269 - Scott Aaronson: What Is Quantum Computing?

35:34A lot of that is based on something that I mentioned earlier, which was Grover's algorithm for search, right? So there's, besides Shor's algorithm, maybe the second most important quantum algorithm is called Grover's, discovered in 1996. Grover's algorithm lets you take a list as sort of any problem that involves searching a list of n possible solutions, where you just know how to check each one. By the way, I enjoy that you have a cat behind you. Running around the whole time. Hopefully not a Schrodinger cat. You know, nothing that... I'd like to keep her safe in the podcast. Brutal, brutal. We'll get done to it.

36:17But yeah. But so Grover's algorithm involves searching. Let's you sort of take any problem that involves searching through a list of n possible solutions. And it lets you solve it in about the square root of n steps. So that's enormously broader in application than Shor's algorithm. Like almost anything in computer science, if you open an algorithms textbook, has some loop in it where you're just checking a list of possibilities. And where that loop could then be groverized, could be sped up by the square root. The disadvantage is that, unlike Shor's algorithm for factoring, the speed up from Grover's algorithm is much more modest.

37:09It's not an exponential speed up. It's a quadratic speed up. It's a square root speed up. OK, so and and and we don't know for the most part, you know, whether we can get advantages for these other problems that is better than the Grover advantage. But, you know, and the Grover advantage, it will probably take quite a long time before it becomes a win in practice. But, you know, we're we're working on it. We're trying to figure out what advantages quantum computers might be able to give beyond those two application areas. Now, unfortunately, once quantum computing moved from an academic subject to an investment and startup type of field, which happened, I would say, around 15 years ago, then you know people needed a narrative of why quantum computers are going to just you know speed up everything just be the next faster kind of computer right and so depressingly often you know their their solution to that to that problem was to just lie about it right and to just say well well look you know quantum computing is confusing so don't worry about the details, just, you know, you know, just trust it's going to speed up everything.

38:36Right. It just, you know, whatever problem you have, machine learning, oil and gas exploration, you know, a financial portfolio optimization. Yeah, that's what it's going to help for. Right. And and and, you know, and and and and in some sense, like this was remarkably successful, like people would throw money at things like having, you know, that were just wildly disconnected from any of the quantum algorithms that we actually know about. Okay. But, you know, what I'm trying to explain is that underneath all of it, yeah, there is a real advantage, right, that really is, I mean, one of the most dramatic things that we've ever found in computer science.

39:20You know, it is a miracle that it ever works. It seems to mostly help for problems with very specific structure, Like factoring numbers or like simulating quantum systems seems to help, you know, only more modestly as you as you move away from that kind of structure. So that's, you know, I've been trying to explain this stuff for, you know, a quarter century, I guess. And that's about as far as I can compress it. I haven't managed to compress it to five minutes yet. Well, that was an excellent compression, no matter how long it was. It was exactly what I was hoping for. Thank you. I have a couple of more tangential questions at the beginning of your response.

40:11You said that you can't understand quantum computing without understanding a bit about what quantum mechanics says about the world. Yes. the thing is that i know that many physicists think quantum mechanics says very different things about the world yes they all of course follow the same sort of formalism at least as it's been developed to this point but some think that there are i mean well you know the various interpretations yeah yeah there are the many worlders the bowmians the copenhagenists yes And amazingly, they all make exactly the same prediction for what happens when you do such and such experiment.

40:55Right. And so you could say, you know, as long as they're, you know, as their argument is at the level of metaphysics or, you know, at the level of like what is a scientific theory supposed to be telling us, you know, supposed to be doing for us or telling us about, you know, the reality of the world, let's say. but they all make the same predictions for all the experiments then in particular they're all making the same predictions for what the quantum computer will do when you build it right and so so for that reason like you know it's you know the the the bizarre truth is that like this this whole debate sort of doesn't doesn't really matter you know if if the question is will quantum computers work and what will quantum computers be able to do, right?

41:48Then, you know, then sort of everyone who agrees with quantum mechanics is making the same predictions there. You know, what would matter would be if quantum mechanics was just empirically false, right? And, you know, even to this day, there are some skeptics who say, you know, you will never be able to build to a scalable quantum computer, right? And, you know, this is just science fiction. This is too ridiculous. You'll never be able to control qubits to this degree. And, you know, what I've always said to those people is like, I hope you're right. You know, if you're right, then that is a revolution in physics, right?

42:31You know, I mean, like the idea that a quantum computer will work, right? That's just the conservative prediction. That's just what happens if quantum mechanics works exactly the way that it's supposed to work in all of the textbooks. For quantum computing to not be possible, something would really have to change empirically, and that would be the biggest development in physics for 100 years. OK, so but but now if if there's no empirical problem with quantum mechanics, then, you know, then we're all making the same predictions for what, you know, what it would take to build a quantum computer, what a quantum computer would do.

43:21And the debate is at the level of metaphysics, where very roughly the many worlders would say that this giant vector of amplitudes that I was talking about before, that is the most fundamental reality that there is. And so really what there is is just this giant list of amplitudes. OK. And, you know, all of our experience, all of our experience, the whole everyday world has to be sort of reconstructed out of that. And so one famous way of putting this is that when you measure a quantum system that is in superposition, like let's say it has an amplitude to be zero, an amplitude to be one, the many worlders would say there's nothing really special about measurement.

44:24Right. This is just another ordinary physical interaction that just happens to involve the atoms of your body, you know, of your brain and and so forth. And you but you become entangled with the system that you measure. Right. So now if we were keeping track of all the the the the the wave function of the universe, we would see like one branch where this qubit is in the state zero and you have perceived it being in the state zero. Like, you know, your brain, you know, also, you know, your measuring apparatus has all recorded it as being zero. But there's another branch where the qubit is one and where you're, you know, all your measuring apparatus and your brain and so forth have recorded the qubit as being one.

45:18OK. And and so, you know, you could say that like the thing that people argue about in in interpretation of quantum mechanics is that like that, like that, that is what the equations want to have happen. Right. That just, you know, you you know, you become entangled with a system when you measure it. And now there are just these two branches. And the trouble is, how do you reconcile that with our experience, which is that, you know, we just perceive one outcome, right? You know, we perceive this, you know, we don't perceive this giant vector of amplitudes, right? We perceive a single world. uh and so the many worlders would say uh no you know actually all of those branches continue to exist right you just perceive one of them okay like like each each one of them you know is is is another you know locus of of perception right and so this is this is you know why you know they have this imagery that you know the world keeps splitting right into you know these these parallel copies that remain equally real.

46:28And, you know, and it just, you know, within each branch, there is a perception that corresponding to that branch, but the other ones have exactly the same status. And so then, you know, many worlders would have no problem saying, well, a quantum computer is just an application of this, right? The reason why it's getting all this power is that all these different parallel universes or what would have been parallel universes or if we had let them branch off are all collaborating to solve our problem. Now, it's true that we can't sort of take the results from all these parallel universes and then just combine them in arbitrary ways, right?

47:20The only way that we were ever sensitive to this at all is via the interference of the amplitics, right? So, you know, the only way that we get all these parallel worlds to collaborate to solve our problem, if we're going to use that kind of language, is by choreographing a pattern of interference where for each wrong answer, we get some worlds contributing positively and others negatively. So they cancel out, whereas for the right answer, we get all the worlds, you know, contributing in the same way. So now the the the the the Bohmians, you know, which is which is a second camp in interpretation, they would tell kind of the same story as the many worlders.

48:11Well, they they would be very offended if they hear me describe it that way. Right. Because they they don't want to describe it that way. OK, but they want to say, yes, you still have this whole wave function of the universe. You have this giant vector of amplitudes. But there is one world that is, you know, there is one branch that is the actually real branch, right? That is the one that is sort of actually experienced, you know, and all the other branches are just kind of ghost towns. You know, they're there in the equations. You know, they have to be there. They get the right results, but there's sort of nobody home in them.

48:50They're just sort of mathematical abstractions that sort of have the function of guiding the evolution of the one actually real branch. Okay, so that's, you know, that's a story that's been specifically constructed to give exactly the same empirical predictions as, you know, as standard quantum mechanics, right? So there's no experiment that tells it apart, right? But, you know, it just tells a different story about, okay, that it would say, you know, there is this one, you know, unique history, right? They would say that particles, in addition to having these wave functions, they also have these actual positions in three-dimensional space that are then just sort of jostled around by the wave function.

49:50You know, like sort of corks bobbing on top of an ocean, sort of, right? And they're sort of pushed around by the wave function in a way that would exactly match the predictions of the usual quantum algorithm for calculating the probabilities that things happen. OK, so so so so they would say, you know, in a quantum computer, yes, there is this exponentially large wave function. But then there is also inside of the quantum computer this sort of one path that the qubits are following that is sort of more real than all the other paths. OK, but again, that doesn't change my predictions. Right. And then, you know, and then there were the Copenhagen people.

50:37Copenhagen was sort of the original view of quantum mechanics, of Niels Bohr and Heisenberg and their circle. And basically, they just want to tell everyone to stop asking these questions. Okay. So I've described the Copenhagen interpretation as just shut up and calculate, except that you never shut up about it. Okay. So, you know, so they have sort of a whole philosophy, which was very, very influenced by positivism, you know, in the early 20th century that says like, you know, look, you know, what, what, you know, we, we clearly, you know, we live in a more or less classical world. We communicate our experiences by, you know, writing papers about them or by giving talks.

51:33You know, these are, you know, by in other words, by conveying classical information. All that we could reasonably demand of the laws of physics is that, you know, of a physical theory is that it tell us what are the probabilities of the different experiences that we have. And, you know, if we demand more from physics than that, then we should just get over ourselves, right? Like, you know, we have to sort of meditate about it or sort of until we adopt a more enlightened view where we realize that, like, we had no right to demand, you know, to know what is actually going on with this, you know, quantum system before we measured it, right?

52:18Of course, we can use these wave functions. We can use them as mental abstractions for us to keep track of what is going on. But we have no right to say that that is what nature is doing.

52:35The co-panogonists are constantly making this move. We don't get to talk about that. We don't get to ask this question. So once again, they make the same prediction for what the quantum computer will do. But they just don't want to talk about the reality of what is going on inside the quantum computer. They just want to say, you know, we have no right to discuss that. You know, except that mathematically, you know, if we want to describe it, then we should use wave functions. You know, the same as all the other camps are going to do. So as far as quantum computing is concerned, the various theories all make the same predictions.

53:14They just have different stories for what's going on in the background, but that's just not relevant for the application. Exactly. I mean, we could say if one of them made a different prediction, then it wouldn't be an interpretation of quantum mechanics. It would be a rival physical theory. And the next thing that I wanted to ask you about that is somewhat tangential is I liked this image that you sort of conveyed of nature's scratch paper. Yeah. I think I got that from from Mesh Vazirani, who was my advisor at Berkeley. I found that a very striking image. Yeah. And I was wondering if there's anything really deeper to this or if it's just an analogy.

54:07I mean, what came to mind immediately was holography and how information might be stored in a certain way. Yeah, well, well, look, I mean, I mean, I mean, in some sense, you know, what the interpretations, you know, disagree about so much is what is the nature of this scratch paper? Right. You know, the many worlders would say, you know, the the what I was calling the scratch paper just is the most fundamental ontological reality of the world. You know, we should just bite the bullet. We should, you know, accept what the math seems to be telling us that the, you know, the, you know, this this this gigantic list of amplitudes kind of is the most fundamental, you know, physical reality that there is.

54:56And if that leads to, you know, the view that our experience is constantly splitting, that we ourselves are just one little branch in this gigantic superposition, well then so be it. You know, they'll just accept that consequence. For the Bohmians, the giant scratch paper also has a kind of existence, but its existence is just sort of as a guiding field for this sort of single world that has a trajectory that moves around in a way that matches the same predictions. the predictions of quantum mechanics but there's one world that is sort of elevated above the others and then for the Copenhagenists the scratch paper is just a mental device it's just something for us to keep track of what nature is doing and they wouldn't you know they would just disallow you from even asking you know who what is what is actually going on you know ontologically you know under the hood in nature itself or they would say we simply don't.

56:12Either it's meaningless to ask or else we don't know. All right, moving on in my list of any questions based on that response. You said that a quantum computer does not solve the prime factorization problem by simultaneously trying every possible factor, which is definitely what I had heard many, many times. Yeah, that's like still today, like the popularization of it has not moved beyond this, which is sad in a way, right? Because if the point is that if that were how it worked, then that would be good for way, way more than just prime factorization, right? That could be like just about any problem that you might want that you might want to solve that involves like searching through a huge list of possible solutions.

57:06Right. Like if you could do that, then you could solve all of those problems. But the truth is that Shor's algorithm is very, very specific to factoring and to a few other problems in number theory that have some very, very special structure that they take advantage of. And even within cryptography, and this is a very, very important thing to know, even just for practical purposes, we have other cryptographic codes that seem to resist attack, even by quantum computers. OK, so there is a big push right now to migrate to what are called post-quantum or quantum resistant encryption methods. So, for example, to migrate the web, HTTPS, to using quantum-resistant encryption, migrate Bitcoin and Ethereum and other cryptocurrencies to using these other cryptographic codes.

58:17Okay, maybe the most important one we know is based on problems in high-dimensional lattices, okay? And so we know how to get, like, almost all of the cool stuff that people want from modern cryptography, you know, including, like, public key encryption. That's the kind where you don't have to agree in advance on a secret key, right? And digital signatures and, you know, all kinds of other things. You know, we now know how to base that on problems that, well, you know, there's no proof here. But at least, you know, for 25 years, people have failed to find a quantum algorithm for solving these problems, these lattice problems, right?

59:10Because they have not been able to generalize Shor's algorithm to the kind of mathematical structure that there is in these other problems. OK, so so, you know, to me that that that underscores that, yeah, Shor's algorithm only worked because of very, very special structure in the factoring problem. Right. And it was just, you know, it was a little bit unlucky that we based, you know, modern encryption on on these problems that just have this kind of structure. Although, you know, there was there was a reason for it. Right. The structure is kind of a double edged sword. Like the more special mathematical properties your problem has, you know, the more you can actually exploit those properties, you know, to build useful cryptographic protocols.

1:00:05Right. That's what people have been doing since the 1970s. Right. They just sort of like to get public key encryption. They took advantage of very special properties of factoring, you know, discrete logarithms, you know, these serve problems in number theory. But in that same structure that makes those problems so useful for encryption is also what then enables a quantum algorithm to come in and solve the problems. OK, and break the cryptosystems. systems. So you kind of have to calibrate, you know, how much mathematical structure there is in your problem, right, to have like just enough that it's useful for all the cryptographic protocols that you want, but not enough that a quantum computer can leverage that structure to solve the problem.

1:01:00Okay. And we think that we know how to get to that point now, using, for example, these lattice problems. And so NIST, the federal agency, had a competition that ended in 2022 to agree on standards for this post-quantum encryption. And now the challenge is to just get everyone to switch to these new systems, which is a massive headache when you've built the internet on one basis. to switch it to a different basis. I mean, it's like, you know, it's, it's, it's a little bit like the Y2K issue for, for, for people who remember that. But, you know, this, this is actually much, much bigger than that.

1:01:49There's actually, you know, there, there's, there's a, there's a, there's a bigger change that has to happen here. And of course with the, the other difference is that with Y2K, we knew exactly what the deadline was, right? The deadline was, you know, 11.59 p.m., you know, December 31st, you know, 1999. Right. With with switching to post quantum encryption, we don't know one knows exactly when the deadline is. Right. People have gotten close to. you know i mean i mean you know they've made incredible progress uh toward you know building building the kinds of qubits that that you would need for a scalable quantum computer uh we're not there yet but you know we don't know how many more years it will be until um someone has uh quantum computers that are that are relevant for breaking cryptography so um Um, so, so, so yeah, so, so, um, uh, uh, but you know, but, but, but like no one would be able to understand any of this, right?

1:02:58If they just thought that a quantum computer just tries all the possible solutions in parallel and then magically picks the best one, right? If that's what they thought, then it would be like, well, how could you have any cryptography that could be safe against the quantum computer? Right. So I think, you know, you like, you know, as as as as as much as people, you know, sometimes, you know, dislike taking this like 15 minute detour to explain about amplitudes and interference. You know, you kind of need it to, you know, to even have, you know, say anything about this like strange profile of problems that a quantum computer helps you for and doesn't help you for.

1:03:42where i was heading with my question was i'm wondering if there are also if there are if there are more really prominent myths about quantum quantum computing that you encounter all the time that discussing might be used um another of the the big myths about quantum computing is that, well, you know, if you have 100 qubits, then this just is like having two to the hundred power classical bits, right? If you have a thousand qubits, this just is like having two to the thousand power classical bits and so forth, you know, which would make quantum computers like incredible for information storage, right?

1:04:30The trouble with this is, once again, that, yes, there are 2 to the 100 amplitudes that we need to keep track of what 100 qubits are doing, but we never get to directly see the amplitudes. When we measure, if you measure 100 qubits, then you're just going to see 100 bits. And the only role that the amplitudes will play is in calculating the probability that you're going to see one string of 100 bits versus a different string. So this sort of prevents us from using, let's say, n qubits to store 2 to the n classical bits in a way that's directly useful. I mean, like, yes, in a sense, you could do that, but but then you don't get to read out, you know, the classical bits of your choice.

1:05:34Right. You know, almost all of them disappear as soon as you make a measurement. OK, and so so so so so so once again, I think the the the again and again with with with with quantum mechanics, what you see is like you get something that in a classical world, you know, if the world were classical, then quantum mechanics would take these ridiculous resources to simulate. Right. But that doesn't imply that quantum mechanics itself gives us all of those ridiculous powers. Right. You know, it gives us some additional power. Right. But but the all the extra power that we get from quantum mechanics is is limited by by what we actually see when we make a measurement.

1:06:22Right. You know, there's sort of yet another example of the same phenomenon is, you know, which even predates quantum computing is like when you have two entangled particles. Right. So this is the situation that Einstein, you know, famously described as spooky action at a distance. Right. Where like if I have two qubits, let's say, which are in a superposition of the state zero zero and the state one one. OK, and then, you know, there is no distance limit. Right. These qubits could be, you know, on different planets in different galaxies or whatever. But if I've maintained them in this entangled state, this sort of superposition of 0, 0, and 1, 1, then I know that if anyone measured one of the qubits and they see the outcome 0, then immediately they know that the other qubit will also be a 0 if it's measured the same way.

1:07:26Right. And if anyone measures one of the qubits and they see a one, then they know that the other qubit will also be a one. Right. So this sort of collapse, you know, happens instantaneously, you know, regardless of how far away the qubits are. Right. And so. So so so for generations, you know, this has led to a myth that, you know, quantum mechanics just enables faster than light communication. right uh that you know you could just uh have have one entangled qubit on earth have the other one in the andromeda galaxy and then just sort of instantaneously send the message to andromeda right which of course would would violate uh relativity right and in in in special relativity if you can send a message faster than light then you can also send messages backward in time Those are basically the same thing.

1:08:24And so this would sort of completely break the structure of physics, as we know it. And so the answer is, once again, that something more subtle is going on here.

1:08:40So the issue is that when you measure a qubit, you don't get to control what is the outcome of that measurement. Right. So so like I can measure this qubit and, you know, either see a zero, in which case my friend will also get zero or else I'll see a one, in which case my friend will also see one. But I don't get to choose whether it's a zero or a one. Right. That's that's what I would need in order to send a message to my friend. Right. And, you know, so you might say, well, if this is just a matter of just I'm correlated with my friend, well, then even in just ordinary classical physics, right?

1:09:25Like, you know, if my friend and I had two sealed envelopes, you know, with the same letter in them, right, and we took them to different planets and then I open my envelope, I read what's in it. Well, then immediately I know what my friend will say when they open the same, you know, when they open their envelope. Right. But no one would call that instantaneous communication. Right. That's that that's simply a matter of correlated random variables, as we would say. Okay, and so then there was, you know, the thing that Einstein seems to have wanted was some way of explaining quantum mechanics just in terms of local classical hidden variables, right?

1:10:16where where uh like like for example whenever two entangled particles would get created you know they would just un unseen by us they would be exchanging a little message that would say listen if anyone asks let's both be zero okay and then they would just they would just remember that they would they would you know and then they would remember that however far separated they were and And this way, you wouldn't need any spookiness, you know. But then in the 1960s, John Bell proved this very famous theorem, you know, the Bell inequality. Right. And this was, you know, an important forerunner of quantum information and quantum computing.

1:11:00Right. But what Bell proved was that there was no explanation of the type that Einstein wanted that can possibly explain all the correlation. that you get by if you and your friend were to measure the two entangled particles in a bunch of different ways. OK, so there are different measurements that you can make. And yes, while you can tell the story about correlation for one of them, it can't simultaneously work for all of them. OK, and so you're led to this this really, you know, weird picture. You know, once again, I think a picture that is sort of more subtle than any science fiction writer would have had the imagination to invent.

1:11:43Where, like, yes, if you wanted to simulate, you know, entanglement in a universe that was that was actually classical, you know, then you would need faster than light communication in order to, like, keep track of all the correlations. That is what Bell's theorem tells us. Right. And yet we cannot use entanglement to send the message faster than light. That's another important fact. You can prove that within quantum mechanics. It's called the no communication theorem. So in between the possibility of just the ordinary classical world and the world with the instantaneous communication, there is this third possibility.

1:12:33There is this intermediate zone, right, that quantum mechanics, you know, then fills, even though before quantum mechanics, we might it might not even have occurred to us as a logical possibility. Right. That like you could produce these. Beyond classical correlations, but then you can't use them to send the message faster than light. OK, likewise, with information storage. Right. Like, you know, between, you know, having, you know, N particles storing N bits and N particles storing two to the N bits. there is this intermediate possibility, which quantum mechanics comes along and fills, that yes, you can do, for certain specific tasks, you can do things that classically would have taken you two to the n bits, but you don't get the full power of that because you have to measure the qubits and then you only see n of them.

1:13:35Okay, likewise with quantum computation, you know, between just, you know, in T time steps, I get to do T classical computation and versus in T time steps, I get to do two to the T classical computation. quantum mechanics comes along and is this intermediate possibility that I get to do certain specific things that classically would take me exponential time, but I don't get to do every, I don't get to speed up every exponentially hard classical computation, right? Only those for which I can arrange this interference pattern. Okay, so, you know, what is that telling us about the world you know i don't know but it seems like an important clue to something before we finish today i want to make sure that we at least talk a little bit about the physical implementation of a quantum computer you mentioned that skeptics there are skeptics who think that building a scalable quantum computer will not be possible um and you did speak a bit about this earlier but i was wondering if most of these sort of complaints are um oriented around engineering concerns rather than concerns with theoretical physics yeah so there's a whole spectrum of concerns i mean from the people who think that who who will just explicitly say you know this this uh can't be done because quantum mechanics is wrong you know and how do we know it's wrong because you know because it would let you do quantum computing which is an obvious absurdity right um you know and then and then we say well look you know uh we hope you're right you know but we're we're betting on the more boring outcome that you know quantum computing is merely possible right and then there are people who say okay you know i I don't find, you know, I'm not disputing quantum physics, but there must be some new principle on top of quantum physics that somehow screens off or sensors quantum computation.

1:15:52OK, so there's a mathematician named named Gil Kalai who who who was in that camp, for example. And then, you know, we say to them, well, then, you know, what is that new principle? You know, what can you tell us about it? Right. And what predictions do you make? When will we start seeing the efforts toward quantum computing fail? And what exactly are those failures going to look like? And there are some smart people who have thought about that, but I don't think that they've been able to come up with some alternative picture of the world that coheres, that really makes sense to me. uh and and certainly i think given the experimental results that we've seen just within the last year or two you know those people are in a much much tighter spot that they were before right they um i mean because i feel like if there were some you know some deep new new physical principle that that made this uh impossible like we should have seen it by now right we now have uh um Within the last year, what we've seen with superconducting qubits, with trapped ion qubits, and we're starting to see with neutral atom qubits also, is we can do programmable two qubit operations that are about 99.9 % accurate.

1:17:28okay uh you know when i entered the field uh 25 years ago you know it would have been amazing to do like 50 accurate you know two qubit operations right and then you know that's just like uh uh way way you know uh um you know it's sort of not even close to where you need to be to get a scalable, reliable quantum computation. There is this technology of quantum error correction, something we haven't really talked about, but this was also a big discovery in the mid-1990s that said that if you want to build a reliable quantum computer that can scale up to any number of qubits, any number of operations on them.

1:18:21You don't need perfectly reliable operations. But you just need operations that are reliable enough that error-correcting codes can then get you the rest of the way. So something similar was true about classical computing that was discovered by John von Neumann in the 1950s. uh you know and then and then eventually we we we we almost didn't even need that because transistors were just so reliable that they you know uh you know that they failed you know like like in and your laptop there are like maybe a few hardware uh a few failure physical failures of the chip every year like when a cosmic ray passes through or something like that right and And normally you wouldn't even notice that, you know, it was someone operating a data center at the scale of Google or Amazon does notice that, you know, and does not to use error correction to deal with that.

1:19:25It was not obvious to people that that error correction would work for quantum computing. Right. There were all kinds of technical problems that made, you know, skeptics in the in the in the 90s say, no, you know, that that shouldn't work. But then a really, really beautiful theory of quantum error correction was discovered that says, no, it does work, you know, if you can get your physical qubits to be accurate enough. And at that time, they were estimating that you would, you know, maybe this would work if you had two qubit operations that were, let's say, 99.9999 % accurate. Okay, so six nines of accuracy, right?

1:20:09And that's, you know, and this was at a time when we didn't even have one nine. Right. And so, OK, but, you know, to a theorist like me, you could say, OK, OK, you know, it's just it's just some constant. Right. Which means, you know, this has been reduced to merely an engineering problem. Right. And and indeed, you know, what we've seen over the past 30 years is sort of. tremendous progress on two fronts. First of all, the accuracies that the experimentalists can achieve in the lab, you know, have improved tremendously, right? You know, the 50 % accuracy of two-cubit gate became 90%. At some point, that became 95%, 99%.

1:20:57And now, as I said, within the last year, the new standard is 99.9%, right? And at the same time, people also develop better and better error correcting codes. And so instead of six nines of accuracy, you know, we actually now know codes that work with three nines of accuracy. So basically, like the two numbers that have to meet have basically met each other at this point, right? We're basically at what's called the fault tolerance threshold. And now what remains is merely the sort of staggering problem that you have to build a system with millions and millions of physical qubits being shuttled around to where they need to be, interacting with each other in a way that maintains this 99.9 % or better, 99.99 % accuracy.

1:21:57and then with all of this error correction layered on top. Okay, so, but again, you know, I don't know of any sort of fleshed out proposal for how the physical world could be that would sort of be compatible with the experimental results that we've already seen, you know, many of them just within the last year, and that would not allow, you know, full, full scalable quantum computation, right? So this is why I say that the skeptics are now in a tight spot. Now, you know, there are many different things that you could mean by skeptic, right? So besides the people who just reject quantum mechanics outright, or the people like Gil Kalai, who think that, you know, there must be some new physical principle on top of quantum mechanics that sensors quantum computing.

1:22:58There are also people who just say, no, as an engineering matter, this is just going to be too hard. You know, this is just, you know, the funding is going to run out or this is not going to happen in any foreseeable future. You know, but like at that point, we're just arguing about, you know, how many, like, how hard is this as an engineering problem? How many years does this take? Right. And like people care about this enormously because what they want to know is, you know should i invest in this quantum computing company or should i not invest in them right or like what you know what is going to make money in the next five years that's not that you know i i feel liberated from having to you know worry too much about that kind of thing right that's just not the the thing that that that most interests me um um you know i i i do think that, you know, given the experimental progress that we've seen over the last couple of years in superconducting qubits, in trapped ions, in neutral atoms, like, it would surprise me a lot if we don't have, you know, if we don't start to see at least useful special purpose quantum computation within the next decade, you know, and at some point, Yes, I do expect that I will live to see, you know, quantum computers running Shor's algorithm to factor enormous numbers.

1:24:27You know, if I could predict how many years that would take, I wouldn't be a professor. I would be an investor. Right.

1:24:39But. So, so, you know, but then, you know, they're they're they're sort of yet a fourth thing that people mean by by skeptic, which is they say, well, yeah, maybe all of this works and it leads, you know, it lets you do this quantum simulation and factoring. But the applications of quantum computers have been massively oversold to the public. And and it's not you know, we we don't really know if it's useful for that much beyond these very, very specialized things. I would say that I myself am a skeptic in that fourth sense.

1:25:17right well scott this has been yeah exactly the introduction i was hoping for of course we didn't get into a lot of cutting edge and more granular questions but that's to be expected and we also didn't get to talk about ai so hopefully sometime down the road we'll we'll meet again and and talk more about these subjects thank you so much sure no problem yeah good talk good to talk to you Thank you.