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Mithuna on Quantum Immortality, Self-Studying Quantum Mechanics, PhD research, and Quantum Computing
March 11, 2021
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The Economist covers math, physics, philosophy, and AI in a manner that shows how different countries perceive developments and how they impact markets. They recently published a piece on China's new neutrino detector. They cover extending life via mitochondrial transplants, creating an entirely new field of medicine. But it's also not just science they analyze.
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Today's guest is Mithuna from Looking Glass Universe, a YouTube channel you should subscribe to, which provides explications into obscure physics and math topics such as the Schrodinger equation and Bohmian mechanics.
Mithuna is a bright and promising individual who recently completed her PhD in quantum computing in Cambridge, and we cover her thesis titled, The Power of Restricted Quantum Computational Models. We also touch on quantum foundations and self-studying, since this channel is geared toward the deciphering of variegated theories of everything. For example, there's Kastrup's, there's E8, there's geometric unity, there's M-theory, there's Chris Langan's, CMTU, loop QG, SO10, etc., and math and physics
Is the language of the universe, or at least some part of the universe, and powerfully so?
This means comprehension of math and physics is beneficial. Though, to be fair, there is the counterclaim by the mystic types that the logical mind, when overdeveloped, impedes the intuitive, empirical one, and that it's this latter one that's necessary to perceive the larger, truer picture of reality. Either way, self-studying seems indispensable, so there will be more interviews on this topic. For example, tomorrow I'm speaking with Fields Medalist Richard Borchards on self-learning,
Self-learning mathematics in particular quantum field theories connection to the monster group and general problem solving Apologies for any tiredness on display during this podcast as it was it was the end of a towering day of studying and fasting If you'd like to see more conversations like this, especially those that explore math physics philosophy and consciousness at a relatively high technical level then please consider supporting at patreon.com
Thank you. Welcome, Mithana. I appreciate it. Thank you for having me. Congratulations on your doctorate, by the way.
Thank you. Yeah, like I have technically just finished up, but I finished writing about a year ago. So it's good to finally be done with the paperwork. You run a channel called Looking Glass Universe. What are some of the aspects of that that you enjoy the most and what are some of the more detrimental aspects? Good question. So I really enjoy teaching something that I think I know.
Can you give an example? Like what was something that you thought you had understood and then as you were explaining it you realized okay there are holes here?
Oh my gosh, so many things. Um, but like just, just as a whole, like, uh, something that I, like the reason I started this channel is because I had done some undergrad classes in quantum mechanics. Um, yeah, and like done well in them. And I just was like, Oh, well, you know, I understand this topic and people like to learn about quantum mechanics. So I may as well make some videos explaining what I know. So that's what I thought this channel would be about. But as soon as I started writing those videos,
I realized like, oh, I don't know what a superposition is, like, I don't actually know, you know, philosophically what this wave function thing is. And I realized it's basically everything I thought I knew, I had no idea about. And so I ended up doing a bunch of research on myself by myself, like I took six months off, was just like reading quantum mechanics books. And then I realized like, there's so much more to this than I thought from undergrad.
And that's what led me to the PhD, to kind of like solve some of those problems. You took six months off just to do research? Yeah, basically it just went for my own, like off as in I was doing part-time work to pay for that. But I, yeah, like basically those six months were devoted to just researching things on my own a little bit more.
You know part of when I run this channel, I'm curious if you feel the same I wonder how is it that people understand the concepts that they do without having to explain it to someone else because part of the understanding comes from trying to apprehend it from another point of view and explain it simply or explain it from from some other position and I'm
And there's an advantage to having a YouTube channel. So some people think like you're just wasting your time because it takes quite a bit of time to between the understanding and then actually putting out a video. But at the same time, I wonder how is it that other people understand what they do? You know, teaching has sort of been recognized as a very good way to build understanding yourself for a long time. But
The YouTube medium I feel is really special because you have to try and explain it in a way that someone who may not have the background can understand as well. And that means you have to rely on way less assumptions. And the assumptions are often where your misunderstandings or where your not complete understandings are. What's your process of learning something new in math or physics like? Do you just go to the Wikipedia page first? Do you go to the Stanford Encyclopedia?
Great questions. It depends a lot on the topic. If it's something in quantum mechanics now, I'll just go to the papers.
read the papers. And then when I don't understand things, then I'll go to something like Wikipedia, or more likely it will be some like textbooks that I trust. And like if they have a section on it, then I'll trust that that section. So for example, if it's something in quantum computing, or even sort of related to quantum information, then I will check whether it's in Nielsen and Truong. If it's there, like that's the Bible, I'll just read it from that. But otherwise, like, yeah, it's sort of, yeah, I'll read stuff, just
and then Google the bits that I don't understand. Did you ever feel like math or physics wasn't for you? Oh yeah, 100%. I definitely didn't think I would end up in math or physics, as math especially, but even physics. So when I was in high school, I was quite like an artsy kid. You know, I enjoyed like literature classes and I really loved painting and I thought I wanted to be a graphic designer. And then
I took a physics class about cosmology at some point and was just blown away by it, completely fell in love, was certain that I was going to be a physicist. But even so, I was still really, really bad at math. So I was doing well at physics at the same time that I was basically failing math and like in the lowest grade for lowest band basically in Australia for math. And like I kept
at it and I decided to put myself into some really hard math classes just because I knew I needed it for physics. But I didn't think of myself as a math person at all until university where, yeah in the first year I was doing math classes and I was doing fairly okay in them and you know that was all good but they weren't like the hardest math classes. But in the second year I just like happened to enroll myself in like a fairly abstract like mathematical course
and just loved it so much. Functional analysis? It wasn't functional analysis. I did really love that functional analysis, but my step in was abstract algebra. So yeah, and like, it was really cool because like, you know, I remember one of the first things we were trying to prove was like, you know, zero plus zero equals zero. And, and like,
Getting back to the basics and understanding why things are true is like what I really loved about physics. And it's the same thing that I could love about math. And that was an aspect of math that I hadn't seen in school. And so that's why I thought I was not a math person, because I thought math was just about like following some algorithms to like get to an answer. That's not that's not it at all. For those people who are listening and are interested in physics, how necessary is mathematics to understand physics? Yeah, I think that more than
understanding pieces of mathematics, it's important to understand the philosophy of mathematics in terms of how rigorous you have to be and also how creative you have to be and I think that those are things that people don't usually associate with math and so if someone's out there like thinking like I'm not a math person, I wonder if you know that feeling is from like
a misunderstanding about math. And if you enjoy physics, especially if you enjoy physics, I can't really even imagine a person who enjoys physics without enjoying like the sort of fundamental parts of maths as well. Because ultimately, it's about the same things like getting to the why. So how do you structure your day, Mithuna? How, what time do you go to sleep? Because I imagine it's like 10pm or 11pm right there. And what time do you wake up? And how often do you work? And, and do you meditate? Do you have a schedule?
Yeah, I try. So I don't sleep as regularly as I would like. But I try and you know, sleep at 11. Last night, I slept at two. So you know, that happens. I do, I do meditate, I do find that a good way to start the day. And then like, I mean, what kind of meditation? Sort of mindfulness meditation.
And then I have a planner where I write out my goals for the day, you know, things I'm excited about, and then also schedule the day. And yeah, that's my main process. It's not like I schedule every minute of every day because I'm nowhere near an organized person. But I try and vaguely schedule like, what is the most important thing in the day?
And at least like if I can get that one thing done, then I'll feel good about the day. Um, and so, yeah, that's my, that's my like work day. And then, um, in the evening, I like, like to jot down a few little notes about what I'm going to make YouTube videos about. Oh, okay. So you work on YouTube videos each day? Just a little bit. Yeah. So for example, what'd you do today? Um, well, so it's just, it's morning today, but I'm actually planning right now it's the morning. Yeah. It's, it's, uh, 10 AM, I think.
But I am planning to make a video today. So I was going to, after this, write a script out and just try and film the video all in one day, which I've never been able to do before, but I'm going to see if it's possible today. Are you able to give a sneak preview? This will go out in a few days, so I'm not sure when your video will be released. It doesn't matter either way. It's not a secret idea or anything.
I just want to make a video about what research felt like, because I think it's a, an experience that's sort of hard to, hard for other people to understand if they haven't experienced it. And yeah, and this is, yeah, it's like a really strange thing to be doing, like to do math research. It, I was recently talking to another person who had done a math PhD, and we
We talked about like the dread of doing math and I think that that's something that's really hard for someone who hasn't done it to understand, like doing math research. The feeling of is the thing I'm trying to prove even true and will I have any like hope of being able to prove it in the three-year period that I have. Like yeah, the uncertainty is just unreal.
So yeah, I think I want to make a video about how that feels. How do you deal with the negative comments on your YouTube videos if you get any? I don't really get any. I think that's just I've been super lucky because it's still a very niche channel. And so, you know, I generally just have really nice people who are coming to learn something about physics. So they're not the kind of person who would leave a mean comment. So generally, all the comments are really, really lovely.
Do you get emails from people who try to give you their interpretation of quantum mechanics and why? Okay, so how do you deal with that? What is your mindset? Do you just categorize it as spam? Do you respond? Do you actually read it? Um, the thing is, I don't have the, like, time to go through that sort of thing in detail, like, because people often will send me sort of papers that they've read, sorry, papers that they've written. And it's
it's just I don't have like the capacity to be reading everything. But I guess like, yeah, and so it does suck that like, generally, I don't reply. But it, yeah, because like, it's, it's not that I I'm trying to say like, oh, I think that, you know, this is all rubbish or whatever. It's more that like, I'm definitely not the right medium to be sending it to. And like, I'm just one person and I, you know,
get overwhelmed by the amount of emails that I get on this. And the right medium instead is to go through the geoscientific process of getting other people who actually understand this topic, because I'm not even an expert in a lot of the things that people are sending me, to get people like that on board. And then the other thing is that the times that I have tried to engage with people
via like email or like you know I have called like called them set up a call and stuff like that to talk about it. I've found that some people are quite like I found it hard to interact with some of these people like I've had some really bad experiences where people kind of
I find it hard to accept when I say that I think something is not right. And that's very difficult to engage with. So I try to just avoid it these days. They yell at you or they swear or what? Oh, no, no, nothing like that. No, no, no. People are really nice, of course. But usually I'm used to when you're talking about like a scientific idea that
that it's a debate where if you point out a flaw in someone else's argument, they have to properly respond to that flaw. Whereas instead I find like I found the few times where I've tried this that the person like doesn't respond to evidence. And that's like not a way that I'm used to discussing things. I see. I see. I see. Okay. So let's get to your research. Yeah. One of the questions I had is what's a fat shattering dimension
And and did you point that and I didn't I didn't politically correct. Yes, that's that's our indirect dimensions are something from actually, I won't even say that there's something from classical computer science. I'm not I can't remember exactly what context they were originally from. I want to know. I'm not going to I'm not going to say it and get it wrong. But anyway, but but they are like quite a technical definition. But what they really get at is
how flexible a group of functions is. So by that, I mean, like how well would they fit various types of data? If it's just like a line, right? Like if we're just talking about linear functions, they're not very flexible. Only like, you know, very few sets of data would fit a straight line. And so if you're only allowed straight lines to fit data, then you'll find that like mostly you don't do a good job of fitting that data.
But on the other hand, if you suddenly allow yourself like any degree polynomials, they are much more flexible. And so yeah, this fat-shattering dimension is basically trying to like characterize different classes of functions and how flexible they are. Ah, I see. So it assigns them a number as to how flexible they are?
Essentially. Okay, now you're speaking of abstract algebra before. And from what I understand, the poly group is, well, the Clifford group are the, the stabilizer circuits are the normalizers of the poly group. But then from my understanding, a normalizer is it's in reference to two sets. So there's a group like a large group G and then a subset S and then a normalizer would be
Sorry, I'm trying to, I'm trying to find a way to say this. So you take from a normalizer G would be, I'm sure you know, but anyway, it's almost like commuting in a sense. Yeah. Okay. Okay. But so what is the larger set G with respect to this poly group or is the poly group the larger set G and they're missing some subset because they're two as far as I know in a normalizer. Okay. All right. Let me get these definitions straight in my head as well. Okay.
So how I think of the relationship between the poly group and the Clifford group is like you, yeah, one way to put it is in terms of commutation, as you were saying, but another way to think of it is in terms of conjugation. So what that means is if I have a poly operator, so that's like a certain type of matrix,
and I conjugate it, so I multiply it on the left and the right, the one on the right, I take the inverse, then the result is going to be another poly operator. And like if we translate, if we put that back into the language of commuting, what it means is, okay, so like for the audience, the reason why we care about this is because
Poly operators are sort of important quantum gates. So like if you're, if you have a quantum circuit, they're made up of gates. Um, poly operators are important gates and so are Clifford operators. Um, now if you had a, a Clifford operator and then a poly operator, you can switch their order. And what that would do is it would, the, the Clifford gate would stay as it is. Um, it would be the same one, but the poly would become another poly. And that's important because like the,
poly like operators have really nice properties that we want to kind of preserve under conjugation. We can't exactly keep it the same under conjugation because it does change when it becomes when it swaps with a Clifford, but it still stays a poly, which is still nice. And so that's like the reason why things
This is like a really important idea in quantum computing. How does one go about proving that a particular quantum algorithm is efficiently simulable classically? So is this something like you reduce it down to something else that's been proven to be simulable classically? Yeah, good question. So yeah, maybe to give a little context on like why I was interested in that question. You like might have heard that quantum computing is, you know,
better than classical computing. And that's in the sort of like, sense of algorithmic complexity, you know, there's some questions that a quantum computer can solve in polynomial time that a classical computer can, it seems only solve in exponential time. And, but what I was interested in is like, which computations can a quantum computer do better? Like, why? What's like special about that quantum computation? And
how like one of the main methods I used in my thesis to like study this question was this idea of efficient classical simulability. So you have some quantum computations that are efficiently simulable. And what that means is that computation could have been done on a classical computation in a time like in a similar amount of time. Right, the difference is polynomial. Exactly. And so
The way to do that is actually really straightforward. You find the algorithm. So you have this quantum algorithm and then you want to prove that there exists a classical algorithm that is also fast. Just find the algorithm. Find the classical algorithm. Literally write out what you would have to do step by step to simulate this quantum algorithm.
Is there much creativity involved in that? Is it a fairly standard procedure or do you have to think completely outside the box? There's this mathematician, her name is Lisa Piccarello. Have you heard of her? She determined that the Conway knot was a slice.
and it was like this unknown problem for 20 years and then she just worked on it as a grad student and the most the brilliant part of her of her proof was coming up with another knot like she had to come up with some knot and then to prove that it has some property but just coming up with that knot it's not trivial it's a strange knot why would you come up with that so i'm wondering is it the same with coming up with an algorithm
Yeah, going back to that point of what it feels like to do math research, that's the thing. You never know what is going to be the right idea that's going to prove this fact, or even if that fact is true. And so in her case, she probably tried all kinds of things or had some great insight about why this knot was very related.
It was similar with my research, not to compare myself to anything as grand as anything like that, but you don't know where you're going to go and there is no algorithm for finding any of these things. When you're trying to prove something, it is totally a new thing and you have to really get to the core of why it's true to be able to prove it.
Right. I know you said you don't want to compare yourself to doing anything anywhere near as grand as that, but I think that you have a result. And again, I skimmed your paper. So please, if I get it wrong, it seems like you extended the Gottsman-Knell theorem. And that Gottsman-Knell is already a fairly remarkable result, which means yours is groundbreaking. No, it's really not. Absolutely true that the Gottsman-Knell theorem is
I don't know how it's pronounced. I just read it. Yeah, me neither. I always go both ways. Anyway, is, yeah, an absolutely remarkable and like really important theorem in quantum computing. The way we extended it. Yeah, I am very pleased with but like, I don't feel like I should take a lot of credit for that because basically there was another paper that did a lot of the technical work, but didn't necessarily recognize that that
by adding like one extra step on top, it would become an extension of the Gottesman-Nil theorem. And so like we did that. And so the technical work was not that big. It was more the conceptual work of realizing these things were linked. I see. I see. Okay, so Gottesman-Nil. So I've been calling it Gottesman-Nil. Okay, so Gottesman-Nil, that theorem, it says something about the Clifford group and that if you take elements from that and create a circuit, then you'll be able to be efficiently semi-level as well, something like that. Now, what was your extension to it?
Yeah, sure. So the Gozman-Neil theorem says that, like, a very large class, like a surprisingly large class of quantum computers are efficiently classically simulable. And at the time, this was, this was huge, like, this is just really unexpected. Because the class that you're talking about is like, yeah, the Clifford group, and the Clifford group involved, like, a lot of important quantum computations, or like, sort of
things around quantum computation involve the Clifford group. So for example, error correction, and quantum teleportation, super dense coding, all entirely Clifford. And so like this is an important class of quantum computing. And it also is like quite a large class, because there's this other theorem that if you take just like one other random gate, like pretty much with certainty, you will end up with like universal quantum computing. So if you have like Clifford gates, plus just like one other random gate,
basically get the whole thing. And so in a sense, like any random gate, or with high probability, if you randomly choose a gate with high probability, you will get the universal group. So like, in a sense, you're like one step away from being universal by being Clifford. And yet, like being Clifford is entirely classically simulable. Like you can't do any quantum computations that are super fast using the Cliffords.
Despite all of their good properties and despite being like a really big class. And so that's why the Gauss-Menil theorem is like really interesting and something that like I was very interested in because I was interested in like, yeah, what's special about quantum computing? And it's like, it can't be anything that's inside of the Clifford group, even though, even though a lot of very exciting things are there. Like for example, Bell states, which are the maximally entangled states, you can very easily make them with Cliffords. And yet somehow that doesn't contribute to like
quantum speed up, which is weird. So what I was interested in is like, yeah, like, okay, if you add, if you add like another, if you have a circuit that has Clifford's in it, and then you allow yourself, like one other gate from outside of the Clifford group, how much power is that? Is it like entirely the whole thing? Or, or does it matter how many of these you add?
like, let's say there's a like, you've, okay, there's this thing called the T gate, which is like, the sort of canonical extra gate that you add to. Yeah, I had a question about the T gate. Actually, that's bringing up is that this is that a short name for to folly? Or is that like a phase shift of some kind? Yeah, it's a phase shift. It's not the to folly gate. Yeah, so the to folly gate. Yeah. Okay, I just want to know because I read T, but I wasn't sure what T meant. Yes, never from context. Yeah.
Yeah, exactly. So okay, if I was just allowed to add one of those in, is that hard to simulate? Or if I was to add like a polynomial number of those in, like that, that definitely is hard to simulate. But like, what's the in between? Like, you know, where, how does it go from like, if you have zero of them, it's completely classically simulable. If you have a polynomial amount, it's universal. Like, where, where, like, you know, how important is the dependence on t gates? And
If you found a result like, oh, adding one extra T gate makes your thing like hard to simulate, then it would suggest that the Gottesman-Neil theorem is just sort of like a weird coincidence and it's not really that important. Like it's not really saying that like these other gates are like super important. It's just a like weird fact that if you have zero of them that like, you know, it doesn't, that it's easy to simulate. So I wanted to know whether that was the case or if there, if like,
The amount, the difficulty of classical simulation scales with the number of T gates. So as you add more T gates, it gets harder and harder to classically simulate. And that's like what you would suspect if you, like, if you kind of believe the sort of moral, like, interpretation of, of the Goddess Manila theorem. And that's what we basically proved that, like, you, oh, okay, I shouldn't say that, like,
That had been proved. Sorry, I just got to turn my camera back on. All right, all right. It's a DSLR? Yeah. It's recording again? OK, cool. So no, no, I shouldn't say that we proved that. That had been proved that you can classically simulate. The difficulty of classical simulation scales with the number of T gates had been proved. But what we proved was related to that,
If you have a certain number of T gates in your circuit, can you, in a sense, remove out all of the Clifford stuff, which is all the easy bits, and just leave the hard T gates behind? And we showed that that was possible. Which one of your papers are you most proud of? As far as I can see, there are three, at least referenced in your thesis. I'm going to read them out loud. Quantum advantage of unitary Clifford circuits with magic state inputs.
The one clean qubit model without entanglement is classically simulable and a condition under which classical simulability implies efficient state to learn ability. So which one of those do you think is the most significant? I 100% think it's the middle one. It's the one clean qubit model without entanglement is classically simulable. That was the result basically that I started a PhD to get.
I and also the result that I very nearly didn't get despite spending years on it. I maybe spent five years on that that single topic. So yeah, why it was such a big deal is, yeah, this is very interesting hypothesis in quantum computing, that entanglement is the main ingredient of a quantum computer, that somehow it's like
the weird bit of quantum mechanics that like a quantum computer is taking advantage of to get all these speed ups is entanglement. And like, yeah, it's a very sort of dominant, like ideology in quantum computing, despite the fact that like, yeah, there's, it hasn't been proved either way. And, like the evidence for it is like, I would say fairly weak.
evidence that entanglement does have something to do or doesn't have something to do. That it does. Like I'd say it's, I mean, it's not maybe weak is the wrong term. Like, it's just like, it's not a strong case. It's suggestive, but it's not a strong case. So like my supervisor and like his co author a long time ago had proved that if you have no entanglement inside of your quantum computer, like your errorless quantum computer,
then you get something that's classically simulable, which is very suggestive that entanglement is important. But there were some reasons why this may not extend nicely. One is that
that it works when you have zero entanglement but it doesn't work well when you have like a small but not zero amount of entanglement. Like what you would expect is similar to what I was saying about the Gottesman-Neil theorem. You would expect that like as you increase the entanglement it becomes harder and harder to classically simulate. That result has never been shown and in fact probably
I suspect it can't be shown exactly. By the way, when you say it gets harder and harder to show that it gets classically simulated, why is it not just it is classically simulable or not? Why is it that there's a continuum? Yeah, okay. So when we say something's easy to classically simulate, we mean it's polynomial when it's hard, it's exponential. But if the exponential is so like, let's say,
There's some parameter like the amount of entanglement or the number of T gates. There's some parameter like that, um, where the cost of classically simulating this, um, quantum computer scales with that term. So it's like E to the power of that term. Then it suggests that like, as you add more of that thing, it's getting harder and harder. Yeah. Okay.
So your one qubit clean model. Yeah, so the entanglement case hadn't been shown well, even for like what we call pure state quantum computers. And so these are the sort of idealized quantum computers that have no noise in them. But real quantum computers have noise in them.
And you might think, okay, but that's like not sort of mathematically relevant. Like, okay, that's relevant for engineers, but who cares about that from the maths point of view. But actually from the math point of view, these like noisy quantum computers are super, super interesting because they, they have like very different mathematics and like much more complicated and sort of like in a way that the way where like I'm almost skeptical of results that are approved only for pure state quantum computers and not for mixed state quantum computers.
because it feels like that might just be a quirk, whereas the real thing is these noisy things. And so no result like that had been proved for noisy quantum computers. So the result you would want is without any entanglement for a noisy quantum computer, there is no... If you have no entanglement in a noisy quantum computer, you have no quantum advantage. That would be the result that we would love to show is true or false.
And so I had started this project kind of trying to come up with a counter example. I wanted to find a noisy quantum computer that had no entanglement, that still had a quantum advantage. And so there was like a very good candidate. There's something called the one clean qubit model. And it's like really fascinating. Basically, it's a quantum computer that has one qubit that is like clean or pure. And what that really means is we know exactly what state it's in.
Then you have the rest of the qubits in that quantum computer are completely dirty. In other words, we have no idea what they're doing. They could be doing anything.
Um, and usually if you have like a set of just like dirty qubits, you can't do anything with them. Cause like, if you don't know anything and you do something to them, then you still don't know anything. Right. But adding this like one qubit where you do know what's happening, like completely changes this model. So, um, it's like remarkable, but like, yeah, you have this one qubit, you know, and all these qubits where you don't know anything, you do some processing to it, and then you measure something at the end that is actually genuinely useful and can like solve some like
problems that appear to be classically hard to solve. So that's the one clean qubit model. But the thing that was very interesting about it and why it made it a good like candidate for me to study was that there's this result that the one clean qubit and the rest of those noisy qubits never become entangled with each other, despite like throughout the whole computation, which like is very strange because you like, you know, the one clean qubit is clearly somehow the one that's like
giving its quantum power to the rest of the qubits who have no power. So you would expect that if there's communication between those two sets, that it would be via entanglement, if entanglement is important. And so the fact that there's no entanglement is very suggestive that there's something else going on. And so I wanted to study the one clean qubit model where there's no entanglement, not just between those two qubits, the clean qubits and the noisy ones, but within the noisy ones, there's no entanglement within them as well.
So no entanglement across any of the qubits, like none of the qubits were allowed to talk to each other that way. And yeah, what I found was that, like, yeah, we were studying this this topic for a long time. And I was very, very convinced that this quantum computer with no entanglement would have like some quantum advantage, because it was very complicated. And
If it's complicated, it suggests that it's hard to classically simulate, which suggests it's doing something that's like genuinely quantum. Um, but like, yeah, after a few years of working on it, um, it suddenly occurred to me that I could, I could classically simulate it. Like I figured out what the algorithm was and it was a huge process from that point to like actually writing down the algorithm for sure. But, um, but yeah, like it, uh, it really like surprised me cause I thought I was going to prove the opposite thing.
Now do you need to know something about the dirtiness of the rest of the qubits or are they just left as noisy and you don't care about how noisy? Yeah, you actually assume that they're maximally noisy. There's something called magic distillation and I was reading just the Wikipedia article about it and it says okay well here's what you can do you can have an input you prepare five imperfect states then your output is
An almost pure state having a small error probability and then you repeat until the states have been distilled to the desired purity. Okay, then I was wondering, is there something about five? Because it says prepare five imperfect states, or is that just on Wikipedia? There's not something about five. But the reason why they would have said that, I don't remember exactly. But I think that one of the state distillation protocols involves
Have you studied much of quantum logic? No, actually, almost not at all.
Yeah, I don't even know what it's... Either way, maybe you can speculate. I wanted to know, because Gödel's theorem, Gödel's incompleteness theorem, is based in classical logic. And so I'm curious, is there a quantum logic analog? And what does quantum logic have to say about Gödel's incompleteness theorem, essentially? Do you have any thoughts on that? Yeah, I do. So my gut reaction is not much. And the reason for that is this
So there's sort of two levels of computation that are relevant here. There's, there's the level of like, decidability. And so this is like what the halting problem is about, and what goes in completeness theorem is like, you know, in a sense about, and that is like, okay, if you have a mathematical statement, hear that sound,
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computational complexity point of view, which is like, okay, that's the same question, can you decide whether this is true or false? But can you do it in a reasonable, like, so polynomial amount of space and time? And the quantum, like, so the stuff that's proved about like Turing machines and all of that is true, regardless of quantum mechanics, it's true, regardless of like, what your implementation, like mechanism is.
Whereas the computational complexity stuff is where like the quantum versus classical like difference really is. And since like, yeah, Godel's incompleteness theorem is like on that that side of like, sort of purely about decidability, I would, I would, I would suspect that quantum logic doesn't change.
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Does quantum computing have anything to say about the solution or solving potentially the halting problem? No, because
Quantum computer can be classically simulated just inefficiently, right? Like any quantum computation can be simulated by a classical computer. It would just take a long time. And so if you have a quantum computer that can solve the halting problem, then you already have a classical computer that can solve the quantum halting problem. So no, quantum computers say nothing about that. Is there a difference between quantum computers and a probabilistic Turing machine? Yes. So a probabilistic Turing machine is a
Okay, wait, let me just get this right. Yeah. So a probabilistic Turing machine is like the class of problems, the class of decision problems that a probabilistic Turing machine solve is what we call BQP. And there's like a strong suspicion in the like, computing
community that this is equal to P, and P is like this class of problems that you can solve with a Turing machine, like just a regular Turing machine. Whereas quantum computer is stronger, like we suspect, than a probabilistic Turing machine, although there's some like, yeah, I mean, yeah, with sensible definitions, it's definitely stronger. But then the question is, like, is it strictly bigger
like, is it a strictly bigger class, the class of quantum computations than this one, like the classical ones? So do you find that there's any implication for quantum computing or your research in general, and the problem of P equals NP? Or is there no relation? Yeah, no, no, absolutely. So yeah, like, on the question of P equals NP, the fact that P equals NP hasn't been proved has, is, like,
It's like one of the base assumptions of quantum complexity, not quantum, rather computational complexity. And the fact that it hasn't been proved means that like basically nothing else can be proved. So like, for example, are quantum computers better than classical computers? We have lots of evidence to suggest yes, but we can't prove it because if we could prove it, then we would already be able to prove that P doesn't equal NP.
because, well, at least for decision problems, like if we could find a, so there's like, you know, in the decision problem hierarchy, there's this P and then there's like NP, which we think is bigger. But if we could even find one problem that is definitely in NP and not in P, we would, you know, prove that P doesn't equal NP. But for quantum computing to be better than classical computing, we would have to like, and to be able to prove that we'd have to find a problem outside of P,
So prime factorization, that's an NP, correct?
But it is not 100% proved to not be NP. That's the problem. I see. I see. I see. So NP problems have been proved to definitely not be NP. Okay, as far as I know, there's a difference between NP problems and then NP complete problems. Is that okay? So is the prime factorization NP complete or just NP? Just NP. Okay, okay. Yeah, yeah, certainly. It's certainly not complete because we
Don't suspect that quantum computers can solve NP-complete problems. I don't know if you saw it. Maybe you already saw the video. It's Richard E. Borchardt. I might be butchering his name. Anyway, for the people listening, he's coming on this podcast at some point. He's a fields medalist. And he said, here's how my teapot is a better quantum computer. The reason is that it can solve a problem that quantum computers can't.
And then he's like, well, what is the problem? The problem is, how many pieces can this teapot shatter into? Well, this teapot can solve it better than a quantum computer. It's better than any computer. And then he said, well, this is a foolish example, and it's contrived on purpose, because when you hear in the media that quantum computers are better than classical computers, it's like better
on what? It depends on the test. So if you design a test that a quantum computer is efficient at, well, you haven't said that quantum computers are better as a whole. He said it's like giving an intelligence test to an anteater and showing that it's smarter than Einstein because you say that the intelligence test is how many ants can you eat in a minute? It's like, okay, well, you contrived the test to show that this particular... I think that there's one very big flaw in that analogy.
And that is that we can prove that quantum computers can do everything that a classical computer would do. Like everything that a classical computer can do, a quantum computer can do, and we can write that algorithm like straight off the bat. There's nothing difficult about that. What is up in the air is like, is there extra things that a quantum computer can do? So I agree with him that, you know,
those extra things may not be interesting things. And then who cares about quantum computing? But, but like, it's definitely the case that they are better than classical computers. Like that's not the argument. The argument is like, what things can they do? And well, maybe one of the points that he's making is like, one of the main things that we know a quantum computer can do well is it can simulate quantum mechanics. So that's like probably one of the biggest use cases for quantum computers in the future. Like, you know, drugs are like,
like, you know, molecules are basically like quantum machines, and it's the quantum mechanics aspect of them that makes them very hard to simulate classically. Hopefully, you know, quantum computers will be able to do a better job of them. So like, sure, like we are designing our tests to be like a thing that quantum computers can do very well, which is like quantum mechanics. The question is, do we care about like quantum mechanics? What's the Coulkin-Specker theorem? And then what does it have to say about quantum contextuality?
So I usually say Coaching Speckers. I'll say that. Sure, sure. I'm completely getting that wrong. Anyway, so the Coaching Speckers theorem is a very important theorem in quantum foundations. And what it's addressing is like, so you might have heard of hidden variable theorems. It's like a way to get around the weirdness of quantum mechanics.
So it says that, you know, there are no such thing as no such things as super positions, like these these particles are not doing like all possible things at once. Instead, they are in one particular place doing one particular thing. But the way they act is very complicated. Like it can be like determined by a, you know, forces that like take into account all the possible things that they could be doing, for example. Like, so that's how Bohmian mechanics works.
And there was quite a big push in quantum foundations to try and rule these theorems out, which isn't totally possible because, yeah, for example, Bohmian mechanics exists. It exists whether you like it or not. But what the Cauchy-N-Speck theorem tried to do and what other theorems since have tried to do is prove that these hidden variable theorems have undesirable properties.
And so the undesirable property that the Koshin-Specker theorem shows is something called contextuality. So what that means is, if you have a variable, like a thing that the particle is doing that you're interested in, let's say the spin of the particle, so spin like
you you you want to like in in quantum mechanics, you would say that the particle is like a superposition of spin up and spin down. But in invariable theorem, presumably, you'd want to say this particle is spin up, right? And how would you say that? Well, you'd say like, okay, if I measured it now, and it was spin up, then it was spin up before that, right? But what what the Koshien-Specker theorem shows is that actually,
What do you mean you turned the measurement on its head?
Yeah, so like, so this sort of canonical way to measure spin is to get a stone galact machine, which is like has a certain type of magnetic field that kind of points upwards. And if a particle goes upwards, we would say that spin up. But what we could do instead is we could turn it on its head. Now literally turn on its head. And now a particle that goes I'm gonna get this right.
Yeah. So now the same particle, if it was spin up, should go down. And so we would still say that spin up, but like with, but we've measured it differently, right? So it's just the measurement operators, apparatus that is different, but like the, the sort of results should be the same. But what quotient spec has showed is that in fact, if you had that particle that was that like, you know, we're going to measure and you measure it the normal way, it would go spin up. But if you turn the machine on its head,
Now you should expect it to go to spin down, but it would in fact still go spin up. And so that suggests that this property is not a real property of that object. It's a property of the way we measured the object, which is not nice. The response to the Cauchy and Specker theorem, though, in terms of Bohmian mechanics or other hidden variable things is, well, in Bohmian mechanics, spin is not a real property of a particle.
And in fact, no, like none of the kind of variables that you can make from the quotient specter theorem are real variables, like truly considered to be properties of the particle in Bohmian mechanics. They're essentially emergent properties, like in Bohmian mechanics, the real like properties that matter of the particle are its position, essentially, and then you can derive its momentum from that.
So position is the only real variable, everything else is just like emergent. And so the fact that like, yeah, if you measure it this way, it's up. And if you measure it that way, it's down, like, doesn't matter to Bohmian mechanics, because that wasn't a real property that it cared about about the particle anyway. Okay, now this rotating of the Stern-Gerlach apparatus, is that a contrived example? Or is that actually in the Koch and Specker theorem?
So, the Cauchy-Nusbekin theorem is a much more general theorem than that. Well, the reason I'm asking, sorry, the reason I'm asking is because in that example, physics is invariant under rotations, translations, and so on. So, how does the particle even know if you've rotated your apparatus? Oh, because if you rotate the apparatus, you've changed the direction of the magnetic field. Like, that's real. Like, if you rotated the entire universe, then the particle wouldn't be able to tell. But if you rotate a single part within it, yeah. I see, I see. Okay.
The quotient spectrum theorem is like way more general, but this is like one of the scenarios that it would apply to. Why don't you explain what quantum decoherence is and why it either solves or doesn't solve the measurement problem? Oh, that's such a great question. Okay, so decoherence is a like very on the surface mundane thing about quantum mechanics. And it's just the fact that as you
So you have some particle in a superposition, let's say a superposition of spin up and spin down. And then something interacts with it, let's say a photon of light. And the photon of light will act differently if the particle is spin up or if it's spin down. So that light particle will go into a different state depending on which of those two properties it's in. So now in quantum mechanics, we would say that it's entangled
with the original particle, because its state depends on the state of the original particle. So that's like what entanglement is. And so then, okay, like that's all good. But now imagine that that photon just like leaves, and you never see it again, and you will never be able to measure it. But you try and measure your original particle.
Now, if your original particle is in a superposition, normally you'd be able to tell that it's in a superposition. You can do like a double slit experiment on it, something similar, to tell that it is in that superposition. But even though it's still in a superposition, and like nothing has changed from the quantum mechanics point of view, because you haven't got access to that photon, if you do the math, you can show that this particle now acts as if it's collapsed to one of those two states.
like you will not be able to tell the difference between a collapsed particle and what's really happening, which is it's still in a superposition, but a superposition that involves this photon that is now inaccessible. And so that's like, yeah, on the surface a bit mundane, but the implications are really profound because here is a mechanism
by which you can get measurement collapse without measurement collapse like so something that looks and feels to us exactly like measurement collapse like mathematically entirely equivalent and yet all that's happening is normal quantum mechanics and so you can just get rid of that last postulate of quantum mechanics entirely and just replace it with like just just just delete it and you still get the same results sorry when you say you can get rid of the last postulate of quantum mechanics you're referring to
Oh, yes, the the measurement postulate. So the collapse postulate that so like, yeah, there's the thing that's really nasty about quantum mechanics. And like, the, like, I think real problem with quantum mechanics is that there's two systems, there's like, what how quantum quantum objects like act when there is no
measures around and no devices around to measure them. They just like evolve unitarily. It's very nice. But then suddenly, as soon as you add something that you call a measurement device, and like, who knows what that is, you have to have like different rules of physics that are like incompatible, like they just don't work together. And like, this is just untenable mathematically and philosophically, like it's just ugly. Whereas
the whole decoherence thing gives us a way out. What it says is forget about that second regime. Measurements are not real. Measurements are a phenomenological thing that comes from just the regular quantum mechanics. There is never a measurement collapse. Instead, there's only superpositions. But because some parts of those superpositions become inaccessible to you as you add more particles and they all become entangled and then those particles fly off or whatever,
Does this have any implications for the many worlds interpretation? Yes, absolutely. So many worlds, people often take this decoherence as like a sort of important
important ingredient in their theorem. Like many worlds, I would say, is basically take quantum mechanics seriously, forget about the measurement postulate, like it doesn't exist. And so then the question for them is like, okay, but if you don't have the measurement postulate, how do you, how do you, like, explain what happens in the lab, where it seems like, you know, measurement happens and collapse happens, they would just say, well, it's just decoherence. So we didn't need measurement all along.
And I would say that is the many worlds interpretation. I thought the many worlds is about the splitting of the universe because you measure and it collapses into one. But you're saying that, forget about collapsing. It's not. Yeah. Many worlds, I feel like that's a misinterpretation. Many worlds has nothing to do with measurement. What it says is if you have some objects in superposition, they continue to be in superposition. They never collapse to just one state.
So whereas like the standard interpretation says like, okay, let's say I have a particle, it could be spin up, spin down. I measure it and now it becomes spin up and I measure spin up. So there's only one world and that's the world where it was spin up. Whereas what many worlds would say is, okay, you have this particle, it's a position of up and down. You measure it. What that really means is you interact with the particles like lots of other particles with it.
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thought experiment about this called quantum suicide and immortality. Have you heard of it? Okay, so essentially, what I'm wondering is, under the many worlds interpretation, do you not live forever? Because if we define you as the experiencing you, because by definition, you can't experience when you're dead. So why is it that you don't live forever? Because there's no world where, where you get to live forever, right? Like, okay, let's say,
I'm going to think about myself and all of the many superpositions I can go into from this point. So there's many things that could happen to me that put me in superposition, maybe like something to do with weather as a quantum fluctuation. I don't know how that could happen, but like let's just say, you know, it might rain tomorrow because of quantum mechanics or it might not. So there'll be a version of me that experiences the rain and one that doesn't. But in both of those worlds, I will die eventually. Like there's no immortality there.
And like in every sort of possible world that is like dependent on a quantum fluctuation, like I can't see any of those worlds where I become immortal. Is there not a world where your DNA is constantly repaired and the earth and the sun doesn't burn out and so on? So you do live forever? So the laws of physics have to be obeyed in every one of these universes. So the sun will inevitably burn out. Just there.
Unless like there is, I mean, I can't see it, but like, unless there's some way for it to not happen quantum mechanically, but I don't think so. So the sun will burn out in every one of those universes. My DNA repairing is not down to quantum fluctuations. It's down to other, other factors which like couldn't go both ways.
And so like that, that's also not a path to mortality. And how about this? Okay. Methuna is instantly recreated. You're now 18 and perfect health. You're probably already in perfect health, but you're now 18 and there's a, is there not a small, small, small chance of that occurring right now?
Yeah, so I think that this is like no different from
you know, if I like, because anything could sort of spontaneously come into being, right? Like, because because of like, very freak quantum fluctuations. But like, let's say that, you know, you're sitting here, and then, like, on the other side of the universe, the Eiffel Tower just like materializes on some other random planet, right? Now, it's, it's a sort of philosophical question.
whether you count that as the Eiffel Tower, is it the same thing? Right? And so, like, if a version of me just materializes randomly somewhere else in the galaxy, is that me? Well, I wouldn't experience it being me because I only have my continuous experience from this body. So that person, if they materialize with all my memories, of course, will think of themselves as me, but I would think of them as a person distinct from me.
and that there's no sort of contradiction there. And also it doesn't grant me myself any immortality, even if like this keeps happening. Do you think of yourself as the same person when you wake up? Yeah, so this is like, oh, you know, like, deep philosophical questions have been debated for a long time. But yes, I do think of myself as the same person when I wake up and something to do with the continuity of experience or something about
being able to remember, even if it's inaccurately, what it was like to be that person before, makes me feel like the same person. Whereas if there's another version of me, even if they have the same memories as me, and they themselves therefore think of themselves as me, both of us imagine our past as their past, and that is 100% accurate.
I would not associate with that person because that person is not sharing any experiences with me. I'm curious about the implications if the universe is discretized spatially or temporally, does that have any implications for quantum computing? Because I imagine that a large part of the power comes from that there's an infinite amount of intermediate states between zero and one. And so if you can discretize in some manner, then the Bloch sphere is also discretized or is it not?
That's a good question. There's different ways to discretize, right? There's just discreteness in time, in space, and then what you're talking about, which is discreteness in terms of what superpositions are allowed. I can't remember this result off the top of my head, but I have this vague feeling of reading a result that was along the lines of discretizing what superpositions are allowed, and you still get like the regular power of quantum computing.
So I would disagree that the power of quantum computing comes from the continuity. Is there a limit? So for example, like if it's broken up into a thousand different, instead of an infinite amount of superposition, it's a thousand discrete superposition. Yeah, that would certainly be a problem. No, that would definitely be a problem. I was thinking of like, if you discretized it as in like, you don't allow it to be real numbers, but you allow it to be any
I think if you start putting into finite numbers, yeah, that would be a problem. Have you heard of Wolfram's principle of computational equivalence? I'm not sure if I have. Okay, so it's like an extension of the church thesis, church Turing thesis, except he says that all physical phenomena have a computational basis. Okay, do you agree with that? Yeah, that sounds 100%
like, like, I mean, I'm very biased as a person who studied quantum computing. Because like, the reason why quantum computing is interesting to me is because I fundamentally accept that, that everything in the universe is a computation in the sense that a computation is like, you have some objects, and they follow some rules. And that just determines what they're doing at the next time step. And so that, like, to me is exactly what physics is. And so I've like, yeah, no, no, like,
Yeah, to me, that's like definitely true. Okay, great. Okay, now you have some some choice words to say about the Bohmian pilot wave theory. Okay, why do you not particularly like it? Oh, I do particularly like it. Um, so I, I actually think that, um, like, I don't think I believe it. But I think that is a really, really important theory to have in mind.
Because a lot of the things that we want to say about quantum mechanics, or we think is obviously true about quantum mechanics, Bohmian mechanics provides an excellent counterexample for. So it's something to always be keeping in mind when you're talking about the foundations of quantum mechanics. And yeah, I think it's an ingenious theory. I think that it doesn't extend well to relativity, which is why I don't think it's true.
But for just straight up quantum mechanics itself, it is like, yeah, just such a beautiful counterexample to a lot of things people say. Yeah, I heard you say that on the Eichenbrau's podcast that it doesn't extend to, well, you said that it's non-renormalizable, but I wasn't able to find that result. Did you, can you, there's a paper on that, I'm assuming. There are some papers on this, but it's not, it's not that it isn't possible, but that, that it seems, so it is,
probably possible to reproduce the phenomena of special relativity, but not to reproduce the sort of like, underlying beauty of special relativity, which is like relativity, that like, you know, frames of reference don't matter and that sort of thing. There's a paper, a fairly recent paper 2019, this guy named Pinto Neto, and Struve, I don't know if you heard of them? No,
Okay, well they show that with a Bohmian interpretation you can have quantum gravity and in a way that doesn't have the parts of heterotic string theory and supersymmetric string theory and loop quantum, they have some pestiferous parts to them when it comes to quantizing gravity. So what they used is an approach of canonical quantum gravity and apparently when you use a Bohmian interpretation it helps form some
even predictive aspects of quantum cosmology. So that's why I was wondering, why is it non-renormalizable when like, I couldn't find that result. And I heard you say that on the Eigenbrows podcast and I was like, where's, and then they're like, yeah, it is non-renormalizable. I'm like, what? And I searched for this, but I couldn't. Yeah. Okay. So there, I don't know if I said non-renormalizable, but definitely like the thing that I was thinking of was like that, that it is frame dependent.
Um, so it has like a privilege frame of reference, which is quite like not in the spirit of, of relatively, even if it can reproduce the results and, and like, to be fair, like if it can reproduce the results very well, or even like have good, um, predictions about like, you know, where, where all these things are going to go, then, then that is very exciting. And we like, you know, maybe should give up on like the beauty of relativity a little bit if it's going to be useful.
So I'm not like I don't have a strong position on that. But my my like sort of gut feeling was like having not read this paper that you're mentioning, that like if it had to have like a sort of privileged frame of reference, that it would probably make the math of it, like kind of too hard to like be really workable. And so that was why I wasn't a fan of it. Like I didn't feel like it could extend well.
Do you have an opinion that the laws of physics, like, let's say the theory of everything is ultimately beautiful, symmetric, and so on? Or do you, or you're like, be it as it comes? Yeah, no, I like, I mean, I maybe should be one of those people is like, Oh, you know, whatever it is, that's, that's the truth. Um, but like, of course, like my training is in physics and we get this like idea sort of have it into us the whole way along that, that things that are true are beautiful.
Um, and it just so happens to have been the case for so long. And even in mathematics, um, I feel like this is true, that the things that are true are beautiful because, um, like the beauty of it is like us recognizing how like elegant and simple the solution is. Um, and it feels it would just be weird for all this like complexity in the universe to exist without some like
We're going to wrap up, but I have some specific questions for some of the people who are, let's say, in their second year of physics, so they're just taking quantum mechanics, and then some audience questions too. Okay, so Miles Ignotis says, I'd like to know her thoughts on cubism. Yeah.
Okay, so this is like a really great question. And it is something that I've been wanting to like learn more about to actually make a video about and just just generally know more about for myself. But I don't know enough. But my sort of gut reaction to it is like, I just feel uncomfortable with physical theories that put
that really privilege the observer and privilege the observer's knowledge about the universe and kind of almost suggest the universe doesn't exist without us processing the knowledge. And like again, this is very much my bias, like coming from physics where it's all about like sort of objectiveness and like humans being removed from the, like humans kind of stumbling onto the universe and like trying to understand it as it is rather than creating the universe in our own minds. So this is my gut reaction against cubism.
But I think that there's like a lot of interesting mathematics that has been derived by cubism that like is definitely worth looking into and something that I really want to do. Just Us Perths, I don't know if I'm pronouncing that correctly, says, how can a person who is self-studying deal with gaps in knowledge? When I get stuck on a new concept, I'm often unsure what exactly it is that's preventing me from understanding it, i.e. I don't know what I'm missing and what I need to study in order to get it.
This is really tough. I had the same problem many times when studying myself. In some ways, being a beginner and getting stuck in these ways is a real privilege. I know this sounds really weird to say, but being a beginner and recognizing what you don't know
is a state that you can like almost not get back into. In fact, I think that one of the reasons I like teaching beginners is because then I have to put myself in that mindset. And like, yeah, so being able to recognize what you don't know is like really, really valuable. And as you go on, you'll basically like plaster over the bits that you don't actually understand. So definitely like try and recognize what you don't understand. And when you get to that situation,
Like if you can like look for sort of, you know, introductory textbooks or some material like that and understand it from that, that's great. But if it doesn't solve your problem, like keep that as a question mark, like, you know, keep it as like, okay, I still don't understand this bit. I'm going to keep this as a question. I don't know the answer. I'll move on. Like I'll read some other things either like, you know, tangentially, or I'll just go on in whatever I'm reading.
But as I read, like if something answers that question for me, I'll come back. I imagine that as you're doing your PhD, you don't have the time to go through the books and solve all the problems. And I know that solving the problems helps your understanding greatly. But because you have to cover such a vast amount of research so quickly, that means that you have to have a superficial understanding of so much. But then you have to know what is it okay for me to have a superficial understanding of so that I can
pretty much with a hop, skip and a jump, go to the, go to where I need to be. So how do you get, how do you balance that, that tight rope of, of having tenuous knowledge and strengthen deep knowledge? Okay. Yeah. So, um, during my PhD, the thing I was just saying about the benefit of being a beginner, I tried to really take that to heart.
Um, so when there was a topic I didn't know, I mostly avoided it only like kind of knowing it superficially from talks that I would go to just enough to kind of like understand what the vague, like what the problem was in that, in that area and like what they were trying to solve. But I would like purposely not really jump into it. And then I would like take various topics, like new topics that I didn't know. So, so one of them was like conamara correction.
like I'd heard about it in a lot of talks, and I knew what the problem was. I'd never dived into it. So then I took some time to specifically go and read all the introductory material on that, and like really dive into it. Because I feel like there isn't that much benefit of having like a more than superficial knowledge of, of certain topics of physics. Whereas there's a huge amount of benefit to being an absolute beginner, and like really, really diving into a topic.
Because like, yeah, I remember one of the examples that comes to mind is like, I tried to learn about fermions and bosons in the context of computing. Because there was like a bunch of really interesting results about like boson sampling and fermionic linear optics. And I wanted to like, like I knew about them, but I wanted to go back to the basics. Like I want to understand what is a fermion? What is a boson? What have they got to do on computing? And so like,
I really, really, really went back to the absolute basics, spent ages on it. And I remember giving this presentation to my group and a few other people who were there who were basically experts in the topic of how this relates to computing. And I was talking about something super basic. But even so, I felt like there were some parts where I knew stuff
better and like I'd been able to make some connections that I think weren't as clear if you um uh like you know like again not not as the like the experts obviously knew more but the people who were like fairly well versed in it I feel like there were some points in which I like knew more than them just from like really diving into like but what does this mean and where do I have uncertainty and just like keep going until you really get some get to the bottom of it.
Yeah, and when you're doing this process of diving in and finding out where your holes are, are you taking a blank sheet of paper and writing out almost like the Feynman method? I'm sure you've heard where you teach yourself or you pretend there's a third person hear that sound.
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Yeah, so what I do is I collect like, so in this case, it was papers, I collected a whole bunch of papers, but you know, it could be books. I never read through a book, like front to back. Like I never sort of want to get something from just one source.
Instead, I'll read one source, kind of get like something from it. Like maybe I'll read the introduction, and then I'll kind of write down what I think I know. And then I'll go into another source and see if that kind of like gels well. They might be using different notation, they might be looking at it from a slightly different perspective. Your fans, your photographer fans. Yeah, okay. So yeah, I'll never read
I'll never read anything front to back. Instead, I'll read a lot of different things with different perspectives. And as I go, I'll be keeping a whole lot of notes where I'm basically trying to explain it to myself. I'll be like, a fermion is, and then I'll write one definition. And then in the other source, it'll have an entirely different but equivalent definition.
And I'll like, like, I'll read that they don't reference each other, they don't talk about how they're related to each other. So then I have to like, you know, in my writing, like figure out how is this thing that they said the same as what they said, just in a different language. And so like the translation process is really interesting. And like, I'll learn a lot from that. Then like, yeah, just just like, kind of like keeping many sources
in mind as I'm writing these notes that are like how would I explain this to someone else is very useful. Do you find that books are most helpful or do you watch lectures online? I almost never watch lectures online. I think it's mostly an attention thing. I actually kind of find it hard to watch video and a lot easier to read but what I feel what I find lectures better for than textbooks is to get
opinion from the person. Like opinions during talks are so useful, you get the sort of sense of like, what this person thinks is the interesting parts of this field, or like, what are the real mysteries according to this person. Whereas I feel like books are, you know, a lot more long winded in their introduction. So it's harder to get that feel of like the person's opinion. But then I think books are better for like diving in.
I'm going to just read this one verbatim. So how is it specifically that the mathematical notion of an observable as an operator corresponds to a physical device? So what you're doing is you're manipulating symbols in the abstract, and it's not clear how it corresponds to what's going on experimentally. Now, that's something that when you're in second, third, even fourth, you don't get, unless you take experimental physics, you don't get an understanding of. So what the heck does it mean that the operator is
position operators x in the or the derivative if it's momentum is onto how does that correspond to what's going on when you observe in the lab? Yeah, yeah, this is a great question. No, this is a great question. And it confused me for a long time. And, and we kind of realized, much later that there is no good science to the way that we make the operators. In fact, there's a lot of art to it. What we usually do is we so like, okay, to make an operator for a
measurement, you've got to consider what, what are you like, physically doing? So you know, in the Stern-Gerlach experiment, we're actually physically applying a magnetic field, ultimately, that's what we're doing. And whatever measurement you're doing, you're ultimately physically doing something. And you've got to write down like, what are the, so the Hamiltonian, which is essentially like, what are the forces that you're, you're, you're
creating in this measurement device. And then you write that down classically. And then you just do the sort of like, cheap trick of quantization, where you take like the, the quantum like, so the classical version of a certain object, like the magnetic field, and then you make it a quantum operator, and then you're like, Okay, just do that. And there we go. That's my quantum operator for this, this measurement, whatever I'm doing. So it's not that satisfying.
What's the operator for determining the charge of an electron or its mass if operators correspond to observables? Yeah, so this one is not an observable. The reason is because you couldn't observe a electron to be in a different, to have a different mass or charge. On the other hand, now that I say that, you could come up with a
How do operators look in terms of experiments? Now, can one design an experiment and work backward to find the operator? Yeah, that's what you do. You've got to look at the experiment, look at what forces you're applying, and then write those out, do quantization, that will get you the operator pretty much.
Three more questions. Ryan Conlin says, when you study, how much time do you spend thinking about your own particular background knowledge and skills that is relating it to previous knowledge versus how much time do you spend? Do you spend thinking about it without relating? Oh, super interesting question. Actually, I find it's really, really useful to relate it to your own background knowledge, at least for me during the PhD. I think maybe that's partly a quirk of the PhD where like you you're studying, but you also want to be able to add something new to the knowledge.
like the knowledge base. And so going from the angle of like, how can I relate this to the particular quirky things that I know, is like a good way to sort of start making new things. But just generally, I think it's like really a good strategy when you're studying to, you know, you've learned some new concept, let's say you've just learned what a group is, and in abstract algebra, and
If you can find like some examples that are related to things you've learned. So for example, if you related that to the symmetries in relativity, because you've just learned about relativity, that will make it way more concrete and way easier for you to understand. So I think that is actually a really important thing that's like super neglected by students. So yeah, great question.
At the same time, I can see how sometimes trying to relate it back can be counterproductive. For example, in quantum mechanics, they say, just forget what you know, that's going to hold you back. So at what point do you abandon versus relate? I think that's the thing on quantum mechanics. I think that's not true. Like, if you're learning quantum mechanics, mathematically, like you're trying to understand the math is extremely important to
Michael McGuffin says, what has she been reading recently?
And then also part two is like if her financial incomes were met, say she's given $10 million, what would you spend your time doing? Books and then time? Okay, cool. Thank you for those questions. So what am I reading? I'm reading a few things. I recently finished a book by the the director of Pixar, creativity, Inc. And it was about how to create
like a creative product in in a corporation, which like often kind of stifle creativity. So how do you keep that alive? That was super interesting. On a sort of similar vein, a friend of mine recommended the idea factory. And that was about Bell Labs. So Bell Labs is like quite famous for having invented a whole bunch of like, really ahead of their times, devices. And it was a similar deal to Pixar in a way where
like they managed to come up with like a corporate environment, because it was a corporation, it wasn't a university or anything, a corporate environment that somehow could still stimulate creativity, and in this case in science. So yeah, I think that's like a really interesting topic to me, like something that I'm really interested in about, like it's just just innovation in general, but how do you, how do you foster it? And then like, I guess if someone was to give me $10 million,
There are a bunch of projects that I'm interested in. I'm very keen on understanding what the future of education is going to be. I think that there needs to be even more research. I mean, there's lots of great research at the moment, but even more research and even more focus put into how can we really change the way that
humans learn so that they are really achieving their maximum human potential. I think that schools are really wonderful, and I'm not one of those people who is advocating for just ripping it all down. But I think that they're inefficient in certain ways. They just have to be because of how they were made and because of all the various pressures that are on schools. So I would love to understand, if we were going to make it from scratch, what would we keep, but what would we change?
Have you heard of Peter Gray's unschooling?
I'm blanking. Can you essentially it's not like tear down the schools. But what I'm saying is that the that kids is taking an evolutionary psychological approach to learning that kids learn best in mixed age groups. And one of the reasons is that there's no bullying because you're eight, you're not going to compete with a 16 year old, and you're not vice versa. And then 16 year old is not going to compete with a 24 year old. And he takes this from observing tribes that don't have schools. And the kids just learn automatically because play is so important. And when they're playing, they just
They happen to learn and it's spontaneous and you allow the kid to follow their own interests and you encourage it. Yeah. That of imposing one. Yeah. So I think this, this whole movement of inquiry based learning is very, very interesting, but also I think we have to be a little careful with it. I I'm, I'm definitely for,
kids being able to like figure out what they like themselves and just like go down that rabbit hole like that's you know a big part of like my education was that but I think on the other hand like letting kids have completely free rein I mean there has been some research about this like it just doesn't work as well if you have like no sort of either discipline or like guidance about where to go
you know, you're not going to expect a child playing on their own to rediscover Mutian's laws, like that's just not possible. But on the other hand, if you had like a supervising figure who was there to like encourage the, you know, the interests as they as they develop and sees that, you know, this person's interested in how things work and it's like, oh, have you read these interesting books? Like that could potentially work. I think that to make that work, we need to put like a lot more thought into
just how like we can guide that experience without, you know, fully determining what the kid is going to do ourselves. Beer's Attitude says, it would be cool to know her opinion on Donald Hoffman's work. What is the most fundamental level in her opinion? I don't know what that last sentence means. What does she make of consciousness? So I don't know if you've heard of Donald Hoffman and his theories on consciousness, but this person would like to know. Yeah. Okay. Oh, that's, that's disappointing because the person's like, Oh, thank you, dude.
Sorry. Wait, who is this? Donald Hoffman is a cognitive scientist. He's a cognitive scientist who says that what we can do is model conscious agents with something like a Markov kernel where you just have, let's say, the set of experiences. You don't even give them names like love or whatever. You just give them whatever you like and then give them some structure like, well, you can read his papers.
And then he says that what you can do from there is develop the laws of quantum mechanics. Now, I'm skeptical of that. And I read his research. But it's something like, it's so general. You've heard of these claims where it's like, yeah, I can derive quantum mechanics. But I derived it from something so general that it's, well, I'd be surprised if you couldn't derive quantum mechanics from that. Fair enough. But either way, Donald Hoffman is a bright, bright, bright, bright individual. Yeah, sorry I couldn't answer that question. That's all right. That's all right. And I also realized that I have a question on quantum, the quantum parallel thesis. I wanted to know,
I imagine that you think it's true given that you adopt the many worlds interpretation, but I was wondering what are some ways that the quantum parallel thesis could be true without the many worlds interpretation? What do you mean by the quantum parallel thesis? Quantum parallel thesis is that the, it's something like that the computation is being performed simultaneously on the superpositions.
Okay, have you heard of the quantum parallel thesis? Yeah, like a doish's. Yes. Yeah, that's correct. That's correct. That's correct. Yeah. Um, yeah. Uh, I think what I don't understand about that idea, um, and what makes me skeptical of it is that it's not clear how computation from distinct branches of the superposition can be, be transferred, like how that information can be transferred.
So let's say you want to do a huge number of computations, so you split into many different worlds, and then you do one of the computations in each one of these worlds. Then you have the result in each of these worlds. So let's say you're looking for a one, and world number three has found a one, and it needs to communicate now to all the rest of them. The way that that communication is done inside of quantum computing
It depends on those superpositions not being distinct worlds in the sort of many world sense. So in the many world sense, like any superposition is not a different world. It only becomes like a different world once it interacts with other things and therefore can't interact with itself anymore. So if you have a superposition of two things,
those sort of worlds can kind of like split in a sense, and they become distinct from each other. But if they don't interact with anything else, they can kind of reconvene. So one way that this could happen is like, if you have a spin particle, you start it in spin up, and then you change the magnetic field, so it becomes spin up, spin down, and then you change the magnetic field back and so it's been up again.
a way you've deleted the superposition but this is like this is totally fine and this is what happens in quantum computing but in many worlds you wouldn't say that that was like two worlds and they recombined for many worlds the worlds can't recombine for them to be like worlds
I have a quote here about the many worlds interpretation. This is hardly the most economical view, the most economical of viewpoints, but my own personal objections don't spring from its lack of economy. And in particular, I don't see why conscious being need be aware of only one of the alternatives in a linear superposition. What is it about consciousness that demands that one cannot be aware of the tantalizing linear combination of being both dead and alive?
It seems to me that a theory of consciousness will be needed before the many worlds viewed can be squared with what one actually observes. So what do you say to that? Yeah, I think that that is an understandable objection, but I think like an objection that is met by the mathematics. So what I mean is, okay, let's say you have a object that's in a superposition in many worlds, like so it's in two different worlds.
It can only experience like, so let's say it's not a conscious thing. It's just a, let's say an atom. Um, it can only experience all of the other objects in its world in that, in the state that they are in that world. So like in this state, like, so let's say in this world, all of the objects are in state zero and in that world, they're all in state one. If you take one of the atoms inside of here and you get it to measure one of its partners, it will say that its partner is zero.
or here, if you've got it to measure its partner, it would say it's one. It can only experience that world, like with all of the things that are in that world as they are like, you know, in that state. And so let's say now I'm a conscious being and I'm inside of like both of these branches. I've just done a measurement of my, of my atom and my atom is now like in state zero, according to in this branch and in state one, according to that branch.
If I was to, if I was able to experience both, then I should be able to see the atom being in state zero and in state one. But because of how many worlds works, how the mathematics works out, there is no measurement that I can do inside of this world that would show me the result one, it would only say zero. And in that world, I would only say one. And so there's no like, I don't experience the other world to me, it just doesn't exist. There's no evidence of it anywhere. So of course I don't consciously experience it.
Oh, so now that there's no evidence of it anywhere, what is the reason for you believing in it? Oh, so there's evidence, there's all the evidence that I could possibly want that I'm in the world where everything is in state zero. I'm sorry, I meant, I meant, why does Mithuna, Mithuna, sorry, believe in the many worlds interpretation? To me, it seems like a religious choice, because there's not evidence for it unless you just say, well, the math says. Exactly. So no, um,
It's back to that question of like, do I want a theory of the universe to be beautiful or not? My bias is very much towards beauty. And I think that many worlds is a much more beautiful theorem, theory rather.
And that's because it has less assumptions. So in a statement there, oh, many worlds is less economical. In one sense, yes, if you're like counting worlds, but I think that's not the sort of important sense of like, you know, how economical a theory is, how economical it is, is like, how many sort of distinct ad hoc rules does it have? And many worlds deletes the ad hoc rule that quantum mechanics has. And therefore, I think it is a more economical, more beautiful theory. That's why I believe it.
Thank you so much. Thank you so much. So what's next for you? After this next YouTube video? Yeah, well, so the thing I've been thinking the most about is how to improve online education. I think that that's like a really, like
Interesting and new medium. People on YouTube have done really wonderful things, but I think we can push it even further. So yeah, that's the direction I hope to put myself. And it's sad that I'm not doing physics research. I miss it. But I feel like this is higher impact. I feel like the world needs this more than the small bit of physics that I could have contributed. So are you more driven by that altruistic
part of you or the passion part of you that just wants to do research? Yeah, um, I think that, um, yeah, like I really am passionate about physics research. And so it was like a super hard decision, but because, um, education will impact like way more people. And also because it is still a very interesting thing to research. Um, ultimately like both of those things combined made it a pretty good choice.
Thank you so much for spending so much time with me and putting up with my sleepy questions. Oh, good. I'm sorry for catching up. Oh, no, no, no, no. No, it's all right. It's all right. I just for weeks and weeks, like weeks, I haven't been getting enough sleep. And so it just compiles and compiles. Yeah. Yeah. And then I've been studying some quantum computing to prep for this. Oh, no. Thanks so much. Well, I'm just going to ask this.
Yeah, yeah, no problem, no problem. There's so many other somewhat technical questions I had like about zx calculus. And I was wondering about the relationship between graph states and the spider diagrams. Oh my gosh. Is there a way of... I know that graph states... See, the way that I understand graph states are like, in particle physics, there's the Feynman diagrams, and then there's rules to translate those to equations. It looks like graph states have a simple rule.
And then I was wondering, is there a way to go from graph states to ZX spiders? Yeah, well, anyway, I'm just, I'm curious, is there? Yeah. Um, I don't actually know. Like they have different uses, I'm sure. But as far as I know from my depthless understanding of quantum computing, they're just representations of the circuits. So I don't, so I don't see why one is more advantageous than the other or why they can't be easily translated to one another.
Yeah, that's a good question. Yeah, that is a very good question. And I genuinely don't know the answer to that. Yeah. Okay. Okay. Well, anyway, whatever. Anyway, well, no, thank you so much for this interview. Thank you. Thank you.
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"text": " But do you know what's not okay? Not knowing how effective your birth control is. Talk to your doctor about effective birth control options so you can make an informed decision. Tap to learn more. All right, hello Toll listeners, Kurt here. That silence is missed sales. Now, why? It's because you haven't met Shopify, at least until now."
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"text": " Now that's success. As sweet as a solved equation. Join me in trading that silence for success with Shopify. It's like some unified field theory of business. Whether you're a bedroom inventor or a global game changer, Shopify smooths your path. From a garage-based hobby to a bustling e-store, Shopify navigates all sales channels for you. With Shopify powering 10% of all US e-commerce and fueling your ventures in over"
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"text": " Self-learning mathematics in particular quantum field theories connection to the monster group and general problem solving Apologies for any tiredness on display during this podcast as it was it was the end of a towering day of studying and fasting If you'd like to see more conversations like this, especially those that explore math physics philosophy and consciousness at a relatively high technical level then please consider supporting at patreon.com"
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"text": " Thank you. Welcome, Mithana. I appreciate it. Thank you for having me. Congratulations on your doctorate, by the way."
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"text": " Thank you. Yeah, like I have technically just finished up, but I finished writing about a year ago. So it's good to finally be done with the paperwork. You run a channel called Looking Glass Universe. What are some of the aspects of that that you enjoy the most and what are some of the more detrimental aspects? Good question. So I really enjoy teaching something that I think I know."
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"text": " Oh my gosh, so many things. Um, but like just, just as a whole, like, uh, something that I, like the reason I started this channel is because I had done some undergrad classes in quantum mechanics. Um, yeah, and like done well in them. And I just was like, Oh, well, you know, I understand this topic and people like to learn about quantum mechanics. So I may as well make some videos explaining what I know. So that's what I thought this channel would be about. But as soon as I started writing those videos,"
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"text": " I realized like, oh, I don't know what a superposition is, like, I don't actually know, you know, philosophically what this wave function thing is. And I realized it's basically everything I thought I knew, I had no idea about. And so I ended up doing a bunch of research on myself by myself, like I took six months off, was just like reading quantum mechanics books. And then I realized like, there's so much more to this than I thought from undergrad."
},
{
"end_time": 444.121,
"index": 18,
"start_time": 419.957,
"text": " And that's what led me to the PhD, to kind of like solve some of those problems. You took six months off just to do research? Yeah, basically it just went for my own, like off as in I was doing part-time work to pay for that. But I, yeah, like basically those six months were devoted to just researching things on my own a little bit more."
},
{
"end_time": 467.005,
"index": 19,
"start_time": 445.043,
"text": " You know part of when I run this channel, I'm curious if you feel the same I wonder how is it that people understand the concepts that they do without having to explain it to someone else because part of the understanding comes from trying to apprehend it from another point of view and explain it simply or explain it from from some other position and I'm"
},
{
"end_time": 488.575,
"index": 20,
"start_time": 467.278,
"text": " And there's an advantage to having a YouTube channel. So some people think like you're just wasting your time because it takes quite a bit of time to between the understanding and then actually putting out a video. But at the same time, I wonder how is it that other people understand what they do? You know, teaching has sort of been recognized as a very good way to build understanding yourself for a long time. But"
},
{
"end_time": 517.858,
"index": 21,
"start_time": 489.121,
"text": " The YouTube medium I feel is really special because you have to try and explain it in a way that someone who may not have the background can understand as well. And that means you have to rely on way less assumptions. And the assumptions are often where your misunderstandings or where your not complete understandings are. What's your process of learning something new in math or physics like? Do you just go to the Wikipedia page first? Do you go to the Stanford Encyclopedia?"
},
{
"end_time": 531.544,
"index": 22,
"start_time": 518.148,
"text": " Great questions. It depends a lot on the topic. If it's something in quantum mechanics now, I'll just go to the papers."
},
{
"end_time": 561.596,
"index": 23,
"start_time": 531.937,
"text": " read the papers. And then when I don't understand things, then I'll go to something like Wikipedia, or more likely it will be some like textbooks that I trust. And like if they have a section on it, then I'll trust that that section. So for example, if it's something in quantum computing, or even sort of related to quantum information, then I will check whether it's in Nielsen and Truong. If it's there, like that's the Bible, I'll just read it from that. But otherwise, like, yeah, it's sort of, yeah, I'll read stuff, just"
},
{
"end_time": 590.725,
"index": 24,
"start_time": 561.937,
"text": " and then Google the bits that I don't understand. Did you ever feel like math or physics wasn't for you? Oh yeah, 100%. I definitely didn't think I would end up in math or physics, as math especially, but even physics. So when I was in high school, I was quite like an artsy kid. You know, I enjoyed like literature classes and I really loved painting and I thought I wanted to be a graphic designer. And then"
},
{
"end_time": 620.794,
"index": 25,
"start_time": 591.374,
"text": " I took a physics class about cosmology at some point and was just blown away by it, completely fell in love, was certain that I was going to be a physicist. But even so, I was still really, really bad at math. So I was doing well at physics at the same time that I was basically failing math and like in the lowest grade for lowest band basically in Australia for math. And like I kept"
},
{
"end_time": 648.387,
"index": 26,
"start_time": 621.135,
"text": " at it and I decided to put myself into some really hard math classes just because I knew I needed it for physics. But I didn't think of myself as a math person at all until university where, yeah in the first year I was doing math classes and I was doing fairly okay in them and you know that was all good but they weren't like the hardest math classes. But in the second year I just like happened to enroll myself in like a fairly abstract like mathematical course"
},
{
"end_time": 671.698,
"index": 27,
"start_time": 648.712,
"text": " and just loved it so much. Functional analysis? It wasn't functional analysis. I did really love that functional analysis, but my step in was abstract algebra. So yeah, and like, it was really cool because like, you know, I remember one of the first things we were trying to prove was like, you know, zero plus zero equals zero. And, and like,"
},
{
"end_time": 699.906,
"index": 28,
"start_time": 672.108,
"text": " Getting back to the basics and understanding why things are true is like what I really loved about physics. And it's the same thing that I could love about math. And that was an aspect of math that I hadn't seen in school. And so that's why I thought I was not a math person, because I thought math was just about like following some algorithms to like get to an answer. That's not that's not it at all. For those people who are listening and are interested in physics, how necessary is mathematics to understand physics? Yeah, I think that more than"
},
{
"end_time": 728.131,
"index": 29,
"start_time": 700.316,
"text": " understanding pieces of mathematics, it's important to understand the philosophy of mathematics in terms of how rigorous you have to be and also how creative you have to be and I think that those are things that people don't usually associate with math and so if someone's out there like thinking like I'm not a math person, I wonder if you know that feeling is from like"
},
{
"end_time": 756.613,
"index": 30,
"start_time": 728.387,
"text": " a misunderstanding about math. And if you enjoy physics, especially if you enjoy physics, I can't really even imagine a person who enjoys physics without enjoying like the sort of fundamental parts of maths as well. Because ultimately, it's about the same things like getting to the why. So how do you structure your day, Mithuna? How, what time do you go to sleep? Because I imagine it's like 10pm or 11pm right there. And what time do you wake up? And how often do you work? And, and do you meditate? Do you have a schedule?"
},
{
"end_time": 782.039,
"index": 31,
"start_time": 757.21,
"text": " Yeah, I try. So I don't sleep as regularly as I would like. But I try and you know, sleep at 11. Last night, I slept at two. So you know, that happens. I do, I do meditate, I do find that a good way to start the day. And then like, I mean, what kind of meditation? Sort of mindfulness meditation."
},
{
"end_time": 808.387,
"index": 32,
"start_time": 783.729,
"text": " And then I have a planner where I write out my goals for the day, you know, things I'm excited about, and then also schedule the day. And yeah, that's my main process. It's not like I schedule every minute of every day because I'm nowhere near an organized person. But I try and vaguely schedule like, what is the most important thing in the day?"
},
{
"end_time": 838.541,
"index": 33,
"start_time": 808.677,
"text": " And at least like if I can get that one thing done, then I'll feel good about the day. Um, and so, yeah, that's my, that's my like work day. And then, um, in the evening, I like, like to jot down a few little notes about what I'm going to make YouTube videos about. Oh, okay. So you work on YouTube videos each day? Just a little bit. Yeah. So for example, what'd you do today? Um, well, so it's just, it's morning today, but I'm actually planning right now it's the morning. Yeah. It's, it's, uh, 10 AM, I think."
},
{
"end_time": 867.722,
"index": 34,
"start_time": 838.985,
"text": " But I am planning to make a video today. So I was going to, after this, write a script out and just try and film the video all in one day, which I've never been able to do before, but I'm going to see if it's possible today. Are you able to give a sneak preview? This will go out in a few days, so I'm not sure when your video will be released. It doesn't matter either way. It's not a secret idea or anything."
},
{
"end_time": 896.101,
"index": 35,
"start_time": 867.961,
"text": " I just want to make a video about what research felt like, because I think it's a, an experience that's sort of hard to, hard for other people to understand if they haven't experienced it. And yeah, and this is, yeah, it's like a really strange thing to be doing, like to do math research. It, I was recently talking to another person who had done a math PhD, and we"
},
{
"end_time": 924.616,
"index": 36,
"start_time": 897.21,
"text": " We talked about like the dread of doing math and I think that that's something that's really hard for someone who hasn't done it to understand, like doing math research. The feeling of is the thing I'm trying to prove even true and will I have any like hope of being able to prove it in the three-year period that I have. Like yeah, the uncertainty is just unreal."
},
{
"end_time": 951.288,
"index": 37,
"start_time": 925.009,
"text": " So yeah, I think I want to make a video about how that feels. How do you deal with the negative comments on your YouTube videos if you get any? I don't really get any. I think that's just I've been super lucky because it's still a very niche channel. And so, you know, I generally just have really nice people who are coming to learn something about physics. So they're not the kind of person who would leave a mean comment. So generally, all the comments are really, really lovely."
},
{
"end_time": 979.753,
"index": 38,
"start_time": 951.732,
"text": " Do you get emails from people who try to give you their interpretation of quantum mechanics and why? Okay, so how do you deal with that? What is your mindset? Do you just categorize it as spam? Do you respond? Do you actually read it? Um, the thing is, I don't have the, like, time to go through that sort of thing in detail, like, because people often will send me sort of papers that they've read, sorry, papers that they've written. And it's"
},
{
"end_time": 1007.807,
"index": 39,
"start_time": 980.128,
"text": " it's just I don't have like the capacity to be reading everything. But I guess like, yeah, and so it does suck that like, generally, I don't reply. But it, yeah, because like, it's, it's not that I I'm trying to say like, oh, I think that, you know, this is all rubbish or whatever. It's more that like, I'm definitely not the right medium to be sending it to. And like, I'm just one person and I, you know,"
},
{
"end_time": 1037.363,
"index": 40,
"start_time": 1008.148,
"text": " get overwhelmed by the amount of emails that I get on this. And the right medium instead is to go through the geoscientific process of getting other people who actually understand this topic, because I'm not even an expert in a lot of the things that people are sending me, to get people like that on board. And then the other thing is that the times that I have tried to engage with people"
},
{
"end_time": 1067.227,
"index": 41,
"start_time": 1037.995,
"text": " via like email or like you know I have called like called them set up a call and stuff like that to talk about it. I've found that some people are quite like I found it hard to interact with some of these people like I've had some really bad experiences where people kind of"
},
{
"end_time": 1093.899,
"index": 42,
"start_time": 1069.889,
"text": " I find it hard to accept when I say that I think something is not right. And that's very difficult to engage with. So I try to just avoid it these days. They yell at you or they swear or what? Oh, no, no, nothing like that. No, no, no. People are really nice, of course. But usually I'm used to when you're talking about like a scientific idea that"
},
{
"end_time": 1122.756,
"index": 43,
"start_time": 1094.104,
"text": " that it's a debate where if you point out a flaw in someone else's argument, they have to properly respond to that flaw. Whereas instead I find like I found the few times where I've tried this that the person like doesn't respond to evidence. And that's like not a way that I'm used to discussing things. I see. I see. I see. Okay. So let's get to your research. Yeah. One of the questions I had is what's a fat shattering dimension"
},
{
"end_time": 1153.541,
"index": 44,
"start_time": 1123.626,
"text": " And and did you point that and I didn't I didn't politically correct. Yes, that's that's our indirect dimensions are something from actually, I won't even say that there's something from classical computer science. I'm not I can't remember exactly what context they were originally from. I want to know. I'm not going to I'm not going to say it and get it wrong. But anyway, but but they are like quite a technical definition. But what they really get at is"
},
{
"end_time": 1183.797,
"index": 45,
"start_time": 1153.882,
"text": " how flexible a group of functions is. So by that, I mean, like how well would they fit various types of data? If it's just like a line, right? Like if we're just talking about linear functions, they're not very flexible. Only like, you know, very few sets of data would fit a straight line. And so if you're only allowed straight lines to fit data, then you'll find that like mostly you don't do a good job of fitting that data."
},
{
"end_time": 1204.258,
"index": 46,
"start_time": 1184.206,
"text": " But on the other hand, if you suddenly allow yourself like any degree polynomials, they are much more flexible. And so yeah, this fat-shattering dimension is basically trying to like characterize different classes of functions and how flexible they are. Ah, I see. So it assigns them a number as to how flexible they are?"
},
{
"end_time": 1233.985,
"index": 47,
"start_time": 1205.316,
"text": " Essentially. Okay, now you're speaking of abstract algebra before. And from what I understand, the poly group is, well, the Clifford group are the, the stabilizer circuits are the normalizers of the poly group. But then from my understanding, a normalizer is it's in reference to two sets. So there's a group like a large group G and then a subset S and then a normalizer would be"
},
{
"end_time": 1262.841,
"index": 48,
"start_time": 1235.896,
"text": " Sorry, I'm trying to, I'm trying to find a way to say this. So you take from a normalizer G would be, I'm sure you know, but anyway, it's almost like commuting in a sense. Yeah. Okay. Okay. But so what is the larger set G with respect to this poly group or is the poly group the larger set G and they're missing some subset because they're two as far as I know in a normalizer. Okay. All right. Let me get these definitions straight in my head as well. Okay."
},
{
"end_time": 1287.108,
"index": 49,
"start_time": 1263.114,
"text": " So how I think of the relationship between the poly group and the Clifford group is like you, yeah, one way to put it is in terms of commutation, as you were saying, but another way to think of it is in terms of conjugation. So what that means is if I have a poly operator, so that's like a certain type of matrix,"
},
{
"end_time": 1313.473,
"index": 50,
"start_time": 1287.91,
"text": " and I conjugate it, so I multiply it on the left and the right, the one on the right, I take the inverse, then the result is going to be another poly operator. And like if we translate, if we put that back into the language of commuting, what it means is, okay, so like for the audience, the reason why we care about this is because"
},
{
"end_time": 1342.466,
"index": 51,
"start_time": 1313.899,
"text": " Poly operators are sort of important quantum gates. So like if you're, if you have a quantum circuit, they're made up of gates. Um, poly operators are important gates and so are Clifford operators. Um, now if you had a, a Clifford operator and then a poly operator, you can switch their order. And what that would do is it would, the, the Clifford gate would stay as it is. Um, it would be the same one, but the poly would become another poly. And that's important because like the,"
},
{
"end_time": 1362.21,
"index": 52,
"start_time": 1342.756,
"text": " poly like operators have really nice properties that we want to kind of preserve under conjugation. We can't exactly keep it the same under conjugation because it does change when it becomes when it swaps with a Clifford, but it still stays a poly, which is still nice. And so that's like the reason why things"
},
{
"end_time": 1389.582,
"index": 53,
"start_time": 1362.449,
"text": " This is like a really important idea in quantum computing. How does one go about proving that a particular quantum algorithm is efficiently simulable classically? So is this something like you reduce it down to something else that's been proven to be simulable classically? Yeah, good question. So yeah, maybe to give a little context on like why I was interested in that question. You like might have heard that quantum computing is, you know,"
},
{
"end_time": 1419.599,
"index": 54,
"start_time": 1389.753,
"text": " better than classical computing. And that's in the sort of like, sense of algorithmic complexity, you know, there's some questions that a quantum computer can solve in polynomial time that a classical computer can, it seems only solve in exponential time. And, but what I was interested in is like, which computations can a quantum computer do better? Like, why? What's like special about that quantum computation? And"
},
{
"end_time": 1446.391,
"index": 55,
"start_time": 1420.452,
"text": " how like one of the main methods I used in my thesis to like study this question was this idea of efficient classical simulability. So you have some quantum computations that are efficiently simulable. And what that means is that computation could have been done on a classical computation in a time like in a similar amount of time. Right, the difference is polynomial. Exactly. And so"
},
{
"end_time": 1467.227,
"index": 56,
"start_time": 1446.852,
"text": " The way to do that is actually really straightforward. You find the algorithm. So you have this quantum algorithm and then you want to prove that there exists a classical algorithm that is also fast. Just find the algorithm. Find the classical algorithm. Literally write out what you would have to do step by step to simulate this quantum algorithm."
},
{
"end_time": 1486.459,
"index": 57,
"start_time": 1467.346,
"text": " Is there much creativity involved in that? Is it a fairly standard procedure or do you have to think completely outside the box? There's this mathematician, her name is Lisa Piccarello. Have you heard of her? She determined that the Conway knot was a slice."
},
{
"end_time": 1511.783,
"index": 58,
"start_time": 1486.459,
"text": " and it was like this unknown problem for 20 years and then she just worked on it as a grad student and the most the brilliant part of her of her proof was coming up with another knot like she had to come up with some knot and then to prove that it has some property but just coming up with that knot it's not trivial it's a strange knot why would you come up with that so i'm wondering is it the same with coming up with an algorithm"
},
{
"end_time": 1536.527,
"index": 59,
"start_time": 1512.056,
"text": " Yeah, going back to that point of what it feels like to do math research, that's the thing. You never know what is going to be the right idea that's going to prove this fact, or even if that fact is true. And so in her case, she probably tried all kinds of things or had some great insight about why this knot was very related."
},
{
"end_time": 1560.708,
"index": 60,
"start_time": 1536.664,
"text": " It was similar with my research, not to compare myself to anything as grand as anything like that, but you don't know where you're going to go and there is no algorithm for finding any of these things. When you're trying to prove something, it is totally a new thing and you have to really get to the core of why it's true to be able to prove it."
},
{
"end_time": 1584.906,
"index": 61,
"start_time": 1561.323,
"text": " Right. I know you said you don't want to compare yourself to doing anything anywhere near as grand as that, but I think that you have a result. And again, I skimmed your paper. So please, if I get it wrong, it seems like you extended the Gottsman-Knell theorem. And that Gottsman-Knell is already a fairly remarkable result, which means yours is groundbreaking. No, it's really not. Absolutely true that the Gottsman-Knell theorem is"
},
{
"end_time": 1614.991,
"index": 62,
"start_time": 1585.162,
"text": " I don't know how it's pronounced. I just read it. Yeah, me neither. I always go both ways. Anyway, is, yeah, an absolutely remarkable and like really important theorem in quantum computing. The way we extended it. Yeah, I am very pleased with but like, I don't feel like I should take a lot of credit for that because basically there was another paper that did a lot of the technical work, but didn't necessarily recognize that that"
},
{
"end_time": 1644.053,
"index": 63,
"start_time": 1615.35,
"text": " by adding like one extra step on top, it would become an extension of the Gottesman-Nil theorem. And so like we did that. And so the technical work was not that big. It was more the conceptual work of realizing these things were linked. I see. I see. Okay, so Gottesman-Nil. So I've been calling it Gottesman-Nil. Okay, so Gottesman-Nil, that theorem, it says something about the Clifford group and that if you take elements from that and create a circuit, then you'll be able to be efficiently semi-level as well, something like that. Now, what was your extension to it?"
},
{
"end_time": 1672.534,
"index": 64,
"start_time": 1644.326,
"text": " Yeah, sure. So the Gozman-Neil theorem says that, like, a very large class, like a surprisingly large class of quantum computers are efficiently classically simulable. And at the time, this was, this was huge, like, this is just really unexpected. Because the class that you're talking about is like, yeah, the Clifford group, and the Clifford group involved, like, a lot of important quantum computations, or like, sort of"
},
{
"end_time": 1703.148,
"index": 65,
"start_time": 1673.2,
"text": " things around quantum computation involve the Clifford group. So for example, error correction, and quantum teleportation, super dense coding, all entirely Clifford. And so like this is an important class of quantum computing. And it also is like quite a large class, because there's this other theorem that if you take just like one other random gate, like pretty much with certainty, you will end up with like universal quantum computing. So if you have like Clifford gates, plus just like one other random gate,"
},
{
"end_time": 1731.869,
"index": 66,
"start_time": 1703.353,
"text": " basically get the whole thing. And so in a sense, like any random gate, or with high probability, if you randomly choose a gate with high probability, you will get the universal group. So like, in a sense, you're like one step away from being universal by being Clifford. And yet, like being Clifford is entirely classically simulable. Like you can't do any quantum computations that are super fast using the Cliffords."
},
{
"end_time": 1758.933,
"index": 67,
"start_time": 1732.329,
"text": " Despite all of their good properties and despite being like a really big class. And so that's why the Gauss-Menil theorem is like really interesting and something that like I was very interested in because I was interested in like, yeah, what's special about quantum computing? And it's like, it can't be anything that's inside of the Clifford group, even though, even though a lot of very exciting things are there. Like for example, Bell states, which are the maximally entangled states, you can very easily make them with Cliffords. And yet somehow that doesn't contribute to like"
},
{
"end_time": 1787.637,
"index": 68,
"start_time": 1759.104,
"text": " quantum speed up, which is weird. So what I was interested in is like, yeah, like, okay, if you add, if you add like another, if you have a circuit that has Clifford's in it, and then you allow yourself, like one other gate from outside of the Clifford group, how much power is that? Is it like entirely the whole thing? Or, or does it matter how many of these you add?"
},
{
"end_time": 1816.237,
"index": 69,
"start_time": 1787.824,
"text": " like, let's say there's a like, you've, okay, there's this thing called the T gate, which is like, the sort of canonical extra gate that you add to. Yeah, I had a question about the T gate. Actually, that's bringing up is that this is that a short name for to folly? Or is that like a phase shift of some kind? Yeah, it's a phase shift. It's not the to folly gate. Yeah, so the to folly gate. Yeah. Okay, I just want to know because I read T, but I wasn't sure what T meant. Yes, never from context. Yeah."
},
{
"end_time": 1845.606,
"index": 70,
"start_time": 1817.346,
"text": " Yeah, exactly. So okay, if I was just allowed to add one of those in, is that hard to simulate? Or if I was to add like a polynomial number of those in, like that, that definitely is hard to simulate. But like, what's the in between? Like, you know, where, how does it go from like, if you have zero of them, it's completely classically simulable. If you have a polynomial amount, it's universal. Like, where, where, like, you know, how important is the dependence on t gates? And"
},
{
"end_time": 1874.787,
"index": 71,
"start_time": 1845.811,
"text": " If you found a result like, oh, adding one extra T gate makes your thing like hard to simulate, then it would suggest that the Gottesman-Neil theorem is just sort of like a weird coincidence and it's not really that important. Like it's not really saying that like these other gates are like super important. It's just a like weird fact that if you have zero of them that like, you know, it doesn't, that it's easy to simulate. So I wanted to know whether that was the case or if there, if like,"
},
{
"end_time": 1902.739,
"index": 72,
"start_time": 1875.196,
"text": " The amount, the difficulty of classical simulation scales with the number of T gates. So as you add more T gates, it gets harder and harder to classically simulate. And that's like what you would suspect if you, like, if you kind of believe the sort of moral, like, interpretation of, of the Goddess Manila theorem. And that's what we basically proved that, like, you, oh, okay, I shouldn't say that, like,"
},
{
"end_time": 1930.247,
"index": 73,
"start_time": 1903.592,
"text": " That had been proved. Sorry, I just got to turn my camera back on. All right, all right. It's a DSLR? Yeah. It's recording again? OK, cool. So no, no, I shouldn't say that we proved that. That had been proved that you can classically simulate. The difficulty of classical simulation scales with the number of T gates had been proved. But what we proved was related to that,"
},
{
"end_time": 1959.155,
"index": 74,
"start_time": 1930.52,
"text": " If you have a certain number of T gates in your circuit, can you, in a sense, remove out all of the Clifford stuff, which is all the easy bits, and just leave the hard T gates behind? And we showed that that was possible. Which one of your papers are you most proud of? As far as I can see, there are three, at least referenced in your thesis. I'm going to read them out loud. Quantum advantage of unitary Clifford circuits with magic state inputs."
},
{
"end_time": 1989.531,
"index": 75,
"start_time": 1959.531,
"text": " The one clean qubit model without entanglement is classically simulable and a condition under which classical simulability implies efficient state to learn ability. So which one of those do you think is the most significant? I 100% think it's the middle one. It's the one clean qubit model without entanglement is classically simulable. That was the result basically that I started a PhD to get."
},
{
"end_time": 2015.828,
"index": 76,
"start_time": 1989.974,
"text": " I and also the result that I very nearly didn't get despite spending years on it. I maybe spent five years on that that single topic. So yeah, why it was such a big deal is, yeah, this is very interesting hypothesis in quantum computing, that entanglement is the main ingredient of a quantum computer, that somehow it's like"
},
{
"end_time": 2041.681,
"index": 77,
"start_time": 2016.937,
"text": " the weird bit of quantum mechanics that like a quantum computer is taking advantage of to get all these speed ups is entanglement. And like, yeah, it's a very sort of dominant, like ideology in quantum computing, despite the fact that like, yeah, there's, it hasn't been proved either way. And, like the evidence for it is like, I would say fairly weak."
},
{
"end_time": 2072.159,
"index": 78,
"start_time": 2042.176,
"text": " evidence that entanglement does have something to do or doesn't have something to do. That it does. Like I'd say it's, I mean, it's not maybe weak is the wrong term. Like, it's just like, it's not a strong case. It's suggestive, but it's not a strong case. So like my supervisor and like his co author a long time ago had proved that if you have no entanglement inside of your quantum computer, like your errorless quantum computer,"
},
{
"end_time": 2090.401,
"index": 79,
"start_time": 2072.517,
"text": " then you get something that's classically simulable, which is very suggestive that entanglement is important. But there were some reasons why this may not extend nicely. One is that"
},
{
"end_time": 2112.602,
"index": 80,
"start_time": 2091.527,
"text": " that it works when you have zero entanglement but it doesn't work well when you have like a small but not zero amount of entanglement. Like what you would expect is similar to what I was saying about the Gottesman-Neil theorem. You would expect that like as you increase the entanglement it becomes harder and harder to classically simulate. That result has never been shown and in fact probably"
},
{
"end_time": 2138.08,
"index": 81,
"start_time": 2113.575,
"text": " I suspect it can't be shown exactly. By the way, when you say it gets harder and harder to show that it gets classically simulated, why is it not just it is classically simulable or not? Why is it that there's a continuum? Yeah, okay. So when we say something's easy to classically simulate, we mean it's polynomial when it's hard, it's exponential. But if the exponential is so like, let's say,"
},
{
"end_time": 2160.828,
"index": 82,
"start_time": 2138.507,
"text": " There's some parameter like the amount of entanglement or the number of T gates. There's some parameter like that, um, where the cost of classically simulating this, um, quantum computer scales with that term. So it's like E to the power of that term. Then it suggests that like, as you add more of that thing, it's getting harder and harder. Yeah. Okay."
},
{
"end_time": 2183.729,
"index": 83,
"start_time": 2161.049,
"text": " So your one qubit clean model. Yeah, so the entanglement case hadn't been shown well, even for like what we call pure state quantum computers. And so these are the sort of idealized quantum computers that have no noise in them. But real quantum computers have noise in them."
},
{
"end_time": 2212.125,
"index": 84,
"start_time": 2184.07,
"text": " And you might think, okay, but that's like not sort of mathematically relevant. Like, okay, that's relevant for engineers, but who cares about that from the maths point of view. But actually from the math point of view, these like noisy quantum computers are super, super interesting because they, they have like very different mathematics and like much more complicated and sort of like in a way that the way where like I'm almost skeptical of results that are approved only for pure state quantum computers and not for mixed state quantum computers."
},
{
"end_time": 2238.814,
"index": 85,
"start_time": 2212.432,
"text": " because it feels like that might just be a quirk, whereas the real thing is these noisy things. And so no result like that had been proved for noisy quantum computers. So the result you would want is without any entanglement for a noisy quantum computer, there is no... If you have no entanglement in a noisy quantum computer, you have no quantum advantage. That would be the result that we would love to show is true or false."
},
{
"end_time": 2268.814,
"index": 86,
"start_time": 2239.224,
"text": " And so I had started this project kind of trying to come up with a counter example. I wanted to find a noisy quantum computer that had no entanglement, that still had a quantum advantage. And so there was like a very good candidate. There's something called the one clean qubit model. And it's like really fascinating. Basically, it's a quantum computer that has one qubit that is like clean or pure. And what that really means is we know exactly what state it's in."
},
{
"end_time": 2278.08,
"index": 87,
"start_time": 2269.189,
"text": " Then you have the rest of the qubits in that quantum computer are completely dirty. In other words, we have no idea what they're doing. They could be doing anything."
},
{
"end_time": 2306.323,
"index": 88,
"start_time": 2278.729,
"text": " Um, and usually if you have like a set of just like dirty qubits, you can't do anything with them. Cause like, if you don't know anything and you do something to them, then you still don't know anything. Right. But adding this like one qubit where you do know what's happening, like completely changes this model. So, um, it's like remarkable, but like, yeah, you have this one qubit, you know, and all these qubits where you don't know anything, you do some processing to it, and then you measure something at the end that is actually genuinely useful and can like solve some like"
},
{
"end_time": 2334.275,
"index": 89,
"start_time": 2306.749,
"text": " problems that appear to be classically hard to solve. So that's the one clean qubit model. But the thing that was very interesting about it and why it made it a good like candidate for me to study was that there's this result that the one clean qubit and the rest of those noisy qubits never become entangled with each other, despite like throughout the whole computation, which like is very strange because you like, you know, the one clean qubit is clearly somehow the one that's like"
},
{
"end_time": 2364.514,
"index": 90,
"start_time": 2335.009,
"text": " giving its quantum power to the rest of the qubits who have no power. So you would expect that if there's communication between those two sets, that it would be via entanglement, if entanglement is important. And so the fact that there's no entanglement is very suggestive that there's something else going on. And so I wanted to study the one clean qubit model where there's no entanglement, not just between those two qubits, the clean qubits and the noisy ones, but within the noisy ones, there's no entanglement within them as well."
},
{
"end_time": 2391.22,
"index": 91,
"start_time": 2365.179,
"text": " So no entanglement across any of the qubits, like none of the qubits were allowed to talk to each other that way. And yeah, what I found was that, like, yeah, we were studying this this topic for a long time. And I was very, very convinced that this quantum computer with no entanglement would have like some quantum advantage, because it was very complicated. And"
},
{
"end_time": 2421.34,
"index": 92,
"start_time": 2391.51,
"text": " If it's complicated, it suggests that it's hard to classically simulate, which suggests it's doing something that's like genuinely quantum. Um, but like, yeah, after a few years of working on it, um, it suddenly occurred to me that I could, I could classically simulate it. Like I figured out what the algorithm was and it was a huge process from that point to like actually writing down the algorithm for sure. But, um, but yeah, like it, uh, it really like surprised me cause I thought I was going to prove the opposite thing."
},
{
"end_time": 2451.544,
"index": 93,
"start_time": 2421.783,
"text": " Now do you need to know something about the dirtiness of the rest of the qubits or are they just left as noisy and you don't care about how noisy? Yeah, you actually assume that they're maximally noisy. There's something called magic distillation and I was reading just the Wikipedia article about it and it says okay well here's what you can do you can have an input you prepare five imperfect states then your output is"
},
{
"end_time": 2481.681,
"index": 94,
"start_time": 2451.988,
"text": " An almost pure state having a small error probability and then you repeat until the states have been distilled to the desired purity. Okay, then I was wondering, is there something about five? Because it says prepare five imperfect states, or is that just on Wikipedia? There's not something about five. But the reason why they would have said that, I don't remember exactly. But I think that one of the state distillation protocols involves"
},
{
"end_time": 2503.251,
"index": 95,
"start_time": 2482.619,
"text": " Have you studied much of quantum logic? No, actually, almost not at all."
},
{
"end_time": 2533.439,
"index": 96,
"start_time": 2503.712,
"text": " Yeah, I don't even know what it's... Either way, maybe you can speculate. I wanted to know, because Gödel's theorem, Gödel's incompleteness theorem, is based in classical logic. And so I'm curious, is there a quantum logic analog? And what does quantum logic have to say about Gödel's incompleteness theorem, essentially? Do you have any thoughts on that? Yeah, I do. So my gut reaction is not much. And the reason for that is this"
},
{
"end_time": 2561.118,
"index": 97,
"start_time": 2533.797,
"text": " So there's sort of two levels of computation that are relevant here. There's, there's the level of like, decidability. And so this is like what the halting problem is about, and what goes in completeness theorem is like, you know, in a sense about, and that is like, okay, if you have a mathematical statement, hear that sound,"
},
{
"end_time": 2588.166,
"index": 98,
"start_time": 2562.073,
"text": " That's the sweet sound of success with Shopify. Shopify is the all-encompassing commerce platform that's with you from the first flicker of an idea to the moment you realize you're running a global enterprise. Whether it's handcrafted jewelry or high-tech gadgets, Shopify supports you at every point of sale, both online and in person. They streamline the process with the internet's best converting checkout, making it 36% more effective than other leading platforms."
},
{
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"start_time": 2588.166,
"text": " There's also something called Shopify Magic, your AI-powered assistant that's like an all-star team member working tirelessly behind the scenes. What I find fascinating about Shopify is how it scales with your ambition. No matter how big you want to grow, Shopify gives you everything you need to take control and take your business to the next level. Join the ranks of businesses in 175 countries that have made Shopify the backbone."
},
{
"end_time": 2640.043,
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"start_time": 2614.258,
"text": " of their commerce. Shopify, by the way, powers 10% of all e-commerce in the United States, including huge names like Allbirds, Rothy's, and Brooklynin. If you ever need help, their award-winning support is like having a mentor that's just a click away. Now, are you ready to start your own success story? Sign up for a $1 per month trial period at shopify.com slash theories, all lowercase."
},
{
"end_time": 2663.592,
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"text": " Go to Shopify.com slash theories now to grow your business no matter what stage you're in Shopify.com slash theories. Can you decide whether it's true or false? Right? And like this is sort of like given an infinite amount of time and resources. And then there's like the sort of"
},
{
"end_time": 2691.22,
"index": 102,
"start_time": 2664.019,
"text": " computational complexity point of view, which is like, okay, that's the same question, can you decide whether this is true or false? But can you do it in a reasonable, like, so polynomial amount of space and time? And the quantum, like, so the stuff that's proved about like Turing machines and all of that is true, regardless of quantum mechanics, it's true, regardless of like, what your implementation, like mechanism is."
},
{
"end_time": 2712.91,
"index": 103,
"start_time": 2691.493,
"text": " Whereas the computational complexity stuff is where like the quantum versus classical like difference really is. And since like, yeah, Godel's incompleteness theorem is like on that that side of like, sort of purely about decidability, I would, I would, I would suspect that quantum logic doesn't change."
},
{
"end_time": 2732.329,
"index": 104,
"start_time": 2714.531,
"text": " Razor blades are like diving boards. The longer the board, the more the wobble, the more the wobble, the more nicks, cuts, scrapes. A bad shave isn't a blade problem, it's an extension problem. Henson is a family-owned aerospace parts manufacturer that's made parts for the International Space Station and the Mars Rover."
},
{
"end_time": 2754.155,
"index": 105,
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"text": " Now they're bringing that precision engineering to your shaving experience. By using aerospace-grade CNC machines, Henson makes razors that extend less than the thickness of a human hair. The razor also has built-in channels that evacuates hair and cream, which make clogging virtually impossible. Henson Shaving wants to produce the best razors, not the best razor business,"
},
{
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"text": " So that means no plastics, no subscriptions, no proprietary blades and no planned obsolescence. It's also extremely affordable. The Henson razor works with the standard dual edge blades that give you that old school shave with the benefits of this new school tech. It's time to say no to subscriptions and yes to a razor that'll last you a lifetime."
},
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"end_time": 2803.319,
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"start_time": 2774.172,
"text": " Does quantum computing have anything to say about the solution or solving potentially the halting problem? No, because"
},
{
"end_time": 2832.654,
"index": 108,
"start_time": 2803.507,
"text": " Quantum computer can be classically simulated just inefficiently, right? Like any quantum computation can be simulated by a classical computer. It would just take a long time. And so if you have a quantum computer that can solve the halting problem, then you already have a classical computer that can solve the quantum halting problem. So no, quantum computers say nothing about that. Is there a difference between quantum computers and a probabilistic Turing machine? Yes. So a probabilistic Turing machine is a"
},
{
"end_time": 2857.295,
"index": 109,
"start_time": 2832.944,
"text": " Okay, wait, let me just get this right. Yeah. So a probabilistic Turing machine is like the class of problems, the class of decision problems that a probabilistic Turing machine solve is what we call BQP. And there's like a strong suspicion in the like, computing"
},
{
"end_time": 2884.787,
"index": 110,
"start_time": 2857.432,
"text": " community that this is equal to P, and P is like this class of problems that you can solve with a Turing machine, like just a regular Turing machine. Whereas quantum computer is stronger, like we suspect, than a probabilistic Turing machine, although there's some like, yeah, I mean, yeah, with sensible definitions, it's definitely stronger. But then the question is, like, is it strictly bigger"
},
{
"end_time": 2915.162,
"index": 111,
"start_time": 2885.282,
"text": " like, is it a strictly bigger class, the class of quantum computations than this one, like the classical ones? So do you find that there's any implication for quantum computing or your research in general, and the problem of P equals NP? Or is there no relation? Yeah, no, no, absolutely. So yeah, like, on the question of P equals NP, the fact that P equals NP hasn't been proved has, is, like,"
},
{
"end_time": 2944.974,
"index": 112,
"start_time": 2917.346,
"text": " It's like one of the base assumptions of quantum complexity, not quantum, rather computational complexity. And the fact that it hasn't been proved means that like basically nothing else can be proved. So like, for example, are quantum computers better than classical computers? We have lots of evidence to suggest yes, but we can't prove it because if we could prove it, then we would already be able to prove that P doesn't equal NP."
},
{
"end_time": 2973.49,
"index": 113,
"start_time": 2945.196,
"text": " because, well, at least for decision problems, like if we could find a, so there's like, you know, in the decision problem hierarchy, there's this P and then there's like NP, which we think is bigger. But if we could even find one problem that is definitely in NP and not in P, we would, you know, prove that P doesn't equal NP. But for quantum computing to be better than classical computing, we would have to like, and to be able to prove that we'd have to find a problem outside of P,"
},
{
"end_time": 3002.79,
"index": 114,
"start_time": 2973.78,
"text": " So prime factorization, that's an NP, correct?"
},
{
"end_time": 3030.094,
"index": 115,
"start_time": 3002.944,
"text": " But it is not 100% proved to not be NP. That's the problem. I see. I see. I see. So NP problems have been proved to definitely not be NP. Okay, as far as I know, there's a difference between NP problems and then NP complete problems. Is that okay? So is the prime factorization NP complete or just NP? Just NP. Okay, okay. Yeah, yeah, certainly. It's certainly not complete because we"
},
{
"end_time": 3056.135,
"index": 116,
"start_time": 3030.162,
"text": " Don't suspect that quantum computers can solve NP-complete problems. I don't know if you saw it. Maybe you already saw the video. It's Richard E. Borchardt. I might be butchering his name. Anyway, for the people listening, he's coming on this podcast at some point. He's a fields medalist. And he said, here's how my teapot is a better quantum computer. The reason is that it can solve a problem that quantum computers can't."
},
{
"end_time": 3075.913,
"index": 117,
"start_time": 3056.408,
"text": " And then he's like, well, what is the problem? The problem is, how many pieces can this teapot shatter into? Well, this teapot can solve it better than a quantum computer. It's better than any computer. And then he said, well, this is a foolish example, and it's contrived on purpose, because when you hear in the media that quantum computers are better than classical computers, it's like better"
},
{
"end_time": 3104.804,
"index": 118,
"start_time": 3076.323,
"text": " on what? It depends on the test. So if you design a test that a quantum computer is efficient at, well, you haven't said that quantum computers are better as a whole. He said it's like giving an intelligence test to an anteater and showing that it's smarter than Einstein because you say that the intelligence test is how many ants can you eat in a minute? It's like, okay, well, you contrived the test to show that this particular... I think that there's one very big flaw in that analogy."
},
{
"end_time": 3128.114,
"index": 119,
"start_time": 3105.282,
"text": " And that is that we can prove that quantum computers can do everything that a classical computer would do. Like everything that a classical computer can do, a quantum computer can do, and we can write that algorithm like straight off the bat. There's nothing difficult about that. What is up in the air is like, is there extra things that a quantum computer can do? So I agree with him that, you know,"
},
{
"end_time": 3156.032,
"index": 120,
"start_time": 3128.353,
"text": " those extra things may not be interesting things. And then who cares about quantum computing? But, but like, it's definitely the case that they are better than classical computers. Like that's not the argument. The argument is like, what things can they do? And well, maybe one of the points that he's making is like, one of the main things that we know a quantum computer can do well is it can simulate quantum mechanics. So that's like probably one of the biggest use cases for quantum computers in the future. Like, you know, drugs are like,"
},
{
"end_time": 3183.968,
"index": 121,
"start_time": 3156.323,
"text": " like, you know, molecules are basically like quantum machines, and it's the quantum mechanics aspect of them that makes them very hard to simulate classically. Hopefully, you know, quantum computers will be able to do a better job of them. So like, sure, like we are designing our tests to be like a thing that quantum computers can do very well, which is like quantum mechanics. The question is, do we care about like quantum mechanics? What's the Coulkin-Specker theorem? And then what does it have to say about quantum contextuality?"
},
{
"end_time": 3211.067,
"index": 122,
"start_time": 3184.701,
"text": " So I usually say Coaching Speckers. I'll say that. Sure, sure. I'm completely getting that wrong. Anyway, so the Coaching Speckers theorem is a very important theorem in quantum foundations. And what it's addressing is like, so you might have heard of hidden variable theorems. It's like a way to get around the weirdness of quantum mechanics."
},
{
"end_time": 3240.213,
"index": 123,
"start_time": 3211.391,
"text": " So it says that, you know, there are no such thing as no such things as super positions, like these these particles are not doing like all possible things at once. Instead, they are in one particular place doing one particular thing. But the way they act is very complicated. Like it can be like determined by a, you know, forces that like take into account all the possible things that they could be doing, for example. Like, so that's how Bohmian mechanics works."
},
{
"end_time": 3267.312,
"index": 124,
"start_time": 3240.538,
"text": " And there was quite a big push in quantum foundations to try and rule these theorems out, which isn't totally possible because, yeah, for example, Bohmian mechanics exists. It exists whether you like it or not. But what the Cauchy-N-Speck theorem tried to do and what other theorems since have tried to do is prove that these hidden variable theorems have undesirable properties."
},
{
"end_time": 3287.841,
"index": 125,
"start_time": 3267.79,
"text": " And so the undesirable property that the Koshin-Specker theorem shows is something called contextuality. So what that means is, if you have a variable, like a thing that the particle is doing that you're interested in, let's say the spin of the particle, so spin like"
},
{
"end_time": 3314.838,
"index": 126,
"start_time": 3288.029,
"text": " you you you want to like in in quantum mechanics, you would say that the particle is like a superposition of spin up and spin down. But in invariable theorem, presumably, you'd want to say this particle is spin up, right? And how would you say that? Well, you'd say like, okay, if I measured it now, and it was spin up, then it was spin up before that, right? But what what the Koshien-Specker theorem shows is that actually,"
},
{
"end_time": 3338.114,
"index": 127,
"start_time": 3315.196,
"text": " What do you mean you turned the measurement on its head?"
},
{
"end_time": 3364.582,
"index": 128,
"start_time": 3338.609,
"text": " Yeah, so like, so this sort of canonical way to measure spin is to get a stone galact machine, which is like has a certain type of magnetic field that kind of points upwards. And if a particle goes upwards, we would say that spin up. But what we could do instead is we could turn it on its head. Now literally turn on its head. And now a particle that goes I'm gonna get this right."
},
{
"end_time": 3393.916,
"index": 129,
"start_time": 3365.503,
"text": " Yeah. So now the same particle, if it was spin up, should go down. And so we would still say that spin up, but like with, but we've measured it differently, right? So it's just the measurement operators, apparatus that is different, but like the, the sort of results should be the same. But what quotient spec has showed is that in fact, if you had that particle that was that like, you know, we're going to measure and you measure it the normal way, it would go spin up. But if you turn the machine on its head,"
},
{
"end_time": 3424.087,
"index": 130,
"start_time": 3394.138,
"text": " Now you should expect it to go to spin down, but it would in fact still go spin up. And so that suggests that this property is not a real property of that object. It's a property of the way we measured the object, which is not nice. The response to the Cauchy and Specker theorem, though, in terms of Bohmian mechanics or other hidden variable things is, well, in Bohmian mechanics, spin is not a real property of a particle."
},
{
"end_time": 3447.363,
"index": 131,
"start_time": 3424.428,
"text": " And in fact, no, like none of the kind of variables that you can make from the quotient specter theorem are real variables, like truly considered to be properties of the particle in Bohmian mechanics. They're essentially emergent properties, like in Bohmian mechanics, the real like properties that matter of the particle are its position, essentially, and then you can derive its momentum from that."
},
{
"end_time": 3469.77,
"index": 132,
"start_time": 3447.654,
"text": " So position is the only real variable, everything else is just like emergent. And so the fact that like, yeah, if you measure it this way, it's up. And if you measure it that way, it's down, like, doesn't matter to Bohmian mechanics, because that wasn't a real property that it cared about about the particle anyway. Okay, now this rotating of the Stern-Gerlach apparatus, is that a contrived example? Or is that actually in the Koch and Specker theorem?"
},
{
"end_time": 3497.79,
"index": 133,
"start_time": 3470.299,
"text": " So, the Cauchy-Nusbekin theorem is a much more general theorem than that. Well, the reason I'm asking, sorry, the reason I'm asking is because in that example, physics is invariant under rotations, translations, and so on. So, how does the particle even know if you've rotated your apparatus? Oh, because if you rotate the apparatus, you've changed the direction of the magnetic field. Like, that's real. Like, if you rotated the entire universe, then the particle wouldn't be able to tell. But if you rotate a single part within it, yeah. I see, I see. Okay."
},
{
"end_time": 3527.159,
"index": 134,
"start_time": 3498.046,
"text": " The quotient spectrum theorem is like way more general, but this is like one of the scenarios that it would apply to. Why don't you explain what quantum decoherence is and why it either solves or doesn't solve the measurement problem? Oh, that's such a great question. Okay, so decoherence is a like very on the surface mundane thing about quantum mechanics. And it's just the fact that as you"
},
{
"end_time": 3551.664,
"index": 135,
"start_time": 3527.449,
"text": " So you have some particle in a superposition, let's say a superposition of spin up and spin down. And then something interacts with it, let's say a photon of light. And the photon of light will act differently if the particle is spin up or if it's spin down. So that light particle will go into a different state depending on which of those two properties it's in. So now in quantum mechanics, we would say that it's entangled"
},
{
"end_time": 3573.046,
"index": 136,
"start_time": 3551.903,
"text": " with the original particle, because its state depends on the state of the original particle. So that's like what entanglement is. And so then, okay, like that's all good. But now imagine that that photon just like leaves, and you never see it again, and you will never be able to measure it. But you try and measure your original particle."
},
{
"end_time": 3602.756,
"index": 137,
"start_time": 3573.473,
"text": " Now, if your original particle is in a superposition, normally you'd be able to tell that it's in a superposition. You can do like a double slit experiment on it, something similar, to tell that it is in that superposition. But even though it's still in a superposition, and like nothing has changed from the quantum mechanics point of view, because you haven't got access to that photon, if you do the math, you can show that this particle now acts as if it's collapsed to one of those two states."
},
{
"end_time": 3622.602,
"index": 138,
"start_time": 3603.234,
"text": " like you will not be able to tell the difference between a collapsed particle and what's really happening, which is it's still in a superposition, but a superposition that involves this photon that is now inaccessible. And so that's like, yeah, on the surface a bit mundane, but the implications are really profound because here is a mechanism"
},
{
"end_time": 3651.305,
"index": 139,
"start_time": 3622.807,
"text": " by which you can get measurement collapse without measurement collapse like so something that looks and feels to us exactly like measurement collapse like mathematically entirely equivalent and yet all that's happening is normal quantum mechanics and so you can just get rid of that last postulate of quantum mechanics entirely and just replace it with like just just just delete it and you still get the same results sorry when you say you can get rid of the last postulate of quantum mechanics you're referring to"
},
{
"end_time": 3674.36,
"index": 140,
"start_time": 3651.834,
"text": " Oh, yes, the the measurement postulate. So the collapse postulate that so like, yeah, there's the thing that's really nasty about quantum mechanics. And like, the, like, I think real problem with quantum mechanics is that there's two systems, there's like, what how quantum quantum objects like act when there is no"
},
{
"end_time": 3700.06,
"index": 141,
"start_time": 3674.855,
"text": " measures around and no devices around to measure them. They just like evolve unitarily. It's very nice. But then suddenly, as soon as you add something that you call a measurement device, and like, who knows what that is, you have to have like different rules of physics that are like incompatible, like they just don't work together. And like, this is just untenable mathematically and philosophically, like it's just ugly. Whereas"
},
{
"end_time": 3730.094,
"index": 142,
"start_time": 3700.418,
"text": " the whole decoherence thing gives us a way out. What it says is forget about that second regime. Measurements are not real. Measurements are a phenomenological thing that comes from just the regular quantum mechanics. There is never a measurement collapse. Instead, there's only superpositions. But because some parts of those superpositions become inaccessible to you as you add more particles and they all become entangled and then those particles fly off or whatever,"
},
{
"end_time": 3757.568,
"index": 143,
"start_time": 3730.299,
"text": " Does this have any implications for the many worlds interpretation? Yes, absolutely. So many worlds, people often take this decoherence as like a sort of important"
},
{
"end_time": 3786.493,
"index": 144,
"start_time": 3758.456,
"text": " important ingredient in their theorem. Like many worlds, I would say, is basically take quantum mechanics seriously, forget about the measurement postulate, like it doesn't exist. And so then the question for them is like, okay, but if you don't have the measurement postulate, how do you, how do you, like, explain what happens in the lab, where it seems like, you know, measurement happens and collapse happens, they would just say, well, it's just decoherence. So we didn't need measurement all along."
},
{
"end_time": 3814.121,
"index": 145,
"start_time": 3786.749,
"text": " And I would say that is the many worlds interpretation. I thought the many worlds is about the splitting of the universe because you measure and it collapses into one. But you're saying that, forget about collapsing. It's not. Yeah. Many worlds, I feel like that's a misinterpretation. Many worlds has nothing to do with measurement. What it says is if you have some objects in superposition, they continue to be in superposition. They never collapse to just one state."
},
{
"end_time": 3843.695,
"index": 146,
"start_time": 3814.497,
"text": " So whereas like the standard interpretation says like, okay, let's say I have a particle, it could be spin up, spin down. I measure it and now it becomes spin up and I measure spin up. So there's only one world and that's the world where it was spin up. Whereas what many worlds would say is, okay, you have this particle, it's a position of up and down. You measure it. What that really means is you interact with the particles like lots of other particles with it."
},
{
"end_time": 3872.125,
"index": 147,
"start_time": 3844.002,
"text": " Hi, I'm here to pick up my son Milo. There's no Milo here. Who picked up my son from school? I'm gonna need the name of everyone that could have a connection. You don't understand, it was just the five of us."
},
{
"end_time": 3886.203,
"index": 148,
"start_time": 3872.654,
"text": " So this was all planned? What did you get it to? I will do whatever it takes to get my son back. I honestly didn't see this coming. These nice people killing each other. All Her Fault, a new series streaming now only on Peacock."
},
{
"end_time": 3939.172,
"index": 149,
"start_time": 3912.688,
"text": " thought experiment about this called quantum suicide and immortality. Have you heard of it? Okay, so essentially, what I'm wondering is, under the many worlds interpretation, do you not live forever? Because if we define you as the experiencing you, because by definition, you can't experience when you're dead. So why is it that you don't live forever? Because there's no world where, where you get to live forever, right? Like, okay, let's say,"
},
{
"end_time": 3968.404,
"index": 150,
"start_time": 3939.616,
"text": " I'm going to think about myself and all of the many superpositions I can go into from this point. So there's many things that could happen to me that put me in superposition, maybe like something to do with weather as a quantum fluctuation. I don't know how that could happen, but like let's just say, you know, it might rain tomorrow because of quantum mechanics or it might not. So there'll be a version of me that experiences the rain and one that doesn't. But in both of those worlds, I will die eventually. Like there's no immortality there."
},
{
"end_time": 3997.415,
"index": 151,
"start_time": 3968.797,
"text": " And like in every sort of possible world that is like dependent on a quantum fluctuation, like I can't see any of those worlds where I become immortal. Is there not a world where your DNA is constantly repaired and the earth and the sun doesn't burn out and so on? So you do live forever? So the laws of physics have to be obeyed in every one of these universes. So the sun will inevitably burn out. Just there."
},
{
"end_time": 4019.343,
"index": 152,
"start_time": 3997.756,
"text": " Unless like there is, I mean, I can't see it, but like, unless there's some way for it to not happen quantum mechanically, but I don't think so. So the sun will burn out in every one of those universes. My DNA repairing is not down to quantum fluctuations. It's down to other, other factors which like couldn't go both ways."
},
{
"end_time": 4038.234,
"index": 153,
"start_time": 4019.787,
"text": " And so like that, that's also not a path to mortality. And how about this? Okay. Methuna is instantly recreated. You're now 18 and perfect health. You're probably already in perfect health, but you're now 18 and there's a, is there not a small, small, small chance of that occurring right now?"
},
{
"end_time": 4060.52,
"index": 154,
"start_time": 4038.456,
"text": " Yeah, so I think that this is like no different from"
},
{
"end_time": 4090.401,
"index": 155,
"start_time": 4060.811,
"text": " you know, if I like, because anything could sort of spontaneously come into being, right? Like, because because of like, very freak quantum fluctuations. But like, let's say that, you know, you're sitting here, and then, like, on the other side of the universe, the Eiffel Tower just like materializes on some other random planet, right? Now, it's, it's a sort of philosophical question."
},
{
"end_time": 4120.247,
"index": 156,
"start_time": 4090.657,
"text": " whether you count that as the Eiffel Tower, is it the same thing? Right? And so, like, if a version of me just materializes randomly somewhere else in the galaxy, is that me? Well, I wouldn't experience it being me because I only have my continuous experience from this body. So that person, if they materialize with all my memories, of course, will think of themselves as me, but I would think of them as a person distinct from me."
},
{
"end_time": 4150.52,
"index": 157,
"start_time": 4120.674,
"text": " and that there's no sort of contradiction there. And also it doesn't grant me myself any immortality, even if like this keeps happening. Do you think of yourself as the same person when you wake up? Yeah, so this is like, oh, you know, like, deep philosophical questions have been debated for a long time. But yes, I do think of myself as the same person when I wake up and something to do with the continuity of experience or something about"
},
{
"end_time": 4175.23,
"index": 158,
"start_time": 4150.93,
"text": " being able to remember, even if it's inaccurately, what it was like to be that person before, makes me feel like the same person. Whereas if there's another version of me, even if they have the same memories as me, and they themselves therefore think of themselves as me, both of us imagine our past as their past, and that is 100% accurate."
},
{
"end_time": 4203.507,
"index": 159,
"start_time": 4175.725,
"text": " I would not associate with that person because that person is not sharing any experiences with me. I'm curious about the implications if the universe is discretized spatially or temporally, does that have any implications for quantum computing? Because I imagine that a large part of the power comes from that there's an infinite amount of intermediate states between zero and one. And so if you can discretize in some manner, then the Bloch sphere is also discretized or is it not?"
},
{
"end_time": 4230.759,
"index": 160,
"start_time": 4204.872,
"text": " That's a good question. There's different ways to discretize, right? There's just discreteness in time, in space, and then what you're talking about, which is discreteness in terms of what superpositions are allowed. I can't remember this result off the top of my head, but I have this vague feeling of reading a result that was along the lines of discretizing what superpositions are allowed, and you still get like the regular power of quantum computing."
},
{
"end_time": 4259.77,
"index": 161,
"start_time": 4231.049,
"text": " So I would disagree that the power of quantum computing comes from the continuity. Is there a limit? So for example, like if it's broken up into a thousand different, instead of an infinite amount of superposition, it's a thousand discrete superposition. Yeah, that would certainly be a problem. No, that would definitely be a problem. I was thinking of like, if you discretized it as in like, you don't allow it to be real numbers, but you allow it to be any"
},
{
"end_time": 4289.07,
"index": 162,
"start_time": 4259.957,
"text": " I think if you start putting into finite numbers, yeah, that would be a problem. Have you heard of Wolfram's principle of computational equivalence? I'm not sure if I have. Okay, so it's like an extension of the church thesis, church Turing thesis, except he says that all physical phenomena have a computational basis. Okay, do you agree with that? Yeah, that sounds 100%"
},
{
"end_time": 4319.411,
"index": 163,
"start_time": 4289.531,
"text": " like, like, I mean, I'm very biased as a person who studied quantum computing. Because like, the reason why quantum computing is interesting to me is because I fundamentally accept that, that everything in the universe is a computation in the sense that a computation is like, you have some objects, and they follow some rules. And that just determines what they're doing at the next time step. And so that, like, to me is exactly what physics is. And so I've like, yeah, no, no, like,"
},
{
"end_time": 4348.37,
"index": 164,
"start_time": 4320.06,
"text": " Yeah, to me, that's like definitely true. Okay, great. Okay, now you have some some choice words to say about the Bohmian pilot wave theory. Okay, why do you not particularly like it? Oh, I do particularly like it. Um, so I, I actually think that, um, like, I don't think I believe it. But I think that is a really, really important theory to have in mind."
},
{
"end_time": 4376.715,
"index": 165,
"start_time": 4348.746,
"text": " Because a lot of the things that we want to say about quantum mechanics, or we think is obviously true about quantum mechanics, Bohmian mechanics provides an excellent counterexample for. So it's something to always be keeping in mind when you're talking about the foundations of quantum mechanics. And yeah, I think it's an ingenious theory. I think that it doesn't extend well to relativity, which is why I don't think it's true."
},
{
"end_time": 4407.039,
"index": 166,
"start_time": 4377.329,
"text": " But for just straight up quantum mechanics itself, it is like, yeah, just such a beautiful counterexample to a lot of things people say. Yeah, I heard you say that on the Eichenbrau's podcast that it doesn't extend to, well, you said that it's non-renormalizable, but I wasn't able to find that result. Did you, can you, there's a paper on that, I'm assuming. There are some papers on this, but it's not, it's not that it isn't possible, but that, that it seems, so it is,"
},
{
"end_time": 4437.449,
"index": 167,
"start_time": 4407.449,
"text": " probably possible to reproduce the phenomena of special relativity, but not to reproduce the sort of like, underlying beauty of special relativity, which is like relativity, that like, you know, frames of reference don't matter and that sort of thing. There's a paper, a fairly recent paper 2019, this guy named Pinto Neto, and Struve, I don't know if you heard of them? No,"
},
{
"end_time": 4466.971,
"index": 168,
"start_time": 4437.637,
"text": " Okay, well they show that with a Bohmian interpretation you can have quantum gravity and in a way that doesn't have the parts of heterotic string theory and supersymmetric string theory and loop quantum, they have some pestiferous parts to them when it comes to quantizing gravity. So what they used is an approach of canonical quantum gravity and apparently when you use a Bohmian interpretation it helps form some"
},
{
"end_time": 4495.418,
"index": 169,
"start_time": 4467.312,
"text": " even predictive aspects of quantum cosmology. So that's why I was wondering, why is it non-renormalizable when like, I couldn't find that result. And I heard you say that on the Eigenbrows podcast and I was like, where's, and then they're like, yeah, it is non-renormalizable. I'm like, what? And I searched for this, but I couldn't. Yeah. Okay. So there, I don't know if I said non-renormalizable, but definitely like the thing that I was thinking of was like that, that it is frame dependent."
},
{
"end_time": 4525.469,
"index": 170,
"start_time": 4496.544,
"text": " Um, so it has like a privilege frame of reference, which is quite like not in the spirit of, of relatively, even if it can reproduce the results and, and like, to be fair, like if it can reproduce the results very well, or even like have good, um, predictions about like, you know, where, where all these things are going to go, then, then that is very exciting. And we like, you know, maybe should give up on like the beauty of relativity a little bit if it's going to be useful."
},
{
"end_time": 4552.159,
"index": 171,
"start_time": 4525.862,
"text": " So I'm not like I don't have a strong position on that. But my my like sort of gut feeling was like having not read this paper that you're mentioning, that like if it had to have like a sort of privileged frame of reference, that it would probably make the math of it, like kind of too hard to like be really workable. And so that was why I wasn't a fan of it. Like I didn't feel like it could extend well."
},
{
"end_time": 4581.476,
"index": 172,
"start_time": 4552.619,
"text": " Do you have an opinion that the laws of physics, like, let's say the theory of everything is ultimately beautiful, symmetric, and so on? Or do you, or you're like, be it as it comes? Yeah, no, I like, I mean, I maybe should be one of those people is like, Oh, you know, whatever it is, that's, that's the truth. Um, but like, of course, like my training is in physics and we get this like idea sort of have it into us the whole way along that, that things that are true are beautiful."
},
{
"end_time": 4609.053,
"index": 173,
"start_time": 4581.834,
"text": " Um, and it just so happens to have been the case for so long. And even in mathematics, um, I feel like this is true, that the things that are true are beautiful because, um, like the beauty of it is like us recognizing how like elegant and simple the solution is. Um, and it feels it would just be weird for all this like complexity in the universe to exist without some like"
},
{
"end_time": 4630.981,
"index": 174,
"start_time": 4609.258,
"text": " We're going to wrap up, but I have some specific questions for some of the people who are, let's say, in their second year of physics, so they're just taking quantum mechanics, and then some audience questions too. Okay, so Miles Ignotis says, I'd like to know her thoughts on cubism. Yeah."
},
{
"end_time": 4651.937,
"index": 175,
"start_time": 4631.186,
"text": " Okay, so this is like a really great question. And it is something that I've been wanting to like learn more about to actually make a video about and just just generally know more about for myself. But I don't know enough. But my sort of gut reaction to it is like, I just feel uncomfortable with physical theories that put"
},
{
"end_time": 4681.032,
"index": 176,
"start_time": 4652.21,
"text": " that really privilege the observer and privilege the observer's knowledge about the universe and kind of almost suggest the universe doesn't exist without us processing the knowledge. And like again, this is very much my bias, like coming from physics where it's all about like sort of objectiveness and like humans being removed from the, like humans kind of stumbling onto the universe and like trying to understand it as it is rather than creating the universe in our own minds. So this is my gut reaction against cubism."
},
{
"end_time": 4709.872,
"index": 177,
"start_time": 4681.271,
"text": " But I think that there's like a lot of interesting mathematics that has been derived by cubism that like is definitely worth looking into and something that I really want to do. Just Us Perths, I don't know if I'm pronouncing that correctly, says, how can a person who is self-studying deal with gaps in knowledge? When I get stuck on a new concept, I'm often unsure what exactly it is that's preventing me from understanding it, i.e. I don't know what I'm missing and what I need to study in order to get it."
},
{
"end_time": 4740.06,
"index": 178,
"start_time": 4710.913,
"text": " This is really tough. I had the same problem many times when studying myself. In some ways, being a beginner and getting stuck in these ways is a real privilege. I know this sounds really weird to say, but being a beginner and recognizing what you don't know"
},
{
"end_time": 4764.121,
"index": 179,
"start_time": 4740.384,
"text": " is a state that you can like almost not get back into. In fact, I think that one of the reasons I like teaching beginners is because then I have to put myself in that mindset. And like, yeah, so being able to recognize what you don't know is like really, really valuable. And as you go on, you'll basically like plaster over the bits that you don't actually understand. So definitely like try and recognize what you don't understand. And when you get to that situation,"
},
{
"end_time": 4790.128,
"index": 180,
"start_time": 4764.445,
"text": " Like if you can like look for sort of, you know, introductory textbooks or some material like that and understand it from that, that's great. But if it doesn't solve your problem, like keep that as a question mark, like, you know, keep it as like, okay, I still don't understand this bit. I'm going to keep this as a question. I don't know the answer. I'll move on. Like I'll read some other things either like, you know, tangentially, or I'll just go on in whatever I'm reading."
},
{
"end_time": 4818.268,
"index": 181,
"start_time": 4790.452,
"text": " But as I read, like if something answers that question for me, I'll come back. I imagine that as you're doing your PhD, you don't have the time to go through the books and solve all the problems. And I know that solving the problems helps your understanding greatly. But because you have to cover such a vast amount of research so quickly, that means that you have to have a superficial understanding of so much. But then you have to know what is it okay for me to have a superficial understanding of so that I can"
},
{
"end_time": 4845.401,
"index": 182,
"start_time": 4818.831,
"text": " pretty much with a hop, skip and a jump, go to the, go to where I need to be. So how do you get, how do you balance that, that tight rope of, of having tenuous knowledge and strengthen deep knowledge? Okay. Yeah. So, um, during my PhD, the thing I was just saying about the benefit of being a beginner, I tried to really take that to heart."
},
{
"end_time": 4872.398,
"index": 183,
"start_time": 4845.879,
"text": " Um, so when there was a topic I didn't know, I mostly avoided it only like kind of knowing it superficially from talks that I would go to just enough to kind of like understand what the vague, like what the problem was in that, in that area and like what they were trying to solve. But I would like purposely not really jump into it. And then I would like take various topics, like new topics that I didn't know. So, so one of them was like conamara correction."
},
{
"end_time": 4901.971,
"index": 184,
"start_time": 4872.602,
"text": " like I'd heard about it in a lot of talks, and I knew what the problem was. I'd never dived into it. So then I took some time to specifically go and read all the introductory material on that, and like really dive into it. Because I feel like there isn't that much benefit of having like a more than superficial knowledge of, of certain topics of physics. Whereas there's a huge amount of benefit to being an absolute beginner, and like really, really diving into a topic."
},
{
"end_time": 4932.432,
"index": 185,
"start_time": 4902.449,
"text": " Because like, yeah, I remember one of the examples that comes to mind is like, I tried to learn about fermions and bosons in the context of computing. Because there was like a bunch of really interesting results about like boson sampling and fermionic linear optics. And I wanted to like, like I knew about them, but I wanted to go back to the basics. Like I want to understand what is a fermion? What is a boson? What have they got to do on computing? And so like,"
},
{
"end_time": 4957.022,
"index": 186,
"start_time": 4932.722,
"text": " I really, really, really went back to the absolute basics, spent ages on it. And I remember giving this presentation to my group and a few other people who were there who were basically experts in the topic of how this relates to computing. And I was talking about something super basic. But even so, I felt like there were some parts where I knew stuff"
},
{
"end_time": 4983.831,
"index": 187,
"start_time": 4957.5,
"text": " better and like I'd been able to make some connections that I think weren't as clear if you um uh like you know like again not not as the like the experts obviously knew more but the people who were like fairly well versed in it I feel like there were some points in which I like knew more than them just from like really diving into like but what does this mean and where do I have uncertainty and just like keep going until you really get some get to the bottom of it."
},
{
"end_time": 4998.063,
"index": 188,
"start_time": 4984.019,
"text": " Yeah, and when you're doing this process of diving in and finding out where your holes are, are you taking a blank sheet of paper and writing out almost like the Feynman method? I'm sure you've heard where you teach yourself or you pretend there's a third person hear that sound."
},
{
"end_time": 5025.094,
"index": 189,
"start_time": 4998.985,
"text": " That's the sweet sound of success with Shopify. Shopify is the all-encompassing commerce platform that's with you from the first flicker of an idea to the moment you realize you're running a global enterprise. Whether it's handcrafted jewelry or high-tech gadgets, Shopify supports you at every point of sale, both online and in person. They streamline the process with the internet's best converting checkout, making it 36% more effective than other leading platforms."
},
{
"end_time": 5051.203,
"index": 190,
"start_time": 5025.094,
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},
{
"end_time": 5074.565,
"index": 191,
"start_time": 5051.203,
"text": " of their commerce. Shopify, by the way, powers 10% of all e-commerce in the United States, including huge names like Allbirds, Rothies, and Brooklynin. If you ever need help, their award-winning support is like having a mentor that's just a click away. Now, are you ready to start your own success story? Sign up for a $1 per month trial period at Shopify.com"
},
{
"end_time": 5103.882,
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"start_time": 5074.565,
"text": " Yeah, so what I do is I collect like, so in this case, it was papers, I collected a whole bunch of papers, but you know, it could be books. I never read through a book, like front to back. Like I never sort of want to get something from just one source."
},
{
"end_time": 5133.234,
"index": 193,
"start_time": 5104.138,
"text": " Instead, I'll read one source, kind of get like something from it. Like maybe I'll read the introduction, and then I'll kind of write down what I think I know. And then I'll go into another source and see if that kind of like gels well. They might be using different notation, they might be looking at it from a slightly different perspective. Your fans, your photographer fans. Yeah, okay. So yeah, I'll never read"
},
{
"end_time": 5154.974,
"index": 194,
"start_time": 5134.258,
"text": " I'll never read anything front to back. Instead, I'll read a lot of different things with different perspectives. And as I go, I'll be keeping a whole lot of notes where I'm basically trying to explain it to myself. I'll be like, a fermion is, and then I'll write one definition. And then in the other source, it'll have an entirely different but equivalent definition."
},
{
"end_time": 5178.695,
"index": 195,
"start_time": 5155.23,
"text": " And I'll like, like, I'll read that they don't reference each other, they don't talk about how they're related to each other. So then I have to like, you know, in my writing, like figure out how is this thing that they said the same as what they said, just in a different language. And so like the translation process is really interesting. And like, I'll learn a lot from that. Then like, yeah, just just like, kind of like keeping many sources"
},
{
"end_time": 5208.66,
"index": 196,
"start_time": 5179.718,
"text": " in mind as I'm writing these notes that are like how would I explain this to someone else is very useful. Do you find that books are most helpful or do you watch lectures online? I almost never watch lectures online. I think it's mostly an attention thing. I actually kind of find it hard to watch video and a lot easier to read but what I feel what I find lectures better for than textbooks is to get"
},
{
"end_time": 5232.056,
"index": 197,
"start_time": 5209.002,
"text": " opinion from the person. Like opinions during talks are so useful, you get the sort of sense of like, what this person thinks is the interesting parts of this field, or like, what are the real mysteries according to this person. Whereas I feel like books are, you know, a lot more long winded in their introduction. So it's harder to get that feel of like the person's opinion. But then I think books are better for like diving in."
},
{
"end_time": 5256.834,
"index": 198,
"start_time": 5232.551,
"text": " I'm going to just read this one verbatim. So how is it specifically that the mathematical notion of an observable as an operator corresponds to a physical device? So what you're doing is you're manipulating symbols in the abstract, and it's not clear how it corresponds to what's going on experimentally. Now, that's something that when you're in second, third, even fourth, you don't get, unless you take experimental physics, you don't get an understanding of. So what the heck does it mean that the operator is"
},
{
"end_time": 5287.637,
"index": 199,
"start_time": 5257.654,
"text": " position operators x in the or the derivative if it's momentum is onto how does that correspond to what's going on when you observe in the lab? Yeah, yeah, this is a great question. No, this is a great question. And it confused me for a long time. And, and we kind of realized, much later that there is no good science to the way that we make the operators. In fact, there's a lot of art to it. What we usually do is we so like, okay, to make an operator for a"
},
{
"end_time": 5315.811,
"index": 200,
"start_time": 5288.046,
"text": " measurement, you've got to consider what, what are you like, physically doing? So you know, in the Stern-Gerlach experiment, we're actually physically applying a magnetic field, ultimately, that's what we're doing. And whatever measurement you're doing, you're ultimately physically doing something. And you've got to write down like, what are the, so the Hamiltonian, which is essentially like, what are the forces that you're, you're, you're"
},
{
"end_time": 5344.77,
"index": 201,
"start_time": 5316.476,
"text": " creating in this measurement device. And then you write that down classically. And then you just do the sort of like, cheap trick of quantization, where you take like the, the quantum like, so the classical version of a certain object, like the magnetic field, and then you make it a quantum operator, and then you're like, Okay, just do that. And there we go. That's my quantum operator for this, this measurement, whatever I'm doing. So it's not that satisfying."
},
{
"end_time": 5371.544,
"index": 202,
"start_time": 5345.503,
"text": " What's the operator for determining the charge of an electron or its mass if operators correspond to observables? Yeah, so this one is not an observable. The reason is because you couldn't observe a electron to be in a different, to have a different mass or charge. On the other hand, now that I say that, you could come up with a"
},
{
"end_time": 5401.954,
"index": 203,
"start_time": 5372.125,
"text": " How do operators look in terms of experiments? Now, can one design an experiment and work backward to find the operator? Yeah, that's what you do. You've got to look at the experiment, look at what forces you're applying, and then write those out, do quantization, that will get you the operator pretty much."
},
{
"end_time": 5432.005,
"index": 204,
"start_time": 5402.159,
"text": " Three more questions. Ryan Conlin says, when you study, how much time do you spend thinking about your own particular background knowledge and skills that is relating it to previous knowledge versus how much time do you spend? Do you spend thinking about it without relating? Oh, super interesting question. Actually, I find it's really, really useful to relate it to your own background knowledge, at least for me during the PhD. I think maybe that's partly a quirk of the PhD where like you you're studying, but you also want to be able to add something new to the knowledge."
},
{
"end_time": 5457.841,
"index": 205,
"start_time": 5432.346,
"text": " like the knowledge base. And so going from the angle of like, how can I relate this to the particular quirky things that I know, is like a good way to sort of start making new things. But just generally, I think it's like really a good strategy when you're studying to, you know, you've learned some new concept, let's say you've just learned what a group is, and in abstract algebra, and"
},
{
"end_time": 5480.674,
"index": 206,
"start_time": 5458.166,
"text": " If you can find like some examples that are related to things you've learned. So for example, if you related that to the symmetries in relativity, because you've just learned about relativity, that will make it way more concrete and way easier for you to understand. So I think that is actually a really important thing that's like super neglected by students. So yeah, great question."
},
{
"end_time": 5508.814,
"index": 207,
"start_time": 5480.879,
"text": " At the same time, I can see how sometimes trying to relate it back can be counterproductive. For example, in quantum mechanics, they say, just forget what you know, that's going to hold you back. So at what point do you abandon versus relate? I think that's the thing on quantum mechanics. I think that's not true. Like, if you're learning quantum mechanics, mathematically, like you're trying to understand the math is extremely important to"
},
{
"end_time": 5535.981,
"index": 208,
"start_time": 5509.292,
"text": " Michael McGuffin says, what has she been reading recently?"
},
{
"end_time": 5565.043,
"index": 209,
"start_time": 5536.152,
"text": " And then also part two is like if her financial incomes were met, say she's given $10 million, what would you spend your time doing? Books and then time? Okay, cool. Thank you for those questions. So what am I reading? I'm reading a few things. I recently finished a book by the the director of Pixar, creativity, Inc. And it was about how to create"
},
{
"end_time": 5595.026,
"index": 210,
"start_time": 5565.401,
"text": " like a creative product in in a corporation, which like often kind of stifle creativity. So how do you keep that alive? That was super interesting. On a sort of similar vein, a friend of mine recommended the idea factory. And that was about Bell Labs. So Bell Labs is like quite famous for having invented a whole bunch of like, really ahead of their times, devices. And it was a similar deal to Pixar in a way where"
},
{
"end_time": 5622.756,
"index": 211,
"start_time": 5595.64,
"text": " like they managed to come up with like a corporate environment, because it was a corporation, it wasn't a university or anything, a corporate environment that somehow could still stimulate creativity, and in this case in science. So yeah, I think that's like a really interesting topic to me, like something that I'm really interested in about, like it's just just innovation in general, but how do you, how do you foster it? And then like, I guess if someone was to give me $10 million,"
},
{
"end_time": 5651.834,
"index": 212,
"start_time": 5623.114,
"text": " There are a bunch of projects that I'm interested in. I'm very keen on understanding what the future of education is going to be. I think that there needs to be even more research. I mean, there's lots of great research at the moment, but even more research and even more focus put into how can we really change the way that"
},
{
"end_time": 5682.022,
"index": 213,
"start_time": 5652.363,
"text": " humans learn so that they are really achieving their maximum human potential. I think that schools are really wonderful, and I'm not one of those people who is advocating for just ripping it all down. But I think that they're inefficient in certain ways. They just have to be because of how they were made and because of all the various pressures that are on schools. So I would love to understand, if we were going to make it from scratch, what would we keep, but what would we change?"
},
{
"end_time": 5693.609,
"index": 214,
"start_time": 5682.278,
"text": " Have you heard of Peter Gray's unschooling?"
},
{
"end_time": 5723.148,
"index": 215,
"start_time": 5694.48,
"text": " I'm blanking. Can you essentially it's not like tear down the schools. But what I'm saying is that the that kids is taking an evolutionary psychological approach to learning that kids learn best in mixed age groups. And one of the reasons is that there's no bullying because you're eight, you're not going to compete with a 16 year old, and you're not vice versa. And then 16 year old is not going to compete with a 24 year old. And he takes this from observing tribes that don't have schools. And the kids just learn automatically because play is so important. And when they're playing, they just"
},
{
"end_time": 5749.002,
"index": 216,
"start_time": 5723.422,
"text": " They happen to learn and it's spontaneous and you allow the kid to follow their own interests and you encourage it. Yeah. That of imposing one. Yeah. So I think this, this whole movement of inquiry based learning is very, very interesting, but also I think we have to be a little careful with it. I I'm, I'm definitely for,"
},
{
"end_time": 5778.234,
"index": 217,
"start_time": 5749.497,
"text": " kids being able to like figure out what they like themselves and just like go down that rabbit hole like that's you know a big part of like my education was that but I think on the other hand like letting kids have completely free rein I mean there has been some research about this like it just doesn't work as well if you have like no sort of either discipline or like guidance about where to go"
},
{
"end_time": 5808.524,
"index": 218,
"start_time": 5778.626,
"text": " you know, you're not going to expect a child playing on their own to rediscover Mutian's laws, like that's just not possible. But on the other hand, if you had like a supervising figure who was there to like encourage the, you know, the interests as they as they develop and sees that, you know, this person's interested in how things work and it's like, oh, have you read these interesting books? Like that could potentially work. I think that to make that work, we need to put like a lot more thought into"
},
{
"end_time": 5837.09,
"index": 219,
"start_time": 5808.712,
"text": " just how like we can guide that experience without, you know, fully determining what the kid is going to do ourselves. Beer's Attitude says, it would be cool to know her opinion on Donald Hoffman's work. What is the most fundamental level in her opinion? I don't know what that last sentence means. What does she make of consciousness? So I don't know if you've heard of Donald Hoffman and his theories on consciousness, but this person would like to know. Yeah. Okay. Oh, that's, that's disappointing because the person's like, Oh, thank you, dude."
},
{
"end_time": 5868.746,
"index": 220,
"start_time": 5839.07,
"text": " Sorry. Wait, who is this? Donald Hoffman is a cognitive scientist. He's a cognitive scientist who says that what we can do is model conscious agents with something like a Markov kernel where you just have, let's say, the set of experiences. You don't even give them names like love or whatever. You just give them whatever you like and then give them some structure like, well, you can read his papers."
},
{
"end_time": 5897.688,
"index": 221,
"start_time": 5868.968,
"text": " And then he says that what you can do from there is develop the laws of quantum mechanics. Now, I'm skeptical of that. And I read his research. But it's something like, it's so general. You've heard of these claims where it's like, yeah, I can derive quantum mechanics. But I derived it from something so general that it's, well, I'd be surprised if you couldn't derive quantum mechanics from that. Fair enough. But either way, Donald Hoffman is a bright, bright, bright, bright individual. Yeah, sorry I couldn't answer that question. That's all right. That's all right. And I also realized that I have a question on quantum, the quantum parallel thesis. I wanted to know,"
},
{
"end_time": 5925.828,
"index": 222,
"start_time": 5898.319,
"text": " I imagine that you think it's true given that you adopt the many worlds interpretation, but I was wondering what are some ways that the quantum parallel thesis could be true without the many worlds interpretation? What do you mean by the quantum parallel thesis? Quantum parallel thesis is that the, it's something like that the computation is being performed simultaneously on the superpositions."
},
{
"end_time": 5953.66,
"index": 223,
"start_time": 5926.578,
"text": " Okay, have you heard of the quantum parallel thesis? Yeah, like a doish's. Yes. Yeah, that's correct. That's correct. That's correct. Yeah. Um, yeah. Uh, I think what I don't understand about that idea, um, and what makes me skeptical of it is that it's not clear how computation from distinct branches of the superposition can be, be transferred, like how that information can be transferred."
},
{
"end_time": 5983.387,
"index": 224,
"start_time": 5954.206,
"text": " So let's say you want to do a huge number of computations, so you split into many different worlds, and then you do one of the computations in each one of these worlds. Then you have the result in each of these worlds. So let's say you're looking for a one, and world number three has found a one, and it needs to communicate now to all the rest of them. The way that that communication is done inside of quantum computing"
},
{
"end_time": 6012.193,
"index": 225,
"start_time": 5983.814,
"text": " It depends on those superpositions not being distinct worlds in the sort of many world sense. So in the many world sense, like any superposition is not a different world. It only becomes like a different world once it interacts with other things and therefore can't interact with itself anymore. So if you have a superposition of two things,"
},
{
"end_time": 6036.869,
"index": 226,
"start_time": 6012.637,
"text": " those sort of worlds can kind of like split in a sense, and they become distinct from each other. But if they don't interact with anything else, they can kind of reconvene. So one way that this could happen is like, if you have a spin particle, you start it in spin up, and then you change the magnetic field, so it becomes spin up, spin down, and then you change the magnetic field back and so it's been up again."
},
{
"end_time": 6051.834,
"index": 227,
"start_time": 6037.398,
"text": " a way you've deleted the superposition but this is like this is totally fine and this is what happens in quantum computing but in many worlds you wouldn't say that that was like two worlds and they recombined for many worlds the worlds can't recombine for them to be like worlds"
},
{
"end_time": 6082.193,
"index": 228,
"start_time": 6053.66,
"text": " I have a quote here about the many worlds interpretation. This is hardly the most economical view, the most economical of viewpoints, but my own personal objections don't spring from its lack of economy. And in particular, I don't see why conscious being need be aware of only one of the alternatives in a linear superposition. What is it about consciousness that demands that one cannot be aware of the tantalizing linear combination of being both dead and alive?"
},
{
"end_time": 6109.94,
"index": 229,
"start_time": 6082.619,
"text": " It seems to me that a theory of consciousness will be needed before the many worlds viewed can be squared with what one actually observes. So what do you say to that? Yeah, I think that that is an understandable objection, but I think like an objection that is met by the mathematics. So what I mean is, okay, let's say you have a object that's in a superposition in many worlds, like so it's in two different worlds."
},
{
"end_time": 6139.377,
"index": 230,
"start_time": 6110.964,
"text": " It can only experience like, so let's say it's not a conscious thing. It's just a, let's say an atom. Um, it can only experience all of the other objects in its world in that, in the state that they are in that world. So like in this state, like, so let's say in this world, all of the objects are in state zero and in that world, they're all in state one. If you take one of the atoms inside of here and you get it to measure one of its partners, it will say that its partner is zero."
},
{
"end_time": 6167.398,
"index": 231,
"start_time": 6139.821,
"text": " or here, if you've got it to measure its partner, it would say it's one. It can only experience that world, like with all of the things that are in that world as they are like, you know, in that state. And so let's say now I'm a conscious being and I'm inside of like both of these branches. I've just done a measurement of my, of my atom and my atom is now like in state zero, according to in this branch and in state one, according to that branch."
},
{
"end_time": 6194.974,
"index": 232,
"start_time": 6167.705,
"text": " If I was to, if I was able to experience both, then I should be able to see the atom being in state zero and in state one. But because of how many worlds works, how the mathematics works out, there is no measurement that I can do inside of this world that would show me the result one, it would only say zero. And in that world, I would only say one. And so there's no like, I don't experience the other world to me, it just doesn't exist. There's no evidence of it anywhere. So of course I don't consciously experience it."
},
{
"end_time": 6225.572,
"index": 233,
"start_time": 6196.578,
"text": " Oh, so now that there's no evidence of it anywhere, what is the reason for you believing in it? Oh, so there's evidence, there's all the evidence that I could possibly want that I'm in the world where everything is in state zero. I'm sorry, I meant, I meant, why does Mithuna, Mithuna, sorry, believe in the many worlds interpretation? To me, it seems like a religious choice, because there's not evidence for it unless you just say, well, the math says. Exactly. So no, um,"
},
{
"end_time": 6242.671,
"index": 234,
"start_time": 6225.845,
"text": " It's back to that question of like, do I want a theory of the universe to be beautiful or not? My bias is very much towards beauty. And I think that many worlds is a much more beautiful theorem, theory rather."
},
{
"end_time": 6272.261,
"index": 235,
"start_time": 6242.961,
"text": " And that's because it has less assumptions. So in a statement there, oh, many worlds is less economical. In one sense, yes, if you're like counting worlds, but I think that's not the sort of important sense of like, you know, how economical a theory is, how economical it is, is like, how many sort of distinct ad hoc rules does it have? And many worlds deletes the ad hoc rule that quantum mechanics has. And therefore, I think it is a more economical, more beautiful theory. That's why I believe it."
},
{
"end_time": 6295.35,
"index": 236,
"start_time": 6272.534,
"text": " Thank you so much. Thank you so much. So what's next for you? After this next YouTube video? Yeah, well, so the thing I've been thinking the most about is how to improve online education. I think that that's like a really, like"
},
{
"end_time": 6323.302,
"index": 237,
"start_time": 6295.913,
"text": " Interesting and new medium. People on YouTube have done really wonderful things, but I think we can push it even further. So yeah, that's the direction I hope to put myself. And it's sad that I'm not doing physics research. I miss it. But I feel like this is higher impact. I feel like the world needs this more than the small bit of physics that I could have contributed. So are you more driven by that altruistic"
},
{
"end_time": 6349.787,
"index": 238,
"start_time": 6323.951,
"text": " part of you or the passion part of you that just wants to do research? Yeah, um, I think that, um, yeah, like I really am passionate about physics research. And so it was like a super hard decision, but because, um, education will impact like way more people. And also because it is still a very interesting thing to research. Um, ultimately like both of those things combined made it a pretty good choice."
},
{
"end_time": 6381.118,
"index": 239,
"start_time": 6351.203,
"text": " Thank you so much for spending so much time with me and putting up with my sleepy questions. Oh, good. I'm sorry for catching up. Oh, no, no, no, no. No, it's all right. It's all right. I just for weeks and weeks, like weeks, I haven't been getting enough sleep. And so it just compiles and compiles. Yeah. Yeah. And then I've been studying some quantum computing to prep for this. Oh, no. Thanks so much. Well, I'm just going to ask this."
},
{
"end_time": 6409.087,
"index": 240,
"start_time": 6381.613,
"text": " Yeah, yeah, no problem, no problem. There's so many other somewhat technical questions I had like about zx calculus. And I was wondering about the relationship between graph states and the spider diagrams. Oh my gosh. Is there a way of... I know that graph states... See, the way that I understand graph states are like, in particle physics, there's the Feynman diagrams, and then there's rules to translate those to equations. It looks like graph states have a simple rule."
},
{
"end_time": 6438.899,
"index": 241,
"start_time": 6409.787,
"text": " And then I was wondering, is there a way to go from graph states to ZX spiders? Yeah, well, anyway, I'm just, I'm curious, is there? Yeah. Um, I don't actually know. Like they have different uses, I'm sure. But as far as I know from my depthless understanding of quantum computing, they're just representations of the circuits. So I don't, so I don't see why one is more advantageous than the other or why they can't be easily translated to one another."
},
{
"end_time": 6454.548,
"index": 242,
"start_time": 6439.514,
"text": " Yeah, that's a good question. Yeah, that is a very good question. And I genuinely don't know the answer to that. Yeah. Okay. Okay. Well, anyway, whatever. Anyway, well, no, thank you so much for this interview. Thank you. Thank you."
}
]
}No transcript available.