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,
support it on Patreon,
or simply connect with me on Twitter
at Lex Friedman, spelled F R I D M A N.
As usual, I’ll do one or two minutes of ads now
and never any ads in the middle
that can break the flow of the conversation.
I hope that works for you
and doesn’t hurt the listening experience.
Quick summary of the ads.
Two supporters today.
First, get Cash App and use the code LEX PODCAST.
Second, listen to the Tech Meme Ride Home podcast
for tech news.
Search Ride Home, two words, in your podcast app.
This show is presented by Cash App,
the number one finance app in the App Store.
When you get it, use code LEX PODCAST.
Cash App lets you send money to friends,
buy Bitcoin, and invest in the stock market
with as little as one dollar.
Broker services are provided by Cash App Investing,
a subsidiary of Square, a member SIPC.
Since Cash App does fractional share trading,
let me mention that the order execution algorithm
that works behind the scenes
to create the abstraction of fractional orders
is an algorithmic marvel.
So big props to the Cash App engineers
for solving a hard problem that in the end
provides an easy interface that takes a step up
to the next layer of abstraction over the stock market,
making trading more accessible for new investors
and diversification much easier.
So again, if you get Cash App from the App Store
or Google Play and use the code LEX PODCAST,
you’ll get $10 and Cash App will also donate $10 to FIRST,
one of my favorite organizations
that is helping to advance robotics and STEM education
for young people around the world.
This episode is also supported
by the Tech Meme Ride Home Podcast.
It’s a technology podcast I’ve been listening to
for a while and really enjoying.
It goes straight to the point,
gives you the tech news you need to know
and provides minimal but essential context.
It’s released every day by 5 p.m. Eastern
and is only about 15 to 20 minutes long.
For fun, I like building apps on smartphones,
most on Android, so I’m always a little curious
about new flagship phones that come out.
I saw that Samsung announced the new Galaxy S20
and of course, right away, Tech Meme Ride Home
has a new episode that summarizes all that I needed to know
about this new device.
They’ve also started to do weekend bonus episodes
with interviews of people like AWOL founder Steve Case
on investing and Gary Marcus on AI,
who I’ve also interviewed on this podcast.
You can find the Tech Meme Ride Home Podcast
if you search your podcast app for Ride Home, two words.
Then subscribe, enjoy, and keep up to date
with the latest tech news.
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.
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.
Because he had to go to Bletchley Park
and work on something of more immediate importance.
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,
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.
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?
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?
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.
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,
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.
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.
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.
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.
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.
So that’s a basic element of information.
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.
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.
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.
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 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.
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?
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.
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.
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.
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
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.
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
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?
So we can give what are called reductions.
This has been the basic strategy in, you know,
NP completeness, right, in all of theoretical computer science
and cryptography since the 1970s, really.
And so we were able to give some reduction evidence
for the hardness of simulating these sampling experiments,
these sampling based quantum supremacy experiments.
So reduction evidence is not as satisfactory as it should be.
One of the biggest open problems in this area
is to make it better.
But, you know, we can do something.
You know, certainly we can say that, you know,
if there is a fast classical algorithm
to spoof these experiments, then it has to be very,
very unlike any of the algorithms that we know.
TREVOR Which is kind of in the same kind
of space of reasoning that people say P not equals NP.
BENJAMIN Yeah, it’s in the same spirit.
TREVOR Okay, so Andrew Yang, a very intelligent
and a presidential candidate with a lot of interesting ideas
in all kinds of technological fields, tweeted that
because of quantum computing, no code is uncrackable.
Is he wrong or right?
BENJAMIN He was premature, let’s say.
So, well, okay, wrong.
Look, I’m actually, you know, I’m a fan of Andrew Yang.
I like his ideas.
I like his candidacy.
I think that, you know, he may be ahead of his time
with, you know, the universal basic income and so forth.
And he may also be ahead of his time in that tweet
that you referenced.
So regarding using quantum computers
to break cryptography, so the situation is this, okay?
So the famous discovery of Peter Shor, you know, 26 years ago
that really started quantum computing, you know,
as an autonomous field was that if you built a full
scalable quantum computer, then you could use it
to efficiently find the prime factors of huge numbers
and calculate discrete logarithms and solve
a few other problems that are very, very special
in character, right?
They’re not NP complete problems.
We’re pretty sure they’re not, okay?
But it so happens that most of the public key cryptography
that we currently use to protect the internet
is based on the belief that these problems are hard.
Okay, what Shor showed is that once you get
scalable quantum computers, then that’s no longer true, okay?
But now, you know, before people panic,
there are two important points to understand here.
Okay, the first is that quantum supremacy,
the milestone that Google just achieved,
is very, very far from the kind of scalable quantum computer
that would be needed to actually threaten
public key cryptography.
Okay, so, you know, we touched on this earlier, right?
But Google’s device has 53 physical qubits, right?
To threaten cryptography, you’re talking, you know,
with any of the known error correction methods,
you’re talking millions of physical qubits.
Because error correction would be required
to threaten cryptography.
Yes, yes, yes, it certainly would, right?
And, you know, how much, you know,
how great will the overhead be from the error correction?
That we don’t know yet.
But with the known codes, you’re talking millions
of physical qubits and of a much higher quality
than any that we have now, okay?
So, you know, I don’t think that that is, you know,
coming soon, although people who have secrets
that, you know, need to stay secret for 20 years,
you know, are already worried about this,
you know, for the good reason that, you know,
we presume that intelligence agencies
are already scooping up data, you know,
in the hope that eventually they’ll be able to decode it
once quantum computers become available, okay?
So this brings me to the second point I wanted to make,
which is that there are other public key cryptosystems
that are known that we don’t know how to break
even with quantum computers, okay?
And so there’s a whole field devoted to this now,
which is called post quantum cryptography, okay?
And so there is already, so we have some good candidates now.
The best known being what are called
lattice based cryptosystems.
And there is already some push to try to migrate
to these cryptosystems.
So NIST in the US is holding a competition
to create standards for post quantum cryptography,
which will be the first step in trying to get
every web browser and every router to upgrade,
you know, and use, you know, something like SSL
that would be based on, you know,
what we think is quantum secure cryptography.
But, you know, this will be a long process.
But, you know, it is something that people
are already starting to do.
And so, you know, I’m sure this algorithm
is sort of a dramatic discovery.
You know, it could be a big deal
for whatever intelligence agency
first gets a scalable quantum computer,
if no, at least certainly if no one else
knows that they have it, right?
But eventually we think that we could migrate
the internet to the post quantum cryptography
and then we’d be more or less back where we started.
Okay, so this is sort of not the application
of quantum computing.
I think that’s really gonna change the world
in a sustainable way, right?
The big, by the way, the biggest practical application
of quantum computing that we know about by far,
I think is simply the simulation
of quantum mechanics itself.
In order to, you know, learn about chemical reactions,
you know, design maybe new chemical processes,
new materials, new drugs, new solar cells,
new superconductors, all kinds of things like that.
What’s the size of a quantum computer
that would be able to simulate the,
you know, quantum mechanical systems themselves
that would be impactful for the real world
for the kind of chemical reactions
and that kind of work?
What scale are we talking about?
Now you’re asking a very, very current question,
a very big question.
People are going to be racing over the next decade
to try to do useful quantum simulations
even with, you know, 100 or 200 qubit quantum computers
of the sort that we expect to be able to build
over the next decade.
Okay, so that might be, you know,
the first application of quantum computing
that we’re able to realize, you know,
or maybe it will prove to be too difficult
and maybe even that will require fault tolerance
or, you know, will require error correction.
So there’s an aggressive race to come up
with the one case study kind of like Peter Schor
with the idea that would just capture
the world’s imagination of like,
look, we can actually do something very useful here.
Right, but I think, you know, within the next decade,
the best shot we have is certainly not,
you know, using Schor’s algorithm to break cryptography,
you know, just because it requires,
you know, too much in the way of error correction.
The best shot we have is to do some quantum simulation
that tells the material scientists
or chemists or nuclear physicists,
you know, something that is useful to them
and that they didn’t already know,
you know, and you might only need one or two successes
in order to change some, you know,
billion dollar industries, right?
Like, you know, the way that people make fertilizer right now
is still based on the Haber Bosch process
from a century ago.
And it is some many body quantum mechanics problem
that no one really understands, right?
If you could design a better way to make fertilizer, right?
That’s, you know, billions of dollars right there.
So those are sort of the applications
that people are going to be aggressively racing toward
over the next decade.
Now, I don’t know if they’re gonna realize it or not,
but, you know, they certainly at least have a shot.
So it’s gonna be a very, very interesting next decade.
But just to clarify, what’s your intuition?
If a breakthrough like that comes with,
is it possible for that breakthrough to be on 50
to 100 qubits or is scale a fundamental thing
like 500, 1000 plus qubits?
Yeah, so I can tell you what the current studies are saying.
You know, I think probably better to rely on that
than on my intuition.
But, you know, there was a group at Microsoft
had a study a few years ago that said
even with only about 100 qubits,
you know, you could already learn something new
about the chemical reaction that makes fertilizer, for example.
The trouble is they’re talking about 100 qubits
and about a million layers of quantum gates.
Okay, so basically they’re talking about
100 nearly perfect qubits.
So the logical qubits, as you mentioned before.
Yeah, exactly, 100 logical qubits.
And now, you know, the hard part for the next decade
is gonna be, well, what can we do
with 100 to 200 noisy qubits?
Yeah, is there error correction breakthroughs
that might come without the need to do
thousands or millions of physical qubits?
Yeah, so people are gonna be pushing simultaneously
on a bunch of different directions.
One direction, of course,
is just making the qubits better, right?
And, you know, there is tremendous progress there.
I mean, you know, the fidelity is like
the accuracy of the qubits has improved
by several orders of magnitude, you know,
in the last decade or two.
Okay, the second thing is designing better error,
you know, let’s say lower overhead error correcting codes
and even short of doing the full recursive error correction.
You know, there are these error mitigation strategies
that you can use, you know, that may, you know,
allow you to eke out a useful speed up in the near term.
And then the third thing is just taking the quantum algorithms
for simulating quantum chemistry or materials
and making them more efficient.
You know, and those algorithms
are already dramatically more efficient
than they were, let’s say, five years ago.
And so when, you know, I quoted these estimates
like, you know, circuit depth of one million.
And so, you know, I hope that because people will care enough
that these numbers are gonna come down.
So you’re one of the world class researchers in this space.
There’s a few groups like you mentioned,
Google and IBM working at this.
There’s other research labs, but you put also,
you have an amazing blog.
You just, you put a lot, you paid me to say it.
You put a lot of effort sort of to communicating
the science of this and communicating,
exposing some of the BS and sort of the natural,
just like in the AI space, the natural charlatanism,
if that’s a word in this, in the quantum mechanics in general,
but quantum computers and so on.
Can you give some notes about people or ideas
that people like me or listeners in general
from outside the field should be cautious of
when they’re taking in news headings
that Google achieved quantum supremacy?
So what should we look out for?
Where’s the charlatans in the space?
Where’s the BS?
Yeah, so good question.
Unfortunately, quantum computing is a little bit like
cryptocurrency or deep learning.
Like there is a core of something
that is genuinely revolutionary and exciting.
And because of that core, it attracts this sort of
vast penumbra of people making just utterly ridiculous claims.
And so with quantum computing, I mean,
I would say that the main way that people go astray
is by not focusing on sort of the question of,
are you getting a speed up over a classical computer or not?
And so people have like dismissed quantum supremacy
because it’s not useful, right?
Or it’s not itself, let’s say, obviously useful for anything.
Okay, but ironically, these are some of the same people
who will go and say, well, we care about useful applications.
We care about solving traffic routing
and financial optimization and all these things.
And that sounds really good, but their entire spiel
is sort of counting on nobody asking the question,
yes, but how well could a classical computer
do the same thing, right?
I really mean the entire thing is they say,
well, a quantum computer can do this,
a quantum computer can do that.
A quantum computer can do that, right?
And they just avoid the question,
are you getting a speed up over a classical computer or not?
And if so, how do you know?
Have you really thought carefully about classical algorithms
to solve the same problem, right?
And a lot of the application areas
that the companies and investors are most excited about
that the popular press is most excited about
where quantum computers have been things
like machine learning, AI, optimization, okay?
And the problem with that is that since the very beginning,
even if you have a perfect fault tolerant,
scalable quantum computer,
we have known of only modest speed ups
that you can get for these problems, okay?
So there is a famous quantum algorithm
called Grover’s algorithm, okay?
And what it can do is it can solve many,
many of the problems that arise in AI,
machine learning, optimization,
including NP complete problems, okay?
But it can solve them in about the square root
of the number of steps that a classical computer would need
for the same problems, okay?
Now a square root speed up is important, it’s impressive.
It is not an exponential speed up, okay?
So it is not the kind of game changer
that let’s say Shor’s algorithm for factoring is,
or for that matter that simulation of quantum mechanics is,
okay, it is a more modest speed up.
And let’s say roughly, in theory,
it could roughly double the size
of the optimization problems that you could handle, right?
And so because people found that I guess too boring
or too unimpressive, they’ve gone on to like invent
all of these heuristic algorithms
where because no one really understands them,
you can just project your hopes onto them, right?
That, well, maybe it gets an exponential speed up.
You can’t prove that it doesn’t,
and the burden is on you to prove
that it doesn’t get a speed up, right?
And so they’ve done an immense amount of that kind of thing.
And a really worrying amount of the case
for building a quantum computer has come to rest
on this stuff that those of us in this field
know perfectly well is on extremely shaky foundations.
So the fundamental question is,
show that there’s a speed up over the classical.
And in this space that you’re referring to,
which is actually really interesting,
it’s the area that a lot of people excited about
is machine learning.
So your sense is, do you think it will,
I know that there’s a lot of smoke currently,
but do you think there actually eventually
might be breakthroughs where you do get exponential speed ups
in the machine learning space?
Absolutely, there might be.
I mean, I think we know of modest speed ups
that you can get for these problems.
I think, you know, whether you can get bigger speed ups
is one of the biggest questions for quantum computing theory,
you know, for people like me to be thinking about.
Now, you know, we had actually recently
a really, you know, a super exciting candidate
for an exponential quantum speed up
for a machine learning problem
that people really care about.
This is basically the Netflix problem,
the problem of recommending products to users
given some sparse data about their preferences.
Karinidis and Prakash in 2016 had an algorithm
for sampling recommendations that was exponentially faster
than any known classical algorithm, right?
And so, you know, a lot of people were excited.
I was excited about it.
I had an 18 year old undergrad by the name of Yilin Tang,
and she was obviously brilliant.
She was looking for a project.
I gave her as a project,
can you prove that this speed up is real?
Can you prove that, you know, any classical algorithm
would need to access exponentially more data, right?
And, you know, this was a case where if that was true,
this was not like a P versus NP type of question, right?
This might well have been provable,
but she worked on it for a year.
She couldn’t do it.
Eventually she figured out why she couldn’t do it.
And the reason was that that was false.
There is a classical algorithm
with a similar performance to the quantum algorithm.
So Yilin succeeded in dequantizing
that machine learning algorithm.
And then in the last couple of years,
building on Yilin’s breakthrough,
a bunch of the other quantum machine learning algorithms
that were proposed have now also been dequantized.
Okay, and so I would say, yeah.
That’s a kind of important backwards step.
Like a forward step for science,
but a step for quantum machine learning
that precedes the big next forward step.
Right, right, right.
If it’s possible.
Right, now some people will say,
well, you know, there’s a silver lining in this cloud.
They say, well, thinking about quantum computing
has led to the discovery
of potentially useful new classical algorithms.
And so, you know, so you get these spinoff applications,
but if you want a quantum speed up,
you really have to think carefully about that.
You know, Yilin’s work was a perfect illustration of why.
Right, and I think that, you know, the challenge,
you know, the field is now open, right?
Find a better example,
find, you know, where quantum computers
are going to deliver big gains for machine learning.
You know, I am, you know,
not only do I ardently support,
you know, people thinking about that,
I’m trying to think about it myself
and have my students and postdocs think about it,
but we should not pretend
that those speed ups are already established.
And the problem comes when so many of the companies
and, you know, and journalists in this space
are pretending that.
Like all good things, like life itself,
this conversation must soon come to an end.
Let me ask the most absurdly philosophical last question.
What is the meaning of life?
What gives your life fulfillment, purpose,
happiness, and yeah, meaning?
I would say, you know, number one,
trying to discover new things about the world
and share them and, you know, communicate
and learn what other people have discovered.
You know, number two, you know, my friends,
my family, my kids, my students,
you know, just the people around me.
Number three, you know, trying, you know,
when I can to, you know, make the world better
in some small ways.
And, you know, it’s depressing that I can’t do more
and that, you know, the world is, you know,
facing crises over, you know, the climate
and over, you know, sort of resurgent authoritarianism
and all these other things, but, you know,
trying to stand against the things
that I find horrible when I can.
Let me ask you one more absurd question.
What makes you smile?
Well, yeah, I guess your question just did.
I don’t know.
I thought I tried that absurd one on you.
Well, it was a huge honor to talk to you.
We’ll probably talk to you for many more hours, Scott.
Thank you so much.
Well, thank you.
It was great.
Thank you for listening to this conversation
with Scott Aaronson.
And thank you to our presenting sponsor, Cash App.
Download it, use code LexPodcast,
you’ll get $10 and $10 will go to FIRST,
an organization that inspires and educates young minds
to become science and technology innovators of tomorrow.
If you enjoy this podcast, subscribe on YouTube,
give it five stars on Apple Podcast,
support it on Patreon,
or simply connect with me on Twitter at Lex Friedman.
Now, let me leave you with some words
from a funny and insightful blog post
Scott wrote over 10 years ago
on the ever present Malthusianisms in our daily lives.
Quote, again and again,
I’ve undergone the humbling experience
of first lamenting how badly something sucks,
then only much later having the crucial insight
that it’s not sucking
wouldn’t have been a Nash equilibrium.
Thank you for listening.
I hope to see you next time.