Transcript for #72 – Scott Aaronson: Quantum Computing

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. So the ones you mentioned, 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? 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 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. Often answer them and sometimes they actually tell you something about the philosophical questions that sort of, you know, maybe motivated your curiosity as a child, right? You know, 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, you know, 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, you know, math and science are tools that we have for, you know, actually making progress. And, you know, hopefully even, you know, changing our understanding of these philosophical questions, sometimes even more than philosophy itself does.

Well, I'm not sure if they do so more than any other scientist. I mean, I mean, Alan Torring was famously interested in his most famous, one of his two most famous papers was in a philosophy journal mind. It was the one where he proposed the Doring Test. He took a Vittgenstein's course that came bridge, argued with him.

Yeah, well, well, the transcript, you know, of their course, which was in 1939, right, is one of the more fascinating documents that I've ever read, because, you know, a victim's dying is trying to say, well, all of these formal systems are just a complete irrelevancies, right, if a formal system is irrelevant, who cares, you know, why does that matter in real life? And touring is saying, well, look, if you use an inconsistent formal system to design a bridge, the bridge may collapse. So touring in some senses, thinking decades ahead, I think of where Vitt can shine is to where the formal systems are actually going to be used in computers to actually do things in the world. And it's interesting that touring actually dropped the course halfway through. Why? Because he had to go to Bletchley Park and work on something of more immediate importance.

Yeah, and I would say more generally, a lot of scientists are interested in philosophy, but they're also busy, and they have a lot on their plate, and there are a lot of very concrete questions. that are already, you know, not answered, but, you know, look like they might be answerable, right? And so then you could say, well, then why, you know, break your brain over these, you know, metaphysically unanswerable questions when they 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 clashions, then I can actually make progress on something.

Well, I mean, a lot of it just depends on the individual, right? It's hard to make generalizations about entire fields. But I think if we tried to, if we tried to, if we tried to stereotype, we would say that a scientist's very often will be less careful in their use of words. I mean, philosophers are really experts in sort of you know, like when I when I talk to them, they will just pounce if a you know, use the wrong phrase for something.

You could say, like, there's, yeah, yeah, we're, you know, they will, they will sort of interrogate my word choices, let's say, to a much greater extent than scientists would, right? And scientists 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 recent research about neurobiology or best of all research that they personally are involved with. And of course, they will want to talk about that when it is what they will think of. And of course, you could have an argument that maybe it's all interesting as it goes, but maybe none of it touches the philosophical question. But maybe a science at least, as I said, it does tell us concrete things. And even if 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.

So I mean, I would say some of the most famous examples in history of that sort of replacement Well, you know, I mean, I mean, to go back to Alan Torring, right? What he did in his computing machinery and intelligence paper was exactly, you know, 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. You know, could you program a computer so that you couldn't tell the difference between it and a human? Right.

It precise he does precisely that. Or you know, we could look at at at girdle, right, where you know, you had these philosophers arguing for centuries about the limits of mathematical reasoning, right, the limits of formal systems. And you know, then by the early 20th century, uh, logicians, you know, starting with, you know, Fred Gay Russell. And then, you know, most spectacularly girdle, you know, 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? So that would be another example. I had this essay called The Ghost in the Quantum Turing Machine. That's one of the crazier things I've written. But I tried to do 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. Can you have, can you be, you know, or do we mean compatibleist 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, 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.

Well, if you were trying to predict a person, then presumably you would need some model of their brain. 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've written in this envelope what you were going to say next.

Well, but the question is what accuracy at the level of the underlying mechanisms do you need in order to predict the behavior? At the end of the day, the test is just, can you foresee what the person is going to do? And discussions are free will. It seems like both sides want a very quickly dismiss that question as a relevant. Well, to me, it's totally relevant because if someone says, well, I will applause demon that knew the complete state of the universe could predict everything you're going to do, therefore you don't have free will. It doesn't trouble me that much because I've never met such a demon. We even have some reasons to think maybe it could not exist as part of our world. It's only an abstraction, a thought experiment. On the other hand, if someone said, I have this brain scanning machine, you step into it and then 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. 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 walls of physics or what about the behavior of the brain prevents it from existing?

Yeah. Well, you could say the sort of obvious possibility, which was you know, recognized by adding to 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, it's behavior is chaotic, right? It's sort of, it's governed by these hodryhuck skin 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 in neuron will fire or not fire.

Exactly, exactly. And so you could ask, well, well, where does the randomness in the process, you know, that neuroscientists, 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? Well, ultimately, you know, there were some quantum mechanical events at the molecular level that are getting sort of chaoticly 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, had 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 could just calculate the even just the probabilities of all of the possible things that you would do, right? And, you know, You know, if all the things that said you had a 10% chance of doing, you did exactly a 10th of them, you know, and that somehow also takes away the feeling of free. 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 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 and had a superposition over many different positions, as soon as I measure, I localized 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 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. or maybe not, maybe it would suffice to just make some nano robots 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, it is possible to envision what progress on it would look like.

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, a democradist talked about the hard problem of consciousness, you know, a 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.

Well, I mean, well, I mean, there is the whole question of AI, right, of, you know, can you build a a human level, or superhuman level AI, and can it work in a completely different substrate from the brain? Of course, that was how entorings point. Even if that was done, maybe people would still argue about the hard problem of consciousness. My claim is a little different. My claim is that in a world, where, you know, there were, you know, human level AI is where we'd been even overtaken by such AI's 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? If this prediction machine, did I was talking about could actually be built, will now the entire discussion of free will is transformed by that, even if in some sense the metaphysical question hasn't been answered.

But see, if every time I was contemplating a decision, this machine had printed out an envelope where I could open it and see that it knew my decision, I think that actually would change my subjective experience of making decisions.

Well, you know, I mean, the knowledge that this machine had predicted everything I would do. I mean, it might drive me completely insane, but at any rate, it would change my experience to not just discuss such a machine as a thought experiment, but to actually say it. Yeah. I mean, you could say at that point, you know, you could say, you know, what, why not simply call this machine a second instantiation of me and be done with it, right? What, what, why even privilege the original me over this perfect duplicate that that exists in the machine.

That has been one of the big things that theologians have argued about for thousands of years. I'm not a theory agent, maybe I shouldn't go there. So there's not a clear answer in a book like, I mean, I mean, this is, you know, the Calvinists debated this, the, you know, this has been, you know, I mean, different religious movements of taking different positions on that question. That is how they think about it. Meanwhile, a large part of what animates theoretical computer science, we are asking, what are the ultimate limits of what you can know or calculate or figure out. by entities that you can actually build in the physical world. And if I were trying to explain it to a theologian, maybe I would say, we are studying to what extent gods can be made manifest in the physical world. I'm not sure my colleagues would like that.

Yeah, so it's a proposal for a new type of computation. Let's say a new way to harness nature to do computation that is based on the principles of quantum mechanics. Now the principles of quantum mechanics have been in place since 1926. They haven't changed. What's new is how we want to use them. 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 that I can let you not, 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 an eye percent 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 Let's say the possibilities for what a system could be doing are described using numbers called amplitudes, 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 that 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. For example, you might say that an electron has some amplitude for being here and some other amplitude for being there. Now, if you look to see where it is, you will localize it. force the amplitudes to be converted into probabilities that happens by taking their squared absolute value. And then you can say either the electron will be here or it will be there. And knowing the amplitudes, you can predict at least the probabilities that you'll see each possible outcome. 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, and 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 we, 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 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. A quantum computer is a computer that tries to exploit these exactly these phenomena, superposition, amplitudes and interference in order to solve certain problems much faster than we know how to solve them otherwise. So it's the basic building block of a quantum computer is what we call a quantum bed 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 in 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 ampute, you know, I don't just need amplitudes for each cube it separately. Okay, in general, I need an amplitude for every possible setting of all thousands of those bits. Okay, so that what that means is two to the 1,000 power amplitudes. Okay, if I had to write those down, let's say in the memory of a conventional computer, if I had to write down two to the 1,000 complex numbers, that would not fit within the entire observable universe. Okay, and yet quantum mechanics is unequivocal that if these qubits can all interact with each other, and in some sense I need two to the 1,000 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 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, even if there are two to the 1000 of them, right? I can easily do that. The trouble is for a computer to be useful. You've got at some point you've got to look at it and see and see an output. 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. If I just wanted a random answer, well, I could have picked one myself with a lot less trouble. 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.

Oh, well, information is that 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 I bet it's zero or one.

That's right. 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 and manipulated in a superposition of zero and one states. Now, you know, sometimes people ask, well, but, but what is a cube, it physically, right? And there are all these different, you know, proposals that are being pursued in parallel for how you implement Cubits. 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 the 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 just an individual atomic nucleus. 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 so just like in the classical world, 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? Cubits 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 of of of cubits and and how you know how you measure them how you change them over time and so you know that the subject of you know how cubits behave and what you can do with cubits that is quantum information so just to linger on that short so does the physical design implementation of a cubit

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. And the qubits are very far from perfect. And so the lower levels sort of does affect the higher levels. And we sort of have to think about all of them at once. 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, 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 yes, the problem is even a little more specific than noise. So the fundamental problem, if you're trying to actually build a quantum computer of any appreciable size, is something called decoherence. And this was recognized from the very beginning when people first started thinking about this in the 1990s. 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 said talk 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 in one state 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 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. 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 zero nest or the one nest of the qubit to be recorded in, you know, the radiation in the room and 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 tube it has been measured. It is, you know, the state has now collapsed. You know, another way to say it is that it's becoming tangled with its environment. But, you know, from the perspective of someone who's just looking at this tube, it is as though it is 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 finatically 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. That is such a staggering problem. How do I isolate these cubits from the whole universe, but then also tell them exactly what to do? There were distinguished physicists and computer scientists in the 90s who said, this is fundamentally impossible. know, the laws of physics will just never let you control Cubits 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 cubits as I want, you know, in doing as much on them as I want, I do not actually have to get the cubits 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, it's 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. Now, in some sense, that discovery is what set the engineering agenda for quantum computing research from the 1990s until the present. The goal has been engineer cubits that are not perfectly reliable, but reliable enough. that you can then use these error correcting codes to have them simulate cubits that are even more reliable than they are. 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, you're simulated cubits could entern simulate cubits that are even more reliable and so on until you've just, you know, effectively you have arbitrarily reliable cubits. So long story short, we are not at that break even 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 cubist the better because we'll the more cubits the larger the computation you can do, right? I mean, I mean a cubits are what constitute the memory of your quantum computer.

Oh, yes. So, so the way I would say it is that error correction imposes an overhead in the number of cubits. 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 what would it take to actually use a quantum computer to hack your credit card number, which is the most famous application people talk about. Let's say two factor huge numbers in there by break the RSA crypto system. Well, what that would take would be thousands of several thousand logical cubits, but now with the known error correcting codes, each of those logical cubits would need to be encoded itself using thousands of physical cubits. So at that point, you're talking about millions of physical cubits. 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 multiple. 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 1,000 or so. So, you know, there's a lot of work on, you know, inventing better, trying to invent better error correcting codes. Okay, but that is the situation right now. In the meantime, we are now in what the physicist John Presco called the noisy intermediate scale quantum or nisc 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. That would be like true error correction. We are not or something else that would achieve the same effect. We are not there yet. But where we are now, let's say as of a few months ago, as of Google's announcement of quantum supremacy, we are now finally at the point where even with a non-error-corrected quantum computer, 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 a bunch of startup companies.

So there's, you know, there's are excellent questions. My guess would be all of the above. I mean, my guess, you know, I mean, I mean, you know, because they 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, our 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, um, 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 build an error corrected quantum computer as it was envisioned back in the 90s. 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.

Okay. All right. There was a lot there. But just to break off something. I mean, I think we are in an extremely special period of human history. I mean, you could say obviously special in many ways. There are way more people alive than there have been. you know, the whole, you know, a future of the planet is in, is in, is in question in a way that it, it hasn't been, you know, for, for the rest of human history, but, you know, in particular, you know, we are in the era where, you know, we, we finally figured out how to build, you know, universal machines, you could say, you know, the things that we call computers, you know, machines that you program to simulate the behavior of, of whatever machine you want, And once you've crossed this threshold of universality, you've built, you could say, you've instantiated touring machines in the physical world, well then the main questions are ones of numbers. There 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. But as long as it's classical computing, then it's all questions of numbers. And the 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, you know, faster with millions of times more memory. And, you know, I mean, I think there's been an immense economic pressure to, you know, get more and more transistors, you know, get them smaller and smaller, get, you know, add more and more cores. And, you know, in some sense, like a huge fraction of sort 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 you know it has been one of the biggest success stories in the history of technology right there's you know I mean it is I am as amazed by it as as anyone else is right but at the same time you know we also know that it you know and I I I I I really do mean we know that it cannot continue indefinitely, 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, you know, Moore's law has to end. I mean, ultimately, you will reach the limit imposed by quantum gravity. You know, you know, if you were doing, if you tried to build a computer that operated at 10 to the 43 Hertz, that did 10 to the 43 operations per second, that computer would use so much energy that it would simply collapse to a black hole. Okay, so, you know, in reality, we're going to reach the limits long before that, but you know, that is a sufficient proof that there's a limit. Yes, yes.

Yeah, 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, you know, we wanted flying cars and we only got Twitter instead, right? And yeah, yeah, yeah, yeah, right, right.

Absolutely. So quantum supremacy is a term that was coined by again by John Preskell in 2012. Not everyone likes the name, but it's sort of stuck. We sort of haven't found the better alternative. Yeah, 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 tasks much faster than any known algorithm running on any of the classical computers that are available. Okay. So, you know, notice that I did not say a useful task. You know, it could be something completely artificial, but it's important that the task be well defined. So in other words, you know, there is it is something that has right and wrong answers, you know, and that are nowable independently of this device, right? And we can then, you know, run the device, see if it gets the right answer or not.

Everything that a quantum computer can do, a classical computer, can also eventually do. And the reason why we know that is that a classical computer could always, if it had no limits of time and memory, it could always just store the entire quantum state of the quantum, or 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 so anything that quantum computers can do can also be done by classical computers albeit exponentially slower so okay quantum computers don't go into some magical place outside of Alan touring definition of computation precisely they do not solve the whole thing problem They cannot solve anything that is uncomputable in Alan Turing's sense. What we think they do change is what is efficiently computable. And since the 1960s, the word efficiently was 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.

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 well-defined problem. Secondly, we want it to be for a problem where we really believe that a quantum computer has better scaling behavior, right? So it's not just an incidental matter of hardware, but it's that as you went to larger and larger inputs, 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. So I want 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, to this 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.

Precisely, precisely. Yeah, and quantum supremacy does not require error correction, right? We don't, you know, we don't have you could they 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.

Yeah, well, what did they actually do? Great, great questions, because now you get into actually a lot of the work that I, 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 Arkapov at MIT at the time, and independently of some others, including a Bramner, Joseph, and Shappard. 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. So there are many, many, many possible valid outputs. Your computer will probably never even produce the same output twice. If it's running as assuming it's running perfectly. But the key is that some outputs are supposed to be clear than other ones.

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 now how you how 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 So we, you know, that part is almost trivial. 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 what creates a lot of garbage, but you know, very specific garbage, right? So, you know, of all of the, so we're going to talk about Google's device that we're 53 qubits there, okay, and so there are two to the 53 power possible outputs. Now, for some of those outputs, there was a little bit more destructive interference in their amplitude. So their amplitude is real little bit smaller. And for others, there was a little more constructive interference. The amplitudes were a little bit more aligned with each other. And so those had were a little bit likelier. All of the outputs are exponentially unlikely, but some let's say two times or three times unlikely or the others. Okay, and so so you can define, you know, the 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? 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 what is 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. So it's very expensive to do the test on a classical computer. The good news is, it's about nine quadrillion. That doesn't help. Well, you know, it's a you want anything like scientific notation. I don't know what I mean is it is it is it is impossible to run and yes, so we will come back to that it is just barely possible to run we think on the largest super computer that currently exists on earth which is called summit at Oak Ridge National Lab Great. That's the short answer. So ironically, for this type of experiment, we don't want 100 qubits, because with 100 qubits, even if it works, we don't know how to verify the results. So we want 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 that this is where the 53 comes from for the kids. I mean, I mean, I mean, that's also that sort of, you know, the mode, I mean, That's sort of where they are now in terms of scaling. And then soon that point will be passed. And then when you get to larger numbers of qubits, then 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 computations. So with the sampling thing, so the test that Google applied with this linear cross entropy benchmark was basically just take the samples that were generated, which are 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 larger than the mean? So is the quantum computer biased toward outputting the strings that you wanted to be biased toward? 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? How do we know that this couldn't have been spoofed by a classical computer? The first answer is we don't know for sure, because this takes us into questions of complexity theory. The questions of the magnitude of the P versus NP-question. But we don't know how to rule out definitively that there could be classical algorithms for even simulating quantum mechanics and for simulating experiments like these. But we can give some evidence against that possibility. And that was sort of the main thrust of a lot of the work that my colleagues and I did over the last decade, which is then around 2015 or what led to Google deciding to do this experiment.

It's, it's math for the most part. I mean, 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, on, on, you know, these problems and not just theoretically, but with the actual range of parameters that are actually a rising in Google's experiment. So there is an empirical component to it. But now on the theoretical side, basically what we know how to do in theoretical computer science and computational complexity is 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. 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, for you know, you probably were much more confident or we're hard, then those would be easy as well. Okay. So, so we can give what are called reductions. This has been the basic strategy in 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. The 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 we can do something. Certainly, we can say that 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.

He was premature. Let's say. So, well, okay, a wrong. Look, I'm actually, I'm a fan of Andrew Yang. I like his ideas. I like his candidacy. I think that he may be ahead of his time with the universal basic income and so forth. And he may also be ahead of his time in that tweet that you referenced. So guarding, regarding using quantum computers to break cryptography, so the situation is this. So the famous discovery of Peter Shore, 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. They're not NP-complete problems. We're pretty sure they're not. 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 sure showed is that once you get scalable quantum computers, then that's no longer true. Okay, but now, you know, 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. We touched on this earlier, but Google's device has 53 physical cubits. To threaten cryptography, you're talking with any of the known error correction methods, you're talking millions of physical cubits.

Yes. 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 In the hope that eventually they'll be able to decode at one's quantum computers become available. 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. There's a whole field devoted to this now, which is called post quantum cryptography. Okay, and so there is already so so we have some good candidates now the best known being what are called lattice based crypto systems and there is already some push to try to migrate to these crypto systems so NIST in the US is holding a competition to create standards for post quantum cryptography, which will be the first step and trying to get every web browser and every router to upgrade, you know, and use, you know, some like SSL that is 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, so, you know, I'm sure's 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? 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 going to 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 learn about chemical reactions, design, maybe new chemical processes, new materials, new drugs, new solar cells, new superconductors, all kinds of things like that.

Scali we're 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 100 or 200 cubic 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.

But I think within the next decade, the best shot we have is certainly not using shores of algorithm to break cryptography, just because it requires 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? You know, the way that people make fertilizer right now is still based on the hopper Bosch process for 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, 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 going to realize it or not, but you know, they certainly at least have a shot. So it's going to be a very, very interesting next decade.

Yeah, so I can tell you what the current studies are saying. I think probably better to rely on that than on my intuition. But there was a group at Microsoft had a study a few years ago that said, even with only about 100 qubits, you could already learn something new about the chemical reaction that makes fertilizer, for example. The trouble is they're talking about a hundred qubits and about a million layers of quantum gates. Okay, so there's so basically they're talking about a hundred nearly perfect qubits.

Exactly, 100 logical cubits. And now, you know, the hard part for the next decade is going to be, well, what can we do with 100 to 200 noisy cubits? Yeah.

So people are going to be pushing simultaneously on a bunch of different directions. One direction, of course, is just making the qubits better. There is tremendous progress there. The fidelity is like the accuracy of the qubits has improved by several orders of magnitude in the last decade or two. Okay, the second thing is designing better, let's say lower overhead, our correcting codes, and even short of doing the full recursive error correction. They were these error mitigation strategies that you can use that may allow you to eat 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 1 million. And so, you know, I hope that because people will care enough that these numbers are going to come down.

Yeah. So a 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 penombra of people making, you know, just utterly ridiculous claims. And so with quantum computing, I mean, I would say that the main way that people go astray is by, you know, not focusing on sort of the question of, you know, are you getting a speed up over a classical computer or not, right? And so, you know, people have like a dismissed quantum supremacy because it's not useful, right? Or, you know, it's not itself. Let's say obviously useful for anything. Okay, but, you know, ironically, these are some of the same people who will go and say, well, we care about useful applications. We care about solving traffic rooting and financial optimization and all these things. And that sounds really good. You know, but they're, you know, their entire spiel is sort of counting on nobody asking the question, yes, but how well could a classical computer do the same thing? Yes. Right. You know, I really mean the entire thing is, you know, they say, well, quantum computer can do this, the 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, you know, if so, how do you know, have you really thought carefully about classical algorithms to do, you know, to solve the same problem, right? And a lot of the application areas that, you know, companies and investors are most excited about that the popular press is most excited about you know for quantum computers have been things like machine learning AI optimization okay and the problem with that is that since the very beginning you know even if you have a perfect you know fault tolerant you know quantum scalable quantum computer you know We have known of only modest speedups that you can get for these problems. So there is a famous quantum algorithm called Grover's Algorithm. 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. 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, you know, 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, sure, is algorithm for factoring is, or for that matter, that simulation of quantum mechanics. It is a more modest speed up. Let's say, you know, roughly, you know, in theory, it could roughly double the size of the optimization problems that you could handle. And so, you know, because people found that, I guess, too boring or, you know, too unimpressive, you know, they've gone on to, too, like, invent all of these heristic algorithms, where, you know, 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, you know, and the burden is on you to prove that it doesn't get us beat up, right? And, you know, 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.

Absolutely, there might be. I mean, I think we know of modest speed-ups that you can get for these problems. I think 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. Caronitis and precaution 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 Ewan Tang, and she was obviously brilliant. She was looking for a project. 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, this was a case where if that was true, this was not like a P versus NP type of question, right? This, this might well have been proveable, but she, 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 E-win succeeded in decontizing that machine learning algorithm. And then in the last couple of years, building on E-win's breakthrough a bunch of the other quantum machine learning algorithms that were proposed have now also been decontized. Yeah, okay, and so I would type of important backwards step. Yes, I like that.

if it's part. 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 algorithm. That's true. Right. And so you know, so you get these spin-off applications. But if you want a quantum speed up, you really have to think carefully about that. You know, E wins work was a perfect illustration of why. And I think that the challenge, the field is now open. Find a better example, find where quantum computers are going to deliver big gains for machine learning. I am not only do I ardently support 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 journalists in the space are pretending that.

I would say number one trying to discover new things about the world and share them and communicate and learn what other people have discovered. Number two, my friends, my family, my kids. My students, you know, 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 the pressing that I can't do more and that, you know, the world is, you know, in 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.

Well, yeah. I guess your question just did. I don't know.

Well, thank you. Thank you. It was great.