Theories of Everything with Curt Jaimungal - Mithuna on Quantum Immortality, Self-Studying Quantum Mechanics, PhD research, and Quantum Computing

Episode Date: March 11, 2021

YouTube link: https://www.youtube.com/watch?v=r2ct0zv_M-IMithuna Yoganathan is a quantum physicist who specializes in quantum computing, and runs the successful YouTube channel Looking Glass Universe (https://www.youtube.com/channel/UCFk__1iexL3T5gvGcMpeHNA). This podcast serves as a general introduction to quantum foundations and computing for undergraduates and bright autodidacts.Link to Peter Gray video mentioned: https://www.youtube.com/watch?v=AQLkKKERWsIPatreon for conversations on Theories of Everything, Consciousness, Free Will, and God: https://patreon.com/curtjaimungal Help support conversations like this via PayPal: https://bit.ly/2EOR0M4 Twitter: https://twitter.com/TOEwithCurt iTunes: https://podcasts.apple.com/ca/podcast/better-left-unsaid-with-curt-jaimungal/id1521758802 Pandora: https://pdora.co/33b9lfP Spotify: https://open.spotify.com/show/4gL14b92xAErofYQA7bU4e Google Podcasts: https://play.google.com/music/listen?u=0#/ps/Id3k7k7mfzahfx2fjqmw3vufb44 iTunes: https://podcasts.apple.com/ca/podcast/better-left-unsaid-with-curt-jaimungal/id1521758802 Discord Invite Code (as of Mar 04 2021): dmGgQ2dRzS Subreddit r/TheoriesOfEverything: https://reddit.com/r/theoriesofeverything00:00:00 Introduction 00:02:26 What's it like running a 200k+ subscriber YouTube channel? 00:02:56 Using "explanation to others" as a self-learning tool 00:05:27 How do you learn new physics / mathematics? 00:06:22 On feeling like math / physics isn't within your ability to grasp 00:08:29 Is math necessary for understanding physics 00:09:23 Daily schedule / routine 00:12:50 Dealing with people emailing theories 00:15:28 Fat-shattering dimensions 00:17:01 What's the Pauli group's relation to the Clifford group? 00:19:44 How do you prove that a quantum algorithm is efficiently simulable classically 00:22:58 Gottesman-Knill theorem (and its extension, proved by Mithuna) 00:25:41 What's responsible for the "speedup" in Quantum Computing? 00:29:24 Which of her thesis results is the most significant? (on quantum complexity and clean Qubits) 00:37:27 Magic state distillation 00:38:34 Gödel's incompleteness, with quantum logic 00:40:41 Halting problem 00:41:10 Quantum Computers vs Probabilistic Turing Machines 00:42:17 P = NP 00:44:41 Richard Borcherd's comments on Quantum Computers not being "better" than classical (generically) 00:47:05 Quantum Contextuality 00:52:29 Quantum decoherence and why it doesn't solve the measurement problem 00:56:26 On the Many Worlds Interpretation 00:58:45 Quantum Immortality 01:03:19 Is space / time discrete and what would the implications of this be for QC? 01:04:42 Wolfram's "principle of computational equivalence" 01:05:32 Bohemian Pilot wave theory 01:09:28 Are the laws of physics ultimately beautiful and simple? 01:10:31 Audience Q: Thoughts on QBism?

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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 Castrop's, there's E8, there's geometric unity, there's M-theory, there's Chris Langan's, CMTU,

LoopQG, 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 Borchardt 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 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 slash kurtjaimungal as right now preparing and studying for each of these interviews takes the vast majority of my time, besides the time that I spend with my wife, and each dollar, each patron is not only a financial boon, but a large motivational gift of encouragement.

Thank you, and I hope you enjoy. Thank you. Welcome, Mithuna. 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 a good question um so I really enjoy um teaching something that I think I know on on YouTube

because it generally shows me that I don't know it anywhere near as well as I think I know on YouTube because it generally shows me that I don't know it anywhere near as well as I think I do. And I need to end up learning a whole lot more for those videos. And often I feel like I learn more in the process of doing those videos than like I would even when I'm researching them for my PhD. 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. But like, just, just as a whole, like something that I, like the reason I started this channel is because I had done some undergrad classes in quantum mechanics. Yeah.

And like done well in them. And I just was like, oh, you know 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 um and I realized it's basically everything i thought i knew i had no idea about and um so i ended up doing a bunch of research of myself by myself like i took uh six months off i 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 like 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 just for my own like offers and 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 so uh yeah like and also making youtube videos at the same time about what i've been learning 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 the 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 of Philosophy? Do you read it from the textbook? And then how often do you have to reread? Yeah. Oh oh great questions um it depends a lot on the topic if it's something in quantum mechanics now i'll just um go to the papers read the papers um and then when i don't understand things then i'll go to something like um wikipedia or more likely it will be uh 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 Tron if it's there like that's the bible I'll just read it from that um but otherwise like yeah it's sort of uh 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. I 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 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 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 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 uh like mathematical course and just loved it so much like all the functional analysis um it wasn't functional analysis i did really love the functional analysis but my step in was um abstract

algebra so uh 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 like getting back to the basics and understanding why things are true is like what I really loved about physics. And it was 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 thinking, I'm not a a math person I wonder if you know that feeling is from 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 day mithana how what time do you go to sleep because i imagine it's like 10 p.m or 11 p.m 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 um yeah i try um so i don't sleep as regularly as i would like but i try and you know sleep at 11 um last like, but I try and, you know, sleep at 11. Last night I slept at two. So, you know, that happens. 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. 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 am nowhere near an organized person, but I try and vaguely schedule, 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. And so, yeah, that's my that's my like work day. And then in the evening, I like like to jot down a few little notes about what I'm going to make YouTube videos about. That's what I think. Oh, OK. So you work on YouTube videos each day? Just a little bit. Yeah. So for example, what'd you do today? Well, so it's just it's morning today, but I'm actually planning right now. It's morning. Yeah, it's it's 10am 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.

sure when your video will be released? Oh 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 an experience that's sort of hard for other people to understand if they haven't experienced it. And yeah, and this is yeah just 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,

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. Like, 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? respond do you actually read it um the thing is I don't have the um 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 um sorry papers that they've written and it's it's just I don't have like the capacity to

to be reading everything um but I guess like yeah and so it does suck that like generally I don't have like the capacity to to be reading everything um but I guess like yeah and so it does suck that like generally I don't reply um 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 like go through the like geoscientific process of like, you know, getting other people who actually understand this topic. Cause like, I'm not even an expert in a lot of the things that people are sending me to, to like, yeah, to get people like that on board. And then the other thing is that like 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 find it hard to accept when I say that I think something is not right. And, and that, 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 people people are really

nice of course but but um you know like usually i'm used to when you're talking about like a scientific idea um 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 um whereas instead i find like i found the few times where i've tried this that um 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 sound politically correct yes but fat shattering direct dimensions are something from um actually i won't even say that um there's something from classical computer science uh i'm not i can't remember exactly what

context they were originally from i want to no i'm no, I'm not gonna say it and get it wrong, but anyway, 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 looking at 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-sharrowing 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. 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, I'm 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. 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 there I'm missing some subset because there are 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 Pauli 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 Pauli 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 have a quantum circuit, they're made up of gates. Poly operators are important gates and so are Clifford operators. 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 clifid, but it still stays a poly, which is still nice. And so that's like the reason why this is like a really important idea in quantum computing.

And so that's like the reason why 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? Oh, 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.

But what I was interested in is which computations can a quantum computer do better? Why? What's special about that quantum computation? And 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. 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 like also like 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? What I mean is that, is it a fairly standard set of, a fairly standard procedure, or do you have to think completely outside the box? Oh, yeah, yeah. I mean, 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, 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 come coming up with that knot. It's not trivial. It's a strange knot. Why would you come up with some knot and then to prove that it has some property yeah but just come 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 yeah coming up with an algorithm yeah going back to that point of like what it feels like to do math research like that that's that's the thing like you never know where like what is going to be the right idea that's going to prove this fact right or even if that fact is true um and so

you know in her case like that she probably tried all kinds of things and uh or you know had some great insight about like why this knot was like very related um it was similar with like you know my research not not anywhere not to compare myself to anything like as grand as anything like that but um like yeah it you don't know where you're gonna go and there is no algorithm for um finding any of these things like when you're trying to prove something it is totally like a new thing and you have to really like 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, you have a result. And again, I skimmed your paper. So please, if I get it wrong, it seems like you extended the Gotsman-Neal theorem and that

Gotsman-Neal is already a fairly remarkable result, which means yours is groundbreaking. No, it's really not. Like absolutely true. The Gotsman-Neal theorem is Gotsman-Nealil theorem i don't know how it's pronounced i just read it yeah me neither i always go both ways anyway um is yeah an absolutely remarkable and like really important um theorem in quantum computing uh the way we extended it um 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 goddessman 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 goddess manil so i've been calling it godsman nil okay so goddess manil the theorem it says something about the clifford group and

that if you take elements from that and create a circuit then you're you'll be able to be efficiently simulable as well something like that that. Now, what was your extension to it? Yeah, sure. So the Cosmonaut theorem says that a very large class, like a surprisingly large class of quantum computers are efficiently classically simulable. And at the time, this was huge. This is just really unexpected because the class that you're talking about is like, yeah, the Clifford group.

And the Clifford group and the Clifford group involve 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 quite a large class because there's this other theorem that if you take just one other random gate, pretty much with certainty, you will end up with universal quantum computing. So if you have Clifford gates plus just one other random gate, you 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 um 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 guzman neil theorem is like really interesting and something that like i was very interested in um because i was interested in like yeah what's special about quantum computing it's like it can't be anything that's inside of the't be anything inside of the group even though a lot of exciting things are there.

For example, Bell states, which are the maximally entangled states, you can easily make them with Clifford's. And yet somehow that doesn't contribute to quantum speedup. 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 Cliffords 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 does it matter how many of these you add like let's say there's 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 that you're 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 It's not the Toffoli gate. Yeah. So the Toffoli gate, yeah. Okay. I just want to know because I read T, but I wasn't sure what T meant. Yeah, no problem. I was trying to understand it from context. 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 a polynomial number of those in, is that hard to simulate? Or if I was to add a polynomial number of those in, that definitely is hard to simulate. But what's the in between? How does it go from if you have

zero of them, it's completely classically simulable. If you have a polynomial amount, it's universal. 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-Neal 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 that 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 kind of believe the sort of moral, like interpretation of the Gottesman-Neil theorem. And that's what we basically proved that like you, oh, okay, I shouldn't say that, like that had been proved. So this, oh, sorry, I just't say that. Like, that had been proved.

So this, oh, sorry. I just got to turn my camera back on. All right, all right. It's a DSR? Yeah. It's recording again? Okay, cool. So no, no, I shouldn't say that, like, we proved that.

That had been proved, that you can classically simulate, like, the difficulty of classical simulation scales with the number of T gates had been proved. But what we proved was like related to that, like if you have a certain number of T gates in your circuit, can you, in a sense, like remove out all of the Clifford stuff, which is all the easy bits, and just leave like the hard T gates behind? And we showed that that was possible.

Right. So, yeah. 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? 100% think it's the middle one. It's the one clean qubit model without entanglement is classically simulable. clean qubit model without entanglement is classically simulable uh that that was the result basically that i started a phd to get um i and and also the result that i very nearly didn't get um despite spending years on it i i maybe spent five years on that that single topic um so yeah uh why it was such a big deal is, yeah, there's this 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. taking advantage of to get all these speed ups is entanglement and um like yeah it's a very sort of dominant uh like ideology in quantum computing um despite the fact that like yeah there's it hasn't been proved either way um and like the evidence for it is like i would say fairly weak um so

evidence that entanglement does have something to do or doesn't have something to do that it does um like i'd say it's 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 um so like my supervisor and uh um 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. Right. But there were some reasons why this may, like, not sort of extend nicely. One is 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-Neal 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 where the cost of T gates. There's some parameter like that where the cost of classically simulating this quantum computer scales with that term. So, it's like e to the power of that term. Then it suggests that as you add more of that thing, it's getting harder and harder.

I see, I see, I see. Yeah. Okay. Yeah. So, So, your one qubit clean model? Yeah. Clean. Yeah. So, So your one qubit clean model. Yeah, clean qubit. 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 a math point of view, these like noisy quantum computers are super, super interesting because 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 proved only for pure state quantum computers and not for mixed state quantum computers because it it feels like that might just be a quirk whereas like the real thing is these noisy things and so like no result like that had been proved for noisy quantum computers so like the result you would want is without any entanglement for a noisy quantum computer, there is no, like if you have no entanglement in a noisy quantum computer, you have no quantum advantage. That would be the result that like 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. And then you have the rest of the qubits in that quantum computer are completely dirty. In other words, like we have no idea what they're doing. They could be doing anything.

And usually if you have like a set of just like dirty qubits, you can't do anything with them. Because 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 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 uh so 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 um 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 rest of the qubits who have no power. So you would expect that if there's communication between those two sets, that it would via entanglement, if entanglement is important. And so like the fact that there's no entanglements like 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 qubit those like this the clean qubits and all the noisy ones, but within the noisy ones there's no entanglement within them as well.

So like just no entanglement across any of the qubits like none of the qubits were allowed to talk to each other that way um and yeah what i found was that um like yeah we 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 classically simulate it. I figured out what the algorithm was.

It was a huge process from that point to actually writing down the algorithm for sure. It really surprised me because I thought I was going to prove the opposite thing. The fact that we proved this instead actually makes me quite convinced now that entanglement is important. 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? 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 one of the state distillation protocols involves a five-qubit thing. And interestingly, state distillation is done by by cliffords so so this would have been like a particular property of like a particular five qubit sort of set of qubit of um cliffords have you studied much of quantum logic um no actually almost not at all yeah okay, 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 there's sort of two levels of computation that are relevant here. There's the level of like decidability. And so this is like what the halting problem is about and what girls and completeness theorem is like, you know, in a sense about. And that is like, okay, if you have a mathematical statement, 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 computational complexity point of view, which is like, okay, 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 the quantum versus classical difference really is. And since Godel's incompleteness theorem is on that side of purely about decidability, I would suspect that quantum logic doesn't change that outcome. doesn't change that outcome. 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. Now they're bringing that precision engineering to your shaving experience.

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problem? No, because a 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 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. 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 a quantum computer is stronger, 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 np or is there no relation? Yeah, yeah no no absolutely. So yeah like on the question of p equals np, the fact that p equals MP 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 right we would you know prove that p doesn't equal mp but for quantum computing to be better than um uh than um classical computing we we would have to like and to be able to prove that we'd have to find a problem outside of p that um a quantum computer can solve. But if that

problem existed, it probably is inside of NP. And so we've probably already proved P equals NP. And so, yeah, like it is a first step to proving that quantum computers are better than classical computers. And a first step to many things in computational complexity, which like, yeah, all depend on on assuming that's true so prime factorization that's an np correct um yes but it is not a hundred percent proved to not be in p that's the problem i see i see i see so no np problems have been proved to definitely not be in p okay as 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, certainly not complete because we don't suspect that quantum computers can solve NP complete problems. I don't know if you saw, maybe you already saw the video. It's Richard E. Borchards. 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 just, it's like better on what? It depends 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 he said it's like giving an intelligence test to an ant eater and showing that it's but 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 contrive the test to show that this particular I think that um 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 um like everything that a classical computer can do a quantum computer can do and we can we can write that algorithm like straight off the bat.

There's nothing like 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 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 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 with 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 Koch and Specker theorem?

And then what does it have to say about quantum contextuality? So I usually say Koch and Specker. So I'll say that. Sure, sure. I'm completely getting that wrong. Anyway, so the Koch and Specker 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, uh, no such things as superpositions. Like these, these particles are not doing like all possible things at once. Um, instead they are in one particular place doing one particular thing, but the way they act is very complicated. Um, like it can be, uh, like determined by a, um, you know, forces that like take into account all the possible things that they could be doing for example like so that's how bohemian mechanics works um and there was like quite a big push in

quantum foundations to like try and rule these theorems out um which isn't like totally possible because like yeah for example bohemian mechanics exists it exists like whether you like it or not. But what the Cauchy-Specker 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 Cauchy-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 want to, like 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 the quotient speckle theorem shows is that actually that isn't a good way to be thinking about that theorem, because if I had that same particle and instead of measuring it this way, like with a particular instrument this way, if I turn that instrument on its head and measured and then like did the sort of like in post, like figured out like what the spin should be. What do you mean you turn 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's spin up. But what we could do instead is we could turn it on its head. Okay, literal.

Yeah, literally turn it on its head. And now a particle that goes, am I going to get this right? Yeah. So now the same particle, if it was spin up, should go down. And so we would still say that's spin up, 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 um 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 um 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 like is not nice um the the response to the quotient specker theorem though in 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, none of the kind of variables that you can make from the Cauchon-Specker

theorem are real variables, 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 Kochen-Specker theorem?

So the Kochen-Specker theorem is a much more general theorem than that. Like, it... Well, the reason I'm asking, sorry, the reason I'm asking is because in that example, physics is invariant under rotations, translation, 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 yeah the quotient speck of theorem is like way more general um 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 um okay so uh decoherence is a very, on the surface, mundane thing about quantum mechanics. And it's just the fact that as you, like, as you, okay, 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, 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 like 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 um 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 um that so like yeah there's the the thing that's really nasty about quantum mechanics and like the 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 measurers 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 um 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 um whereas the the 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 um a phenomenological thing that comes from just the regular um mechanics. Like there is never measurement collapse. Instead, there's only superpositions. But because some parts of those superpositions become inaccessible to you as like you add

more particles and they all become entangled and then those particles fly off or whatever, you can't measure them. Your object that is still in a superposition now looks as if it's been measured and therefore like that is like measurement but it's not a real thing it's just a an emergent property does this have any implications for the many worlds interpretation yes absolutely um so many worlds uh people often take this um decoherence as like a sort of uh important an important ingredient in their theorem um but they're like many worlds i would say uh 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 um 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 it many worlds i feel like that's a misinterpretation um many worlds has nothing to do with measurement um it is what it says is if you have some objects in superposition um 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, superposition of up and down, you measure it. What that really means is you interact lots of particles, like lots of other particles with it, they decohere. To you, it will look as if the particle is, you know, spin up or spin down. But really what's happening is that there's still a superposition. And then you A 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 um i'm gonna 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 um that is like dependent on a quantum fluctuation uh like i can't see any of those worlds where i become

a model 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 um so the sun will inevitably burn out um 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 factors which couldn't go both ways.

And so that's also not a path to mortality. And how about this? Okay, Methuna is instantly recreated you're now 18 and like 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 just a poof version of mithuna that breaks the laws of physics somehow so the way that i'm imagining this is that there's a continuum of where the electron can be and then that is for every single electron in your body and then that is also for every single proton in your body and so on and so so you just transport yourself yeah so i think that

is a that this is like no different from um you know if i like because anything could uh sort of spontaneously um come into being right. Like, because, cause 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. um now it's it's a sort of philosophical question whether you count that as the Eiffel Tower is it the same thing right um and so like if a version of me just materializes randomly somewhere else in the galaxy uh is is that is that me um 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 there's no sort of contradiction there.

And also it doesn't grant me myself any immortality even if uh like this keeps happening do you think of yourself as the same person when you wake up yeah um 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 like remember even if it's inaccurately what it was like to be that person before like 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, like they, both of us imagine our past Middina

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 the block sphere is also discretized or is it

not it'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 that would be a problem no that would definitely be a problem um i was thinking of like if you uh discretized it as in like you don't allow it to be real numbers but you allow it to be any um like a rational number um 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

um 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 are have have a computational basis okay do you agree with that? And yeah, that sounds, that sounds a hundred percent like, I mean, I'm very biased as a person who, um, study quantum computing because like the reason why quantum computing is interesting to me is because I fundamentally accept that, um, 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 choice words to say about the volmium pilot wave theory. Okay, why do you not particularly like it? Oh, I do particularly like it. So I actually think that, 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, like, obviously true about quantum mechanics, Bohmian mechanics provides an excellent counterexample for. So it's something to, like, always be keeping in mind when you're talking about the foundations of quantum mechanics. And, yeah, like, I think it's an to like always be keeping in mind when you're talking about the foundations of quantum mechanics. And yeah, like 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 Eigenbrow'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 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 but 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 netto and struve i don't know if you you heard of them no okay okay well they show that with a bohmian interpretation you can have 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 Bohhmian 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 eigenbros podcast and i was

like where's and then they're like yeah it is non-renormalizable i'm like what yeah and i searched for this but i could yeah okay so there i don't know if I said non-normalizable, but definitely, like, the thing that I was thinking of was, like, that it is frame-dependent. So it has, like, a privileged frame of reference. I see, I see. Which is quite, like, not in the spirit of relativity. Yeah, yeah, yeah.

Even if it can reproduce the results. not in the spirit of of relative yeah yeah yeah 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 um 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 um that like if it had to have like a sort of privileged frame of reference that it would probably make the the math of it like kind of too hard to like be really workable um 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 are you like yeah i mean be it as it comes yeah no like i mean i i maybe should be one of those people who's 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 hammered 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, I feel like this is true, that the things that are true are beautiful because, like, the beauty of it is, like,

us recognising how, like, elegant and simple the solution is. And it feels it would just be weird for all this like complexity in the university to exist without some like very beautiful, elegant rules to have produced them. But of course it's like very possible. And I, you know, I don't hold onto it too strongly. 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 Ignotus 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 learn more about

to actually make a video about and 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 um 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, 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 Perth's, 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 such, yeah, this is really tough. Like I had the same problem many times when studying myself. Um, I think, uh, you, yeah, like in, in some ways being a beginner and getting stuck in these ways is like a real privilege and I know this sounds really weird to say but um like being a beginner and uh 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,entially, 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 where I need to be. So how do you get, how do you balance that, that tightrope of,

of having tenuous knowledge and, and strengthen deep knowledge? Okay. Yeah. So during my PhD, the thing I was just saying about the benefit of being a beginner, I tried to really take that to heart. 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, um, Conomera correction. Like

I'd heard about it in a lot of talks and I knew what the problem was. Um, 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. Cause I feel like there isn't that much benefit of having like a more than superficial knowledge 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 uh i tried to learn about um fermions and bosons in the context of computing um because there was like a bunch of really interesting results about like boson sampling and um fermionic linear optics and i wanted to like like i i knew about them but i wanted to go back to the basics like i wanted to understand what is a fermion? What is a boson? What have they got to do upon computing?

And so like, I really, really, really went back to like the absolute basics, spent ages on it. And I remember giving this presentation to my group and a few other people who are there, who were basically experts in the topic of like how this relates to computing and I was talking about something like super basic but even so like 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, like, not as 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 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 feinman method i'm sure you've heard where you teach yourself or you

pretend there's a third person 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 um i never read through a book uh like front to back um like i i never sort of want to get something from just one source instead i'll uh read one source kind of get like something from it um 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 um they might be using different notation they might be looking at it from a slightly different perspective sorry your your fans your photographer fans I know um yeah okay so yeah I'll never read I'll never read anything um front back instead 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 like be keeping a whole lot of notes where I'm basically trying to explain it to myself. Like 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. And then like, yeah, 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 find lectures better for than textbooks is to get an opinion from the person. Opinions during talks are so useful. You get the sort of sense of what this person thinks is the interesting parts of this field. 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 in position operators x and or the derivative if its 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 um no this is a

great question and it confused me for a long time um and and we've kind of realized much later that 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 are you like physically doing? So, you know, in the Stern-Gerlach experiment,

we're actually physically applying a magnetic field in the stone girl experiment um we're actually physically applying a magnetic field ultimately that's what we're doing um 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 this sort of like cheap trick of quantization where you take like 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 uh there we go that's my quantum operator for this this measurement of 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 an electron to have a different mass or charge. On the other hand, now that I say that, you could come up with an operator that measures the charge of a particle, just a random particle. operator that measures the charge of a particle, just a random particle. I have no clue what that operator would look like. I think you'd have to ask someone who actually does experiments. 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 that greater 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 thinking about it without relating? 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 this, 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, in, 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 uh the the thing on quantum mechanics i think that's not true like uh if you're learning quantum mechanics mathematically like you're trying to understand the math it's extremely important to relate what you are seeing there to what you know about classical mechanics um like we were just talking about how do you find the operators uh when you've got to know hamiltonian mechanics quite well, and that's from classical, the classical side. So okay, for your intuitions, yes, you have to let go of a lot you don't know. But for like the sort of machinery, often things are building on each other.

Michael McGuffin says, what has she been reading reading recently and then also part two is like if her financial incomes were met say she's given 10 million dollars what would you spend your time doing uh books and then time okay cool um thank you for those questions uh so um what am I reading I'm reading a few things um I recently finished a book by uh director of Pixar, Creativity Inc. And it was about how to create like a creative product 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 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 uh and then like i guess if someone was to give me uh 10 million dollars um there are a bunch of product projects that i'm um like you know interested in um like i'm very keen on like what on understanding what the future of education is going to be um i think that

there needs to be like even more research i mean there's like lots of great research at the moment but even more research and even more focus put into like how can we really change the way that humans learn um so that they are really like achieving their maximum human potential i think that schools are really wonderful um and i'm not one of those people who is like advocating for like just ripping it all down um but i think that they're inefficient in certain ways like they just have to be because of how they were sort of made and because of all the various pressures that are on schools um so i would love to understand like if we were going to make it from scratch um what what would we keep but what would we change have you heard of forgetting this

guy's name starts peter of the evolutionary institute peter peter gray that's right right okay so anyway have you heard of peter gray's unschooling i have but i'm blanking can you so it's not like tear down the schools, but what it's 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 the 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 instead of imposing one yeah so i think this this whole movement um of inquiry-based learning is very, very interesting, but also I think we have to be a little careful with it. 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 reign. 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 because you know you're not going to expect a child playing on their own to rediscover Mution's laws like that's just not possible but on the other hand if you had like a 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 is like, oh, have you read these interesting books? That could potentially work. I think that to make that work, we need to put a lot more thought into just how we can guide that experience without fully determining what the kid is going to do ourselves. Beers Attaju 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 in the oh that's disappointing because the person's like oh thank you dude oh sorry um wait who is this donald hoffman is a

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, 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. And I also realized that I have a question on 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 Deutsche's. Yes, yeah, that's correct. That's correct. That's correct. Yeah. Yeah, I think what I don't understand about that idea and what makes me skeptical of it is

that it's not clear how computation from distinct branches of the superposition can um be be transferred like how that information can be transferred um so like let's say you do uh like you 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 um it's like the way that that communication is done inside of quantum computing um it it depends on those superpositions not being um distinct worlds in the sort of many world sense

so you know in the many world sense um a super 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 like so if you have two if you have a if you have a superposition of two things um 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 reconvert reconvene so one way that this could happen is like if you have a spin particle um 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 spin up again. In 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. So yeah anyway. All right 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 view can be squared with what one actually observes. So what do you say to that? Yeah, I think that that is a, 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 and you get it to measure one of its partners it will say that its partner is zero or here if you 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 um 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 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, it 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 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 the world where everything is in state zero when i'm sorry i meant i meant why does mithuna mithuna sorry yeah believe in the many worlds interpretation if to, it seems like a religious choice because there's not evidence for it unless you just say, well, the math says. Exactly. So no, it's, it's back to that question of like, do I want a theory of the universe to be beautiful or not? I, my, my bias is very much towards beauty um and i think that many worlds

is a much more beautiful theorem uh theory rather um 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. It's not because of the evidence. Thank you so much. Thank you so much, thank you so much so what's next for you

um uh after this next youtube video um yeah uh well so the thing i've been thinking the most about is um how to improve online education i think that that's like a really uh like interesting and new medium um like people on youtube have done really wonderful things but i think like we can push it even further um so yeah that's the direction i hope to to like put myself um and like it's sad that i'm not doing physics research like i i miss it but i feel like this is higher impact like i feel like the world needs this more than, you know, the small bit of physics that I could have contributed. Wait, so are you more driven by that altruistic part of you

or the passion part of you that just wants to do research? Yeah, I think that, 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 with me and putting up with my sleepy questions oh good i'm sorry for oh no no no no it's it's all right it's all right i just for the for weeks and weeks like

weeks i haven't been getting enough sleep and so it's just yeah compiles and compiles yeah yeah and then i've been studying some quantum computing to prep for this. Oh, thanks so much. Well, I'm just going to ask this. 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.

Are they a way of, are they this, I know the graph states. So the way that i i understand graph states are like in particle physics there's the feynman diagrams and then there's rules to translate those to equations then 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'm curious, is there? Yeah, 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 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 um yeah that is a very good question and I 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 you