# S2E1: Dual-Unitary Circuits with Dr Pieter Claeys

*What are exactly solvable quantum systems, and why are they interesting? Take a listen to Season 2, Episode 1 of insideQuantum to find out!*

*This week we’re featuring Dr Pieter Claeys, a research group leader in the Dynamics of Quantum Information Group at the Max Planck Institute for the Physics of Complex Systems in Dresden. Pieter obtained his PhD from the University of Ghent, with a brief stay at the University of Amsterdam, and completed postdoctoral positions at Boston University and the University of Cambridge before taking up his current role.*

π’ **Steven Thomson** (00:06):
Hi there and welcome to insideQuantum, the podcast telling the human stories behind the latest developments in quantum technologies. I’m Dr Steven Thomson, and as usual, I’ll be your host for this episode.

(00:16): In previous episodes, we’ve talked a lot about quantum information and quantum computing, but before we can manipulate and prepare quantum states in experiments or future technologies, we first have to understand their complex properties. For example, how does quantum information move through a many-body quantum system, and how can we protect quantum information and make sure it’s preserved for long time periods? Today we’re going to take a deep dive into the math of quantum theory and discuss some cutting edge fundamental research. It’s a pleasure to welcome Dr Pieter Claeys, a research group leader in the Dynamics of Quantum Information Group at the Max Planck Institute for the Physics of Complex Systems in Dresden. Hi Pieter, and thank you so much for joining us today.

π£ **Pieter Claeys** (00:55):
Thanks all for having me here, both here on the podcast and here physically in Berlin.

π’ **Steven Thomson** (00:59):
It’s great to have you here. So before we get into the mathematical depths of quantum theory, let’s first talk about your journey to this point and let’s start right back at the very beginning. What first got you interested in quantum physics?

π£ **Pieter Claeys** (01:12):
Yeah, so I think I arrived at quantum physics a bit later than most of your usual guests. So in fact, when I went to university, it wasn’t my intention to start studying physics and at that point I wasn’t even aware of the existence of quantum physics. So rather I went to the university to study civil engineering because that’s very much the standard option for students in Belgium, if they’re good at maths, to just go study civil engineering is the pragmatic choice. And then during the first year I actually got some physics courses and I found that I enjoyed those so much more than the actual engineering courses, which then made me decide to switch to engineering physics in the second year. Then I gradually moved away from that to just purely theoretical physics. So it’s been a very gradual slope. And I think also one of the reasons I chose to move into engineering physics is that I saw the courses and I saw that one of the courses was quantum physics. All of the other courses I had some idea of what we were going to be studying, like okay, electronics, programming, that’s fine. But then I just saw quantum physics and I was like, okay, I don’t know what this is and I really want to know what it is. And then fortunately I found out that I really enjoyed it and was really fascinated by it and just wanted to keep learning more about it.

π’ **Steven Thomson** (02:16):
That’s really interesting because as you say, I think a lot of our guests were on physics degrees already and they were exposed to quantum physics kind of gradually from other courses, from other directions. But it sounds like in your case it just sounded like a cool thing and you wanted to know more about it.

π£ **Pieter Claeys** (02:30):
Yes, exactly. And then of course I needed to catch up because I didn’t have all of the background already, but then I spent a lot of my time in university just reading more about quantum physics and about physics in general, which I think is both an advantage and a disadvantage because also I ended up getting an engineering physics degree. So a lot of the fundamental courses that people in a physics degree have had I have not had. But I also feel like because of that engineering, I have a very useful and mathematical background which turn out to be very useful then in my actual research. So it’s quite nice that I think this has given me a slightly different view of physics than other otherwise would’ve had.

π’ **Steven Thomson** (03:04):
So what made you decide to go on to study quantum physics in your PhD in a bit more detail?

π£ **Pieter Claeys** (03:10):
I think it’s mainly that I just wanted to understand quantum physics better. It was really one of the courses that I enjoyed most and I just felt like there was so much still left to learn because I had actually seen very little about quantum many-body physics during my studies and I wanted to learn more about that. So I decided to do my master’s thesis on quantum many-body physics. And then at the end of the thesis I found out that I was actually also really enjoying doing this research and I was a very natural choice to continue doing that in a PhD, which was much more of the desire to just keep learning rather than actually having a strong desire to do research, which I now have, but it wasn’t there at the start.

π’ **Steven Thomson** (03:49):
Was it difficult to find someone to take you on to do a quantum physics PhD when your undergraduate degree wasn’t already in quantum physics?

π£ **Pieter Claeys** (03:56):
No, because we actually had quite a lot of quantum courses during my studies, because also we also had a lot of courses on molecular modeling where quantum physics is quite important, but then just come at it from a more pragmatic point of view. So I then just ended up doing my master thesis with one of those professors and then I had enough of a background in quantum physics to continue doing that during my PhD.

π’ **Steven Thomson** (04:14):
And if you hadn’t gone down that route and if you weren’t doing your current job, what do you think you would’ve done instead?

π£ **Pieter Claeys** (04:20):
I think I still probably still would’ve ended up in research. So I think I also asked myself this question and I basically saw two options either working through machine learning, where I think there’s a lot of really fascinating research going on at the moment and it’s moving so quickly that it would be fascinating just to learn more about that. Then of course, this doesn’t guarantee that I would actually be able to contribute anything. There are some connections with physics, but also that doesn’t guarantee anything. I think the alternate option would be to work in a quantum startup, which again is a field that has recently been, has had a massive development and there’s so many exciting things going on there, and I think if you would’ve just told me five years ago what was possible now, I probably wouldn’t have believed it. So it’s very exciting there. I mean, of course there’s so many quantum startups and I think you also need to be a bit selective in which ones you choose to go work for, invest in or pay attention to, but they’re definitely a lot of very good ones out there.

π’ **Steven Thomson** (05:18):
Yeah, it’s interesting that you say that because it seems like at the moment if you’re finishing a PhD or a first postdoc and then you have this decision between do I want to go into academia or do I want to go into industry? Even five, six years ago, the options in industry, they didn’t seem so good at the time, but now there are so many more options all doing such interesting things and you still get to publish and you still get to go to conferences and it just seems like industry is a much, much bigger draw now for early career quantum physicists than I think it was five or six years ago when I finished my PhD at least. And it’s really interesting to see the way that things have evolved and as you say very, very quickly. The landscape of quantum physics has dramatically changed from being just this academia focused thing to suddenly, as you say, it’s so many startups.

π£ **Pieter Claeys** (06:10):
Yes, I think it’s a really positive development both for academia and for industry because as you mentioned right now, if you’re finishing your PhD or if you’re finishing your first postdoc, I think it’s very good to realise that you actually have options because otherwise it can be a very stressful choice and it’s not always easy to stay in academia. There’s a lot of uncertainty there. So I think that way if you know that you have very good alternatives, I think that makes it easier to deal with this uncertainty of being in academia because that, you know, okay, even if I don’t have another postdoc, even if I don’t get position somewhere, I will still get to find a job that I really enjoy. And I think that makes it a lot easier to deal with all of this uncertainty that you usually have in academia.

π’ **Steven Thomson** (06:50):
Yeah, definitely. And I guess also a job where you can use the skillset that you’ve developed, because quite often people come out of PhDs with a…okay, you have a quite a wide range of transferrable skills, but if you’re an expert in one particular, I dunno, numerical method or analytical method, it is kind of hard to know what job can I do where I get to use these particular skills? And now it does seem like there are many more industry roles where that do value these skills. So programming, many body quantum physics algorithms, for example, things like this that now you can still use these skills from your PhD or your postdoc in industry. And I think that’s been a really interesting development to see.

π£ **Pieter Claeys** (07:26):
Yeah, I completely agree. And of course during my PhD I also always heard like, oh, you have these transferable skills. If you choose leave academia, they’re going to be very useful, but I had no idea what these were. Now of course now it’s a bit more apparent if you have some more experience, but at that time it’s a completely meaningless thing to say. Now you can actually see, okay, yes, I have experience with these algorithms. I know what these circuits look like. I can say run a simulation on IBM’s quantum computer and you can see, okay, this is a skill I can actually use as of academia, which think it’s incredibly useful. And also apart from that, I really feel that a lot of developments in the industry have recently been steering a lot of fundamental research because I think as has been brought up in a lot of the podcasts here, there’s been such developments in quantum computing setups, say by IBM, say by Google, that I don’t think would’ve been possible in academic settings just because they have so much more money to throw at this problem. And that way you can actually get the hardware, which can then in turn be used by people doing fundamental research and stimulate research in academia.

π’ **Steven Thomson** (08:28):
Yeah, that’s true. That’s true. There’s a really interesting feedback loop that has developed between academia and industry. Okay, so let’s talk a little bit about your own research then. And to start off with, can you give us a summary of what kind of field you work in? What’s the big picture goal of your field?

π£ **Pieter Claeys** (08:48):
Yes. So the overall field that I work in is condensed matter physics, which is really concerned with the notion of emergent phenomena where you have a lot of particles that interact in very simple ways, but then when you put them all together, you can get some behavior where the hole already behaves completely different than you would expect just from the microscopic phenomena, just from microscopic interactions. And so that way you can get much more interesting behavior then you would naturally expect. And so I’m of course interested in what happens in quantum systems and right now my focus is really on what happens if you take systems consisting of a lot of quantum particles, you have them interact in some way and you keep them out of equilibrium, so you never allow them to relax to a steady state, to equilibrium, and you just see what the dynamics is there and there’s such a rich variety of possible dynamical behavior you can have.

(09:36): There’s an entire zoo. And so lots of the research in my field is very concerned with trying to better understand and predict and control all these different dynamical behaviors. I think I once heard a quote that was basically riffing on this quote by Tolstoy who starts on Anna Karenina by saying, I think “All happy families are happy in the same way, but all unhappy families are unhappy in different ways”. I think it’s the same thing for out of equilibrium quantum systems - all equilibrium systems, they’re the same, they’re boring, they’re all in equilibrium in the same way. But then the moment you go to out equilibrium systems, there’s so many different things you can have and it’s real challenge trying to understand everything that could possibly happen.

π’ **Steven Thomson** (10:15):
I really like that way of looking at it.

π£ **Pieter Claeys** (10:18):
And then the way I’m currently trying to understand this many body dynamics is by really trying to come up with simple, minimal models that somehow capture a lot of the qualitative behavior that you would expect. So you really want to find some toy model, very simple as in simple enough that you can still understand, you can still analyze it and make some qualitative predictions, but at the same time complex enough that it actually reproduces something non, something interesting. And so it’s always trying to find that fine line and finding these new models that we can analyze and then that we can then use to understand what’s actually going on. And a lot of these models recently that I’ve been using have been inspired by developments in quantum computing or for example, using unitary circuits, which are one of the fundamental models of quantum computing.

π’ **Steven Thomson** (11:01):
I see, okay. So you’re really looking for this balance between something that’s complex enough to be interesting but not so complex that it’s impossible to learn anything about it?

π£ **Pieter Claeys** (11:10):
Yes, exactly. Because one of the things that I found really daunting the moment I moved into research is that you have all these extremely interesting problems and they’re just too big. There’s no way to tackle them. You just can say, okay, it would be really interesting if we understand this, but then you have no idea how to actually proceed. So I’m kind of starting from the opposite direction that I’m really just trying to kind of manufacture problems and setups in a way that I still know how to analyze.

π’ **Steven Thomson** (11:37):
I see. Okay. So what would you say is the biggest outstanding challenge in your field at the moment?

π£ **Pieter Claeys** (11:46):
So I think right now it’s not much of…okay, right now I’m thinking of something that’s much more of an actual possibility rather than a challenge. There have been these massive developments in quantum computing, quantum software, and even if those don’t really allow us to do any significant quantum calculations, so they’re not useful as computers. What we do have is quantum systems where we have incredible control and we have a large amount of interacting particles where we can really probe all the quantum effects. And I think right now one of the challenges or one of the things that we should really be focusing on is trying to find ways of basically using these to probe fundamental physics and come up with setups where we can really try to probe, say some anomalous physics or something interesting in a way that would not have been possible before. I think Google has been really leading the way there. They had these experiments on scrambling, they did their research on time crystals. Of course there’s also been studies on of, for example, transport in IBM’s quantum computer. So there are a lot of really interesting things going on there, and I think this is one direction that we should really keep moving in.

π’ **Steven Thomson** (12:54):
I mean that’s certainly something that I agree with. Using these systems for, I guess what we’d call quantum simulation seems like a really exciting thing now that we have all this control, as you mentioned, now that we can really tailor these quantum systems to behave in particular ways, particularly interesting ways. I agree with you, that seems like a hugely exciting development and a hugely exciting opportunity.

π£ **Pieter Claeys** (13:13):
And it’s also extremely motivating because I started out as a theoretical physicist - okay, not started out, I still am a theoretical physicist, so all of my experience with quantum was just, okay, this mathematical formalism. It’s beautiful, it works really well, but now you can actually apply this in a very systematic way and you can just probe it yourself and you know that there are some quantum effects somewhere. So I feel like it, it’s made a lot of our research so much more tangible, which is incredibly encouraging I think.

π’ **Steven Thomson** (13:41):
Yeah, it’s nice to know that what we work on is actually real, not just pretty math for the sake of it.

π£ **Pieter Claeys** (13:48):
Not just some massive prank that someone has pulled on us.

π’ **Steven Thomson** (13:50):
Yeah! Okay. So if I were to summarize all of your work in a single oversimplified phrase, I might say something like “exactly solvable quantum systems”. So what does it mean for something to be exactly solvable and why are examples of exactly solvable models so hard to find?

π£ **Pieter Claeys** (14:13):
That’s a really good question and also a very hard one to answer. So let me just first focus on the first question. So what does it mean for something to be exactly solvable? What isn’t an exactly solvable system? Because this is a purely mathematical notion. And I think there are many ways to answer this. I think there’s one superficial answer and that’s that a model is exactly solvable if we can calculate some properties of this model that we otherwise wouldn’t be able to calculate, and that works, but also it’s completely meaningless because in principle, all quantum systems are solvable. We know should an equation can essentially just follow a recipe, you take your Hamiltonian, you write down a matrix, you diagonalize it, and then all the information you could possibly want is encoded in the eigenvalues and eigenstates. So we know how to solve quantum systems, but in practice this, it’s very impractical and really impossible for many body systems.

(15:07): So if you have a few body system, we can easily do that. Say if you have the single qubit, that’s an exactly solvable model, two qubits maybe. Then as you go on and on, these equations…they just become exponentially harder to solve. And so then what people typically mean by saying exactly solvable, that’s a property of many body systems that you can somehow find these eigenstates and eigenvalues or you can find some properties and calculate them in a way that does not scale exponentially with, say, your system size. So in a way, in these exactly solvable models, we’ve reduced exponential complexity of quantum dynamics or the quantum many-body problem to polynominal complexity or something smaller. So that’s just a very mathematical answer because it doesn’t tell us anything about the physics that go that’s going on. And of course, if you want say that your system is exactly solvable, you also want this to have some physical meaning and not say that okay, we know how to solve it, which is also a very arbitrary definition.

(16:01): It might be that somebody is able to solve this problem and somebody else is not. So then what does this mean? So the question then is typically if there’s some exact solvability, it does hint at really interesting underlying physics and then that’s what you need to pinpoint. So for example, there are these different ways being of being exactly solvable, and these then typically translate to different physical consequences. And I think one of the examples of an exactly solve models are integrable models, which people have studied almost since the advent of quantum mechanics. And there again you have these mathematical properties that goes hand in hand with some physical properties. Mathematically, what it’s basically saying is that we know how to calculate eigenstates in a way that scales polynomially with system size rather than exponentially. So we can do this very efficiently. And in that sense these systems are solvable, but then it’s only one part of the equation.

(16:55): And the other thing that you find is that if you have this property, what you’re always also going to be having is conserved quantities. So you have some conservation laws in your system, so usually you have conservation of say energy, say momentum, and these models you have many more conserved quantities, which are in a way a direct consequence of the fact that these models actually support infinitely long lived particles. So you have a very clear, not a quasiparticle but actually a particle picture in describing these systems. And then that very strongly constrains your dynamics because you can just describe in term of particles moving around and scattering, and then the moment you understand that, you actually understand the physics of the system. So I think it’s always quite challenging. And basically the most interesting part here is to translate all of these mathematical notions that you have to what’s actually going on in the physics. And that’s something where…so these integral systems, they have existed for a long time, but I really think there’s also been very interesting developments there in the past because people now have access to computers and are able to do much more simulations. And also we have this advent of, for example, generalized hydrodynamics that also really allows us to probe the dynamics in a much more interesting way. And can also get realized in, for example, experiments and quantum simulation.

π’ **Steven Thomson** (18:05):
So integrable systems, the idea is that because they have so many conserved quantities, more conserved quantities than a generic model might, this means that their dynamics are much more constrained and this gives a pathway to solving and understanding them. Do integrable systems exist in nature or are they an example of the kind of toy model that you mentioned, something that’s complex enough to do something interesting but still simple enough to solve?

π£ **Pieter Claeys** (18:30):
So I think a lot of the models you encounter are almost integrable, and that’s also I think one of the crucial or the most important questions in integrability is that you need to know or need to understand how you can use this as a starting point to understand more general dynamics. Because a lot of the concepts that get introduced in the study of integrable systems, you can then apply in a much wider range of systems and they really give you some intuition that I think is always going to be useful. I think one other example is that integrable systems, they’re very hard to find in nature, but that’s not what you would think if you just open a physics textbooks or follow physics courses because then every physical model you’re going to encounter its exactly solvable, so it’s going to be integrable. And then by studying those, you gain the intuition, you understand what’s going on. And then of course you need to know, okay, where does this intuition hold? When does it no longer apply? Which is also very much the case with studying quantum mechanics in general that you need to know where does my intuition hold and when does this really make any sense to me? But say that’s what it is.

π’ **Steven Thomson** (19:29):
I see, okay. So even though a totally generic system might not be integrable, there’s still some aspects of it that you can understand by studying integrable systems and figuring out which ones you can and can’t understand. That’s the value.

π£ **Pieter Claeys** (19:41):
Yes, exactly. And also these models are just very interesting to study in and of themselves because the dynamics you get, they can be very interesting. They’re not going to be generic in the usual sense, which I think is also an opportunity for physicists because since they behave differently, it means we might be able to find some physics there we otherwise would not be able to observe.

π’ **Steven Thomson** (19:59):
One of the other things you’ve worked on in recent years that I think you mentioned in an earlier answer are dual unitary models. Can you tell us a bit more about what they are and why these are interesting?

π£ **Pieter Claeys** (20:08):
Yes, of course. So as you mentioned, for the past two to three years, a large focus of my research has been on unitary circuit models. These are kind of toy, but the nice thing is that these are toy models that can be directly realized in current quantum computing setups. So the idea is again that typically if I give you some systems, some Hamiltonian and some physical forces, I can look at dynamics there. I can prepare my system in some state and let it evolve and the dynamics are just going to be governed by the forces that we have, which are just set by a physical system. But now what we can do – so dynamics is unitary in these and all of quantum mechanics – and rather than just being satisfied with the unitaries that nature has given us, which are just encoded in some Hamiltonian, we can now just try to redesign unitary evolution operators from scratch, which is really just a way of designing the dynamics of your system, but essentially just use some local building blocks.

(21:04): So unitary gates really are some kind of Lego bricks from which you can construct some network which then models some physical evolution. So you’re again doing some kind of quantum simulation where you’re really designing the dynamics from scratch. And then you can have much richer dynamic for example. You can again have these driven systems where you just keep periodically changing your Hamiltonian time, you already have an enormous amount of freedom in doing so, and we use these unitary gates, which are the building block of quantum computation as also the building block in our dynamics. And you can do this for any unitary gate. And in recent years I focused on the specific class of dual unitary gates, which you’ve just mentioned, and these are also exactly solved but in a different way than integrable systems are. But in same way as for integrable systems, there’s some hidden symmetry in these models that allows you to simplify a lot of calculations and actually also has very interesting properties.

(22:01): So usually if you have some dynamics, you have very, a very strong arrow of time. So your system evolves in time, say from yesterday to today, you always have that and the dynamics is reversible. So you could by, say, time reversal let your system evolve back and you’re going to end up with the state that you started from. These dual-unitary circuits actually have some additional arrow of time now along the space direction. So if instead of evolving my system from yesterday to today, I could just evolve it from one meter to the right of me to one meter to the left of me, and this would also be reversible. So in this way, the dynamics in the spatial direction behave the exact same way as the dynamics along the time direction, which of course a completely crazy symmetry if you think of it just on the level of Hamiltonians or the dynamics that we’re used to.

(22:49): But because we have this freedom in designing these circuits, this is something we can very easily do. And it’s actually something that if you just look at a random gate, there’s a very good chance that it’s going to be dual unitary. And now we’ve managed to design these circuits and this symmetry, which might seem a bit restrictive, actually allows us to completely characterize almost all properties that you’ll be interested in. So we can look at how the systems relax to equilibrium, we can look at how entanglement grows, we can look at operator scrambling and we can completely quantify that. And nice thing is that in a lot of ways the system do behave much more generic than integrable systems. So we can use these to get some understanding of general many-body dynamics in a way that I think wasn’t possible before. Also, on a more fundamental level, we have dual-unitary models and we have integrable models. And integrable models, the dynamics there…it’s not generic in any way because we have these particles that prevent your system from reaching terminal equilibrium.

(23:45): And so, which in a way is saying that these integrable systems are not chaotic, but dual unitary models, they do seem to behave much more generic and much more chaotic than you would expect. And so in a way, these are chaotic models that we can completely analyze, which is very counterintuitive and it’s something that people are always surprised by. But the nice thing is that, okay, quantum chaos, it’s something that’s very hard to define and people just typically take an approach of “I know it when I see it”, and you have all these different diagnostics of quantum chaos and you can apply all of them to these entire circuits. And they do seem to be chaotic in every way you could imagine. So it’s quite nice that we have these generic models that we can now use to really understand the dynamics of quantum systems. And because these models are built out of these building blocks from quantum computing, you can also very easily – ‘very easily’, I can’t, but people can – very easily realize them experiments or in quantum computing setups. And for example, I think Google has done this experiment on this operator scrambling where they also contrast what happens in dual unitary circuits with just genetic unitary circuits. So it’s quite nice to see all these, the theoretical predictions that we have can also now just be probed in experiments.

π’ **Steven Thomson** (24:55):
That’s really interesting. So it’s a really nice combination there where it’s something that’s fundamentally quite new and different. And some of the properties you mentioned there sound really exotic and unusual, but also because as you say, these unitary gates are the building blocks of quantum computing, it’s not just some crazy theoretical construct. It’s allowing you to investigate all this really interesting fundamental physics, but from a very practical language, I guess a language that experimenters can implement, as you say, relatively straightforwardly. That’s a really nice combination of traits there, isn’t it?

π£ **Pieter Claeys** (25:30):
Yes, that’s also one of the reasons I’ve gotten so enthusiastic and so interested the past few years is they combine a lot of the best aspects of these integrable models, but then also they’re much more generic and can…they’re much easier to probe. So in a way they’re much more relevant to what is going on just in the field in general then what my previous research was. So I quite like being able to study these quite fundamental questions using these very simple toy models, but now there’s additional advantage that people outside of academia are also very interested now in what’s happening there because the interest in quantum computing.

π’ **Steven Thomson** (26:03):
I see. So it’s the toy models you’re using are in a sense suddenly much more realistic or much more relevant to other experiments in other work that’s happening?

π£ **Pieter Claeys** (26:13):
Yes, exactly. And right now there’s also the advantage that we have these quantum computers, they’re really good at simulating quantum physics, but not that great at doing calculations. But of course people want to promote their quantum computers in a way. So people are really looking for different kind of physical experiments they can do to really highlight the ‘quantumness’ of their quantum computers. It’s very nice to have these models. One additional application for example, is that you can use these models as benchmarking. You have models where you know exactly what to expect, so you can first do your quantum calculation, see if you get the expected result for your entire circuit, and then you can do the actual calculation that you’re interested in, which you would not be able to do just on a classical computer. So I think that’s also one of the possible applications there.

π’ **Steven Thomson** (26:54):
I see. Great. Yeah, I was going to ask how do you make a link between these sort of fundamental questions and current generation technologies and the interest of, as we talked about industrial partners in quantum computing, but yeah, I think you’ve covered all of that already, right? Yeah, that’s why these things are interesting is because you can investigate them on current gen quantum computers and allow you to do a lot of really interesting things. Wow, okay. So obviously I knew a little bit about what you were doing before we spoke, but that answer has sold me on dual unitary circuits as something that’s really, really more interesting than I had actually understood myself before this.

π£ **Pieter Claeys** (27:34):
I’m really happy to hear so. Because what these models have also allowed us to do is, this is not quite related to these practical implementations, but I think they’ve given us a much better understanding of notion of quantum chaos where a lot of results have to do with random matrix theory, but the arguments are typically a bit heuristic. But in these models you can also analytically make the connection with random matrix theory and with quantum chaos in a way that I also completely would not have expected. So it’s not just that these are exactly solvable and chaotic, it’s that they also allow us to make exact statements about quantum chaos. One thing that’s also good to mention is that a lot of the studies that we do in these circuits, they really use the language of quantum information and language of entanglement. So everything we can now calculate can also express in terms of all these different entanglement properties. It’s also quite nice to able to relate those fundamental dynamics to really the basic properties of your building blocks of these gates.

π’ **Steven Thomson** (28:32):
Yeah, wow. Sounds like they can do an awful lot of really incredible things. That’s amazing.

π£ **Pieter Claeys** (28:40):
There are still very much a lot of restrictions, but they’re more flexible than you would initially expect.

π’ **Steven Thomson** (28:44):
Yeah, that’s really interesting. And so, okay, this is the type of things that you work on, but as we mentioned, I think you’ve recently started your own research group at the Max Planck Institute for the Physics of Complex Systems in Dresden. How are you finding the transition from doing this sort of research as a postdoc to now being in a leadership position and do you have any advice for other people who might be going through a similar transition period?

π£ **Pieter Claeys** (29:10):
I think overall it has been a very enjoyable experience for me. Of course this transition, it does include a lot more responsibility, which also applies a lot more pressure. But I think I’ve been very lucky in that I’ve been able to do this in the Max Planck Institute, in Dresden, which…it’s a very supportive environment and they have a lot of experience with helping people get their research group started. So the moment I got there, I also went to the other group leaders to ask for their advice and I also had the opportunity to basically watch them lead their group and see what I wanted to take away from that. In that sense, it’s been a very positive experience. Otherwise, on a more practical level, on the purely practical level, I can definitely say that to my time management skills needed to improve very quickly cause there’s so much more to do.

(29:53): One thing that also took some getting used to is that I have very strong tendency to do a lot of calculations myself because I know that that’s what I can do well, which of course now I should let go of and trust my PhD students to just be able to do these calculation and do all that where I am much more in a supervision role apart from that. One thing that I also need to get used to is that I need to think much more in terms of projects, which was not something that I was actually used to. So I didn’t really have any kind of fixed problems during my PhD. It was more like, okay, do something in this topic and I just read a lot of papers and found something interesting to do. Then when I did my first postdoc or my second postdoc, it was kind of a similar setup.

(30:35): I just decided to work in slightly different fields and see what interesting problems were there and then I just try some things and sell what worked out and then I continued in that direction. But that’s not something you can do if you just have a new PhD student - “Okay, here, read this paper and find something interesting to do”. So I really need to come up with much better defined projects, which I think was a very good exercise for me and also very useful for grant applications and all that. So that took some getting used to, but I think also now it’s much more rewarding that when it pays off. Now I get much more satisfaction when one of my PhD students publishes a paper rather than when I write another paper myself.

π’ **Steven Thomson** (31:12):
One other question that I ask every guest on this podcast is that physics has for a long time historically been a field dominated mostly by white cisgender men, and it feels like things are improving albeit far too slowly. There’s still a long way to go before we reach any kind of level playing field. Over your career, have you seen things changing? Have you seen different attitudes to diversity in the different countries in which you’ve worked? And in particular, how do you approach diversity now that you are in a leadership position where you have to be hiring PhDs and postdocs? Is this a consideration that you have and how do you ensure that your group will be a diverse place that’s welcoming to all possible candidates?

π£ **Pieter Claeys** (31:55):
Okay, that’s really good and really important question actually, that’s quite a few questions disguised as one. So, let’s just tackle these one by one. So in the sense that I’ve seen some evolution in some way, there has been a clear improvement. I think in overall there’s much more awareness of the importance of equality and having academia be more diverse. So I think in that sense, yes, there’s some progress, but I don’t think that necessary translates in practice to having more equality. Now I started a research group and I’m involved in hiring people. I’m going through a lot of applications and it’s extremely clear that the vast majority of applications actually come from male applicants. And if you already started with such an inequality at the beginning, like statistically throughout academic career, women are much more likely to drop out the moment, leave the PhD, and then during the post appears afterwards. So then inequality is only going to increase. So in that sense, people have become more aware of it. I think everywhere I’ve been, there has been this discussion going on. So in that sense I didn’t see that much difference between the different places, but it doesn’t necessarily translate to any actual differences in practice.

(33:02): One of the examples, what I mean by awareness is definitely increasing is I think that this manifests itself when people are organizing, for example, a school or a workshop or a seminar series, that people seem to be making much more of an effort to make sure that the speakers have some equal ratio of men and women. And also I have the impression that a lot of the universities have been part of are making an active effort to promote equality. For example, the Max Planck Institutes have these Lise Meitner fellowships, which are really group leader positions that are just aimed at women and that have been incredibly successful. So in that sense, there are a lot of efforts which I think are mainly aimed at people that are already in academia, already in physics, to try to keep up or rather try to not worsen the inequality throughout the career progression. So I think there’s been very concrete effort, but I think to readdress the imbalance at the start of an academic career seems to be a longer term prospect where maybe we first need to make sure that this equality or these efforts to improve visibility are then eventually going to reflect to outside world and then leads to more female applicants and more equality at that stage. So it’s something I definitely try to be aware of when hiring people, but if there’s already such an imbalance at start, there’s only so much you can do.

π’ **Steven Thomson** (34:13):
Yeah, we’ve heard similar comments I think from a few other people who’ve been involved in positions where they’re hiring or in recruitment roles that the pool of applicants is not sufficiently diverse, and if it’s difficult to find an applicant at all who meets the needs of a project, it can be even more difficult if you’re looking for an applicant who is not just a white man because the majority of applicants already are. So yeah, it certainly seems like there is still a lot more work to go. It’s interesting the distinction you made between raising awareness of the problem and actually fixing the problem. I think that is a really good point.

π£ **Pieter Claeys** (34:47):
I should also say I’ve been parts of groups where it was not just physics. During my PhD, I was part of a molecular modeling group where there was also a lot of chemistry going on. And now in Dresden, I’m part of the Max Planck Institute for the Physics of Complex Systems where we also have a biophysics group and just not just being surrounded by physicists, you can automatically tell that the environment is much more diverse and it’s also very clear than that physics has such a long way to go.

π’ **Steven Thomson** (35:11):
That’s really interesting. In fact, the contrast even within the same, same building, the same department. One final question to end on, if you could go back in time and give yourself just one piece of advice, what would it be?

π£ **Pieter Claeys** (35:24):
So I was thinking about this question and I’m just going to ignore it and give two pieces of advice.

π’ **Steven Thomson** (35:31):
Okay, go for it. Yeah.

π£ **Pieter Claeys** (35:32):
Because I think one thing that reapplied to me that I should have known at the beginning of my PhD, it’s really important to find your community by going to conferences, by going to workshops. And that’s not just to promote your own work, but also just to be aware of what people are interested in and what other people are interested in the same kind of problems that you are interested in. Because at the start of my PhD, I felt a bit isolated in my research because I was the only person at my group that was really interested in the kind of problems that I was working on, and I wasn’t particularly encouraged to attend conferences or summer schools that were relevant to what I was doing. And so it took me a while to get used to this community of people that were interested in these things.

(36:10): And I only really got to experience this during the second half of my PhD. So after three years of my PhD, I actually decided to spend one year at University of Amsterdam because I was partly looking for some external supervisor to work on problems that were a bit closer to what I was interested in. And by doing that, I became much more aware of the other people working in this field and like, oh, I’m actually doing condensed matter physics. Oh, there’s an entire group of people that are just the exact same things that I was doing that I hadn’t been that aware of that up until that point, were just names on papers. So I think if I had known that at the start of my PhD, I think it would’ve been a slightly different experience. And this is not advice to me personally, but I think more generally.

(36:55): Second one is that it’s really important to always keep in mind that you are not your work. And it’s something that I’ve also mentioned to my PhD students and if I haven’t, it’s something they’ll find out now by listening to this podcast, which I should do. I think it’s so important to make sure that you have some life outside of research and that you don’t just define yourself by what it is that you’re doing and have other ways of expressing yourself and finding some meaning there. I think I’ve always said this before, but academia comes with a lot of uncertainty and if your research is really all you have, I think this uncertainty is going to be much harder to tolerate. And I think there’s various reasons for that. I mean, a lot of research is just trying different things and failing a lot. So a large part of what you do will not work out, which can be, I think, quite horrible for the self-esteem if it is all that you are doing. And especially if you’re a beginning PhD student who has really been used to getting top grades just by studying where all effort you put in immediately translates to research. And so there will be peers where your research isn’t going well. And then there’s of course also the rejection when trying to publish papers. And I think if you allow your research and your output to define who you as you are as a person, I don’t think this will be particularly healthy or enjoyable.

π’ **Steven Thomson** (38:06):
Yeah, I think that is a fantastic point to make. Absolutely. Yeah, truly agree with everything that you’ve said there, and I think it’s definitely very good advice for people who are earlier in their career. Definitely.

π£ **Pieter Claeys** (38:19):
Also later in their career

π’ **Steven Thomson** (38:20):
Yes, I guess it never starts being good advice, does it? Well, I think that is a very good note to end on. So if our audience would like to learn a little bit more about you, is there anywhere that they can find you on the internet or on social media, anywhere like that?

π£ **Pieter Claeys** (38:34):
Yes. So I have a personal website, which is pieterwclaeys.com, although I have stopped using that since I have moved to the Max Planck Institute. And now I have a group website, which you can find by just going to the Max Planck website and finding my research group, Dynamics of Quantum Information. I think the link is pks.mpg.de/dqi. I’m sure there will be some links somewhere. And I’m also on Twitter, although I’m not sure for how much longer on @pieter_cl, for ‘Claeys’, my last name.

π’ **Steven Thomson** (39:04):
Okay, perfect. We’ll be sure to leave links to that on our own website, insidequantum.org. So, thank you very much Dr Pieter Claeys for your time today.

π£ **Pieter Claeys** (39:12):
Thank you very much for your time.

π’ **Steven Thomson** (39:14):
Thanks also to the Unitary Fund for supporting this podcast. If you’ve enjoyed today’s episode, please consider liking, sharing and subscribing wherever you like to listen to your podcasts. It really helps us to get our guest stories out to as wide an audience as possible. I hope you join us again for our next episode. And until then, this has been insideQuantum, I’ve been Dr Steven Thomson and thank you very much for listening. Goodbye.