21. From Industry back to Academia: Mario Berta

00:50:08: Thoughts on entanglement Chris] We have lots of questions, but maybe we can like one of the key things in also quantum communication is entanglement. And you have worked a lot of a lot with this. Do you think we are still learning new things about entanglement? And is there like a new sort of discoveries of usage in multipartite systems? [Mario] Yeah, I think we're still learning a lot, at least on a kind of theory perspective. Even this year there has been quite a lot of exciting progress, I find. If this translates into, you know, applications, let's say for quantum internet or something like that, this is of course a little less clear, let's say. But I mean short answer is I think there is still a lot of progress partly because it's so kind of a poorly understood in some sense once you have multi-partite systems. [Chris] And you have this whole debate about post quantum cryptography and I guess some companies are now switching to that. But it's costly, right? Like how do you think Shor’s algorithm will be pushed into the NISQ era and there will be some things happening or is it right? I mean, from my experimental point of view, it looks like at least 10 years down the line or something until somebody does anything meaningful. That's optimistic. [Mario] Yes, probably. I mean, post quantum cryptography is mostly classical cryptography. It's not quantum safe. I mean, you can use also quantum solutions, but they're actually classical solutions kind of that we're happy with. And I mean, this is, even in some of the products they're using, this is, I think, in Chrome also, they use it at some point, like, you know, it works. It's fine. [Chris] We don't need the quantum internet to be safe against Shor’s algorithm. [Mario] That's at least our current understanding of things. So this is, if there is a strong incentive to make this transition; transitions always cost, but I think the technology is basically there if you would want to. Now, Shor, and short-term, I'm not sure how well this is understood, but I think generally, Shor is quite difficult to implement in a noise-resistant way. There are certain algorithms that are believed to be maybe more noise resistant or noise can even be like be made use of. Shor is not necessarily of that type. So I don't expect like any early applications to be going that direction. But maybe the last point to say is that of course, if you record all the conversations that are happening nowadays, you can decrypt them later. So that maybe gives you some urgency of changing your system. [Chris] That milk has already been spilled, let's say. [Mario] Yeah, but that's going to be very interesting like if you can listen to all the world wide whatever central intelligence conversation. [Chris] Yeah, I mean it's the story is that NSA somewhere in the desert or somewhere has some data centers where they're basically just sucking up the internet and putting it on hard disks right. [Mario] Yeah, exactly. And I mean, other countries are doing that as well probably. [Chris] So yeah, this is, yeah, I don't know. This is happening, certainly. 00:53:43On algorithms and algorithms benchmarking [Chris] Let’s switch to algorithms. What’s your favorite quantum algorithm, like softball? [Mario] My favorite quantum algorithm. Well, they are the ones that are very elegant, let's say, and cool. But recently, I think a very important development has been made around quantum Gibbs samplers. So you want to basically create thermal states of quantum many-body systems. So not the ground state at zero temperature, but at some non-zero temperature. And then the question is how you can do that efficiently or more efficiently, like learn stuff about these Gibbs states. And there has been a lot of progress last year and this year on this question. I think this is currently the most exciting avenue to explore further. Not necessarily because we already know it's very good, it's just, it's promising and not explored enough yet. So that's maybe currently my favorite. [Mira] Part of your work also involves benchmarking these quantum algorithms. How important are classical simulations for this? [Mario] Yes, you can benchmark in different ways. You can either run your algorithm actually on a quantum computer. So if you don't do it in a very smart way, you only see noise. You can run it on a simulator of a quantum computer. And then, of course, classical computations are very important. So these simulations would maybe be mostly for typical use case analysis that you try to simulate. But it’s very restricted in the sense that you can only look at a very small instance sizes. But then a lot of the benchmarking is more of a resource analysis like you don't actually run the algorithm you just like count how many quantum gates or elementary steps you think you will need and what type of gates. And then that gives you kind of an estimate, you know, if you want to - with this quantum algorithm - solve a problem that is classically hard, that maybe you can't solve classically, it gives you an estimate of like how many gates you need, like how powerful your hardware needs to be. And of course they also need classical computers but you don't actually simulate the algorithm; you just kind of try to estimate how many gates you would need to actually run it. [Chris] So when you work on these things do you work on the fully abstract level or do you think already about gate sets and like compiling the algorithm? [Mario] There you can go down the chain as far as you want or you don't want, but what I'm familiar with is the quantum circuit model. So there you count elementary gates, but then of course people make this distinction between Clifford and non-Clifford gates and that's basically how far we would go. So they are the type of like easy quantum gates or clipper gates and the non-clipper gates. [Chris] This is basically due to error correction like I mean essentially the reason we call Clifford easy is because we think that error correction will be Clifford. [Mario] Yes, this already makes a lot of assumptions about your system architecture, indeed, but it doesn't make assumptions about the concrete way you realize it, right? So then you would count these non-Clifford gates, and this is usually the number you use, like, okay, you need 10 to the 6 of those, and this gives you an estimate on how many qubits you need and stuff like that, but this is how far down the chain I would usually go. This is not necessarily very near-term relevant, I should add. But I think it gives you good pointers like where you should look for quantum advantage, like realistic quantum advantage, like in the long run. And this is the whole reason, you know, billions are poured into this field. And so that's why I think these are useful pointers. 00:57:33The Quantum Algorithm Zoo [Chris] Yeah, one of the projects you've been involved with here is this sort of big review article on quantum algorithms. How was it to put together; that was originally this website “the quantum algorithm zoo”, but you guys are now making it more concrete writing more details and you have really a big group of theorists to look into this. How did this come together? [Mario] Yeah, there are, of course, a lot of things I could say about that. So, it started when I was at Amazon. And basically, it started out of very many negative results, right? Because we're told by management, you have to look at good algorithms for quantum advantage, like in practice for problems of relevance, whatever. So we look at A, B, C, D, and it would actually maybe invest significant time to understand it much better, but then it would always be like maybe there's some quantum advantage somewhere, but not for what we call end-to-end complexity, right? So you have a certain problem that you want to solve in industry or whatever. And then in the end, you have a whole chain of computations. And in the end, you want the results, like usually classical thing, like a number. And then you need to count all the computational resources used in between. And the question is, if you replace some of these resources with some type of quantum versions, does it help? And if you make that kind of analysis, let's say it's very challenging to find good algorithms, good problems for quantum algorithms. And so then we internally started writing these things up, and that's how it started actually and then it got bigger and bigger, and the idea was actually originally to have a Wikipedia-like kind of thing. And it's different from this quantum algorithm zoo, because the quantum algorithm zoo just focuses on this complex theoretical results for certain subroutines, right? So you have a certain mathematical problem; you can solve it that well with quantum algorithms. But this is not in this end-to-end fashion, in the sense that down this chain of computations maybe you have some subroutine for which quantum is good, but you know, you don't look at it holistically. For example, one of quantum algorithms also looks only looks at it in terms of computational cost, but you know, computer is not only the CPU, right? You have like, maybe GPU, then you have quantum version, you have RAM, you have quantum RAM. You have to look at all the resources. So that's kind of what we're trying to do in this review article. First on the kind of primitives and then really the application side. But yeah, once I left Amazon, I was no longer in charge. I mean, first I was in charge, but then I left and so all the people took over. I was still part of the team, of course. But yeah, it was a mess, as you can imagine, right? And also the next difficulty is that new results come out all the time. So you have to do like a cutoff at some point. But I think it's a very, very valuable resource and the hope or the goal of this is to guide the broader scientific community, especially in industry also to work on the right type of problem that really promise long-term progress. [Chris] It's written not only for physicists but also for people who are just more generally interested in algorithms. [Mario] It's a technical document so it's in that sense for specialists but you have like gazillions of startups that work on algorithms; for people like that maybe don't work on these, there's no long-term promise; like look at these problems these are usually hard problems but if you tell people explicitly this is not leading anywhere look at this instead, I think this can be a good very good service for the community. 01:01:17Thoughts on scalability [Mira] You mentioned that new things keep coming up. So this year also has been really great in terms of, hardware development in quantum computing and things like that. So could you comment on complexity versus scalability for today's architecture and what's your prediction for the skeptics? [Mario] Yes, so I think you recently also had Markus Müller, right, on this podcast? And you should probably ask him about the hardware breakthroughs and the scalability of those. [Mira] But in terms of applying quantum algorithms to now use this. [Mario]The devices, actually. Yes, yes. I mean, we barely have one logical qubit, right? And we can't do any computations on it. So in that sense, we can't do any logical computation at all yet, right? But that's not necessarily the message I want to give. It's kind of hard to say because there are also these competing technologies, right? And then I think certain technologies go to point X, but maybe not further, unless you have an additional scientific breakthrough. I think this is kind of an interesting way of measuring it. These people that develop hardware, do they believe with their current ideas and technologies, how far can they push it? And how far they think they cannot push it? Because then some other effect pops up and you need to fundamentally do things differently. And I think right now with these ideas, you can still push considerably, which is very nice. But there's still a huge gap right between actual hardware and what the complexity theories talk about and then the question is also do you want to do a quantum computation that is classically hard that you cannot do on a classical device because then. We're talking for our future. Or are you just happy to do some logical computations like some proof of principles? This might be sooner. 01:03:26Promising quantum linear algebra type of algorithms [Chris] So there's a lot of algorithms that are sort of sub-exponential but related to generic linear algebra problems because there's a link between quantum mechanics and linear algebra from doing the review of all the algorithms is there things that stick out to you do you think there's potential there? [Mario] Yeah, this is kind of an involved question, I guess, because there's a lot of different types of quantum linear algebra type of algorithm. But I will say that I think it's very challenging to find significant quantum speed up compared to, like, state-of-the-art classical methods. Both in terms of theory and asymptotic complexities as well as in terms of actual finite size relevant instances kind of performance. The thing is just because of the error correction overhead you need large quantum advantages for them to become relevant in any reasonable kind of time frame and this is very challenging. I think there is this kind of wisdom out there in the community that you need at least a super quadratic speed up; this is the threshold in the sense that quadratic is on the one hand relatively generically available. So if you have a quartic speed over something you might already be happy. But even that is very rare and usually if people find something like that then it's also because it's such a contrived problem and instance that you know classical algorithms have not been sufficiently looked at for that problem. So it's actually quite cool sometimes to find a quantum algorithm; people find a classical one and I mean there's good progress but the pattern I see is that people make good proposals and a lot of smart people look into the problem a lot. Then we learn a lot about it but often the message is actually quantum has a small speed up but not that useful. [Chris] And sometimes people have even discovered that the sort of quantum speed up can be implemented completely classically as well. [Mario] That can also happen. I think scientifically - again, this is a great adventure. We learn a lot, right? It's very productive. [Mira] Yes. [Chris] It's also one of the reasons why academia is maybe a good place to be in that sense, because if you work in industry, ultimately they want you to find these holy grail applications. [Mario] Yes, I mean, especially these big tech companies, right? They are known for pouring tens of billions into something and then one day to another they don't feel like it anymore so that can happen. I do feel though that in academia it's taxpayers’ money in the end so we need to really justify what we're doing versus in industry it’s some shareholders that lost this money then I care less [Chris] Maybe we can also just build in this quick disclaimer about NP hard problems and so on and traveling salesman like I don't know what you think about this but there's sort of still even though there's very little evidence people are still saying you know quantum computing will solve logistic logistical challenges. [Mario] Yeah I mean there's the wisdom that probably we can't find super polynomial quantum speed-ups for NP-hard problems. I think people don't think that this is the case so there's no like one-for-all solution. If your optimization problem has a very specific structure, maybe quantum computers are good. It's just that if you simulate physical systems, then you have certain structure and maybe quantum is amenable to that, but if you just look at kind of general linear algebra problem, general optimization problem, it might have nothing to do with quantum at first. Maybe it's a less good structure for quantum, but you really, you have to work on that. You cannot just say it's going to be good. You really, you have to tell me why, right? It's not enough to just have this kind of wishful thinking here. 01:07:45On the mathematics of quantum information [Mira] So we can talk a little about the mathematics of quantum information. First of all, do you think there is such a thing as an atomic unit of information? [Mario] Yes. I mean, there's the unit of information which is in classical physics. It's a bit and in quantum it's a qubit. So in that sense, there is such a unit. But of course, one of the interesting findings of quantum is that this unit depends on the underlying physics. So Shannon's idea was that you can kind of define information independent of its physical representation. But it was implicitly also assuming that it's independent of the physical theory behind it. But now is nowadays knowledge that it's actually not independent of the physics of whatever physics you take you can define this unit of information. I'm not sure what other philosophical implications come with that word. But yeah, I mean, the interesting part is the quantum unit of information is fundamentally different than the classical one in many aspects. [Chris] We have quantum mechanics, and it is sort of this generalization of probability theory. But like when quantum mechanics was discovered, the math for it was sort of to a large extent there. Do you think in this whole pushing for mathematical quantum information, we are discovering some of the properties of this math? But sort of the framework, complex numbers, linear algebra, it was all sort of readily available, right? And we're now moving around in it. What is your feeling for this? [Mario] So back then I think there are objects called von Neumann algebras, right? They were introduced by von Neumann partly because of quantum theory. So some math, at least in this very general abstract sense, was developed also because of the discovery of quantum mechanics. But then given that we mostly work within the framework, just the mathematical rules of quantum mechanics, right? We explore those, maybe we understand more aspects of it, or more consequences, but we rarely go outside. But there was a couple of years ago now this interesting result, right? I'm not sure if this is published by now, probably still not, but that is operator algebra theory. That is con embedding, conjecture, whatever is wrong. And this was work out of quantum information, so to speak. So, I think there is kind of a back action also to mathematics again. And for example, also the mathematical physics community, like the old school mathematical physics community, they are very interested in quantum information. So it's interesting in that sense. And it also goes both ways, I would say. [Mira] You actually work in a way that's very close to mathematics with lemmas and theorems. What do people who look at quantum mechanics this way see that others might miss? [Mario] Well, I'm not sure. I mean, usually, there's a whole spectrum of physicists, you know, experimentalists, and more like applied hands-on physicists, and then you get more and more theory and mathematics. And then what people always joke is if you're really a mathematical physicist, everyone already knows how it works. But then in the very end, you know, the mathematical physics can also prove it, right? So what did you actually learn from that? I mean, it's a good question, you might ask. In certain settings. Like some people try to prove that atoms are stable. If you want to prove that rigorously from first principles, you can only do it for very small atoms and molecules. When you do stuff like that, you can ask what do you actually learn? Of course, you learn mathematical things. But I think when you talk more about these foundational aspects and what is the very core of information, what are the ultimate limits of information processing, you can really gain some insights by fully formalizing things. And often what also happens is that if it's come up with some idea, some conjecture, they seem certain phenomena for certain systems, but then you want to put this in a whole framework and prove things as general as you can. think you bring in a lot of structure to the situation, to the knowledge. But it is true that it's more on the rare side that new physics will be discovered because of mathematical prediction. There are examples, but often it goes the other way. I acknowledge that. 01:12:50The story of revisiting Stein’s lemma [Chris] We are running towards the end of the podcast, but we can just very quickly - because we wanted to give an example - there's this Stein's lemma and there's been a lot of recent debate and you wrote a comment I believe on it. So can we just very quickly tell the story and maybe on the one hand it is mathematical, but on the other hand it's also related to many concrete problems, right? [Mario] Yes. So there was many years ago, I guess 15 years ago or so, there has been this kind of well-known result on entanglement testing, which is called quantum Stein's lemma. The reason people are very interested in that, it's around the question if entanglement transformations are reversible. So if you have a certain state, maybe maximum entangled, another one, maybe less entangled, like when can you convert one state to another and back? This is like kind of the general framework and it has this connection to quantum hypothesis testing, to quantum statistics and this goes under this name Stein's lemma. So it's about understanding entanglement. So, there was this series of papers in Communication Mathematical Physics which is a very prestigious journal in Mathematical Physics. And there were multiple papers in Nature Physics also, which obviously is a high-impact journal. These papers are very difficult to understand and I think very few people even tried including myself. Actually I spent two years in London with a postdoc trying to understand some of these things and we just couldn't. We couldn't see the proof. This was just out there but people were using these results all the time. And then at some point there was another group that wrote a follow-up paper on the original works, that used these original results in a certain way. And then we went through this follow-up work. And this just seemed to be wrong. Like the implications seemed to be too strong. And then we went back, basically. And then one day I got up in California, and my collaborator Marco Tommamichael in Singapore, he had this like counter example to the proof. And then everything kind of fell apart. So the papers were just – the proofs are wrong. And this was kind of a big thing in the community. Lots of interesting things happen. Also, what do the journals do? What do the editors do of these papers that are peer-reviewed? What happens, right? There were like important people on these papers. Anyway, then, there were a couple of papers written. We wrote a note also and a comment in Nature Physics about the situation. But then, luckily this year there are two solutions to the original problem that appeared that seemed to be correct. So it's fixed now, if you want. [Chris] So, the lemma stands, the original proof didn't. [Mario] The original proof didn't, yes. Exactly. And it's a very also socially interesting situation, right? You can kind of question the whole publication, peer-review system. And because what often happens is actually papers are slightly wrong, but it's always fixable. And then people are always like, okay, I know this is wrong, but you know, we can do it a bit differently. But in this case, it wasn't. So this is why I had big implications for once. It was a nice communication in the sense that people were open about it, and it ultimately led to good scientific progress. So in that sense it's a happy end, at least for science. But yeah, I think there are lots of questions that one should ask, right? How were all these papers peer reviewed and no one noticed mistakes? It's kind of a simple mistake, you know. [Chris] Yeah, I think, I mean, we have this in experimental physics as well, that, you know, there was lots of scandals recently, also in the quantum information field. And I mean, there it was much more serious. It was not mistakes, but even, you know, problematic practices, let's say. Maybe not fraud, but you know, at least problematic practices in the science. And I think the problem is peer review, you know, in the end, somebody gets a paper and maybe has a week to spend on it, right? And if you have a complicated mathematical proof, maybe you would need a month or...  [Mario] Yeah, so this is actually also a problem because the field is so interdisciplinary, right? Because, for example, in math or mathematical physics, it's not uncommon to have 12 months’ time to review a paper you get 12 months like a year like this is normal because you need a time. You want to invest that time and now everything is mingled and you have these math papers and people anyway don't review them. It's challenging of course. It's a bigger question about the whole publication system, but I think it's interesting. And all the original papers are wrong. They're still online. I mean take from that whatever you want. [Chris] I mean, another problem. Indeed. I mean, the journals are very slow to like, if even if you want to fix your own work, I mean, if you want to ask, ah, can we please, you know, change these, uh, this formula? We made some typo. It takes a while, right? Like these journals are not fast. [Mario] Some even don't do it. So I have other papers. I know they're wrong. I'm like, okay, I made a mistake. I want to let you retract it. They say no, addendum erratum impossible. Sorry. So this is not something that was thought about properly. I also don't have like immediate solutions, but something we could think about also as a community. 01:18:36Interested in joining Mario’s group? [Mira] So before we come to the end, I just also want to, since you have joined recently at RWTH as a professor and you're growing your group, do you have any positions you'd like to advertise? [Mario] We have open positions at any level. I mean, like Bachelor, Master, PhD or postdoc. It has to fit, of course. I think I also have a call on my homepage, but I encourage people to send me their documents and I would get back to them if I think I see a good fit for an interview. That would be great. I am always looking for people. Thank you. [Chris] So Mario, thanks a lot for being on the podcast. [Mario] Yeah, thank you guys. That was very nice.