, a number of qubits

that is enough that, you know,

the biggest classical computers on Earth

will have to sweat, you know,

and we'll just barely, you know,

be able to keep up with the quantum computer,

you know, using much more time,

but they will still be able to do it

in order that we can verify the results.

Which is where the 53 comes from for the number of qubits?

Basically, well, I mean, that's also,

that's sort of, you know,

I mean, that's sort of where they are now

in terms of scaling, you know?

And then, you know, soon, you know, that point will be passed.

And then when you get to larger numbers of qubits,

then, you know, these types of sampling experiments

will no longer be so interesting

because we won't even be able to verify the results

and we'll have to switch to other types of computation.

So with the sampling thing,

you know, so the test that Google applied

with this linear cross entropy benchmark

was basically just take the samples that were generated,

which are, you know, a very small subset

of all the possible samples that there are.

But for those, you calculate with your classical computer

the probabilities that they should have been output.

And you see, are those probabilities

like larger than the mean?

You know, so is the quantum computer biased

toward outputting the strings that it's,

you know, that you want it to be biased toward?

Okay, and then finally,

we come to a very crucial question,

which is supposing that it does that.

Well, how do we know that a classical computer

could not have quickly done the same thing, right?

How do we know that, you know,

this couldn't have been spoofed by a classical computer, right?

And so, well, the first answer is we don't know for sure

because, you know, this takes us

into questions of complexity theory.

You know, I mean, questions of the magnitude

of the P versus NP question and things like that, right?

You know, we don't know how to rule out definitively

that there could be fast classical algorithms

for, you know, even simulating quantum mechanics

and for, you know, simulating experiments like these,

but we can give some evidence against that possibility.

And that was sort of the, you know,

the main thrust of a lot of the work

that my colleagues and I did, you know,

over the last decade,

which is then sort of in around 2015 or so,

what led to Google deciding to do this experiment.

So is the kind of evidence here,

first of all, the hard P equals NP problem that you mentioned

and the kind of evidence that you were looking at,

is that something you come to on a sheet of paper

or is this something, are these empirical experiments?

It's math for the most part.

I mean, you know, it's also, you know,

we have a bunch of methods

that are known for simulating quantum circuits

or quantum computations with classical computers.

And so we have to try them all out

and make sure that, you know, they don't work,

you know, make sure that they have exponential scaling

on, you know, these problems and not just theoretically,

but with the actual range of parameters

that are actually, you know, arising in Google's experiment.

Okay, so there is an empirical component to it, right?

But now on the theoretical side,

you know, basically what we know how to do

in theoretical computer science and computational complexity

is, you know, we don't know how to prove

that most of the problems we care about are hard,

but we know how to pass the blame to someone else, okay?

We know how to say, well, look, you know,

I can't prove that this problem is hard,

but if it is easy, then all these other things

that, you know, you probably were much more confident

or were hard, then those would be easy as well, okay?