# S2E8: Quantum Complexity with Dr Henry Yuen

*What can complexity theory tell us about the capabilities of near-future quantum devices? Take a listen to Season 2, Episode 8 of insideQuantum to find out!*

*This week, Dr Henry Yuen, an Assistant Professor of Computer Science at Columbia University tells us all about his work in complexity theory, how concepts from classical complexity theory can be modified to be applicable to quantum systems, and how these concepts can be used to tell us what near-term quantum computers can and can’t do.*

*Dr Henry Yuen obtained a B.A. in Mathematics from the University of Southern California, followed by a PhD in Computer Science from MIT. He has since held positions as a Postdoctoral Associate in Computer Science at UC Berkeley, an Assistant Professor at the University of Toronto, and is now an Assistant Professor at Columbia University in the Department of Computer Science.*

*This episode was hosted by Dr Yihui Quek, and primarily edited by JonΓ‘Ε‘ Fuksa.*

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

(00:16): In previous episodes, we’ve talked about quantum materials and quantum benchmarking. Today’s guest works on quantum complexity theory and quantum learning theory, and he is Dr. Henry Yuen, a professor at Columbia University in New York. Hi Henry, and thank you for joining us today. Some of our regular viewers may notice that this is the first time the podcast isn’t being hosted by Steven, and this is actually intentional. I wanted to interview Henry ever since I saw that he had his own podcast, and also because our research areas overlap. So some of you may know me from the first podcast episode. Yeah. So I’m back. So thank you for joining us today.

π£ **Henry Yuen** (01:01):
Hey, Yihui, thanks for having me on.

π’ **Yihui Quek** (01:03):
Before we get into the details of Henry’s work, let’s first talk about your journey to this point. So could you tell us a little bit about what got you to this point? What first got you interested in quantum physics and how did you choose the specific subfield of quantum physics that you’re working in? I guess you don’t even consider it physics, right?

π£ **Henry Yuen** (01:21):
Yeah. I don’t consider myself a physicist, and I think of myself as a computer scientist who happens to work on quantum computing. And in terms of how I got to this point, yeah, I guess I’ve always been interested in physics from a pretty young age. I remember I was in grade school and I had come across a biography of Einstein, I think, and I was just super enthralled by what I read, the fact that here’s this person who just had great imagination and somehow could unlock the secrets of the universe just by thinking about things. And to me, that made a big impression. And also just the types of physics that Einstein thought about was just so weird and so cool. And so I was very interested. And so as a young kid, I read these biographies of people and found it super interesting. One thing led to another, and I just read these books about chemistry and so on, and just thought it was just super cool. But then when I was in middle school and high school, I sort of turned more into computer science type things, and then I got internet access when I was a middle school kid. And thenβ¦

π’ **Yihui Quek** (02:45):
Oh, those were the days.

π£ **Henry Yuen** (02:46):
Those were the days, right?

π’ **Yihui Quek** (02:47):
Yeah. Not everyone grew up with internet access.

π£ **Henry Yuen** (02:49):
Right! Now my one year old, she knows how to use the phone. Not really, but…so I discovered, like, oh, you can make your own websites. And then I discovered the world of programming, and that was super cool. And so actually for a very long time, I totally thought what I was going to get into was video game programming.

(03:15): As a kid, I discovered video games and that you can also make your own video games, and that was such a cool thing. And so I was pretty certain that was my destiny. I was going to become a video game programmer or something. So when I entered college, I couldn’t decide what major I wanted, so I just sort of selected them all. So there was actually a physics/computer science joint major, because I remember that I had liked physics from a young age.

(03:42): So I started off in that, and then I realized I wasn’t really cut out for physics, at least the classes I was taking. It was very interesting. I mean, it was really cool, but somehow, I don’t know, it just didn’t fit. I liked the concepts and the thoughts, but somehow the actual way the math was done and so on, it was somehow kind of weird to me. So I said, okay, I’ll switch into computer engineering. I’m totally going to go down this software engineering video game programming route. So I did that for a while, but then I somehow got in contact with a professor who did math research, math and computer science research. His name is Len Adleman.

(04:31): So he was at USC, which is where I went to undergrad, but he…he’s a computer science professor at USC, but he was doing mostly math research. And so somehow I got into doing math research with him, and that totally changed everything because then I saw, wow, the stuff that he was doing was just so cool. It was just so beautiful. And then that’s when I sort of decided I wanted to become a math major. So I went from physics to computer science, and then I finally switched into math. That’s what I ended up getting my degree in. But where is this leading me? So at the very end of college, I decided to take a quantum computing class because I was like, I remembered I like physics, I liked computer science stuff. This seems to combine both, and it’s also very mathy. So I took that and then I sort of realized, okay, this is exactly what I wanted to do because it combined everything that I had liked. It has the physics - the physics without the physics, in some sense. It has the computing aspects, it has the math. This is what I wanted to do. So after that, when I applied to TCS grad schools and - TCS stands for theoretical computer science - and that’s how I got to this field.

π’ **Yihui Quek** (05:51):
Oh, lovely. I have a couple of observations. So I noticed that you, kind of, tried out many different fields before you eventually settled on a career in quantum physics. So in a sense, I think that’s a testament to the benefits of not having to declare your major before you start your college education.

π£ **Henry Yuen** (06:10):
Absolutely. Yeah.

π’ **Yihui Quek** (06:13):
Which is also, I noticed, a difference between the US and Europe, because in Europe I think many people decide that they want to study physics, and then they just have to study physics for the whole four years, and they don’t really get to switch around.

π£ **Henry Yuen** (06:26):
So that would’ve been really bad news for me in particular, because I guess if I were in that situation, maybe I would’ve felt compelled to stick in one area. Especially I think in certain places, undergraduates are very fast, I think in the UKβ¦

π’ **Yihui Quek** (06:42):
Right? It’s only three years.

π£ **Henry Yuen** (06:43):
There years. So my undergrad was five years. So it was good that I had somehow this extra time to sort of feel like I could switch around and not really have to pursue one thing.

π’ **Yihui Quek** (06:55):
Right. I do appreciate that as well, because my own undergrad experience was also marked by a lot of switching around and trying out different subfields even within physics. So we were chatting yesterday, and I had actually done a summer internship in biophysics as an undergrad – in Germany, yes. Yeah.

π£ **Henry Yuen** (07:19):
And you’re not in biophysics anymore.

π’ **Yihui Quek** (07:20):
I’m not in biophysics anymore, but that experience was successful in contributing to my love for Germany as a country, I guess. Not my love for biophysics.

π£ **Henry Yuen** (07:29):
Not your love for biophysics, I see. But you learned something.

π’ **Yihui Quek** (07:33):
I did, I learned German. Okay. So did you feel that even in your PhD there was the same amount of room for manoeuvring or switching around, or was it, did you already know that you wanted to do quantum physics or quantum computing from the start?

π£ **Henry Yuen** (07:48):
Yeah, so I guess to continue how that journey evolved. So after taking that quantum computing class, I was like, wow, quantum computing is so cool. But I also really liked this complexity theory stuff because the research mentor that I worked with, Len Adleman, he’s a complexity theorist, cryptographer number theorist. And I was also inspired by the stuff that he had worked on back in the day. And so when I went to grad school, I actually wasn’t sure exactly whether I wanted to do quantum computing or classical complexity theory. And so in fact, I ended up working with an advisor who was a classical complexity theorist. Dana Moshkovitz. And so I started working on very, very classical things. I mean, her area is hardness of approximation and probabilistically checkable proofs, which is amazing stuff. And I started working off in that. So I worked on that for a while. But then I sort of kept on returning to quantum computing and quantum complexity theory. And I guess at some point I was able to get results in quantum computing and quantum complexity. And I guess I stuck with that. What’s interesting is in some sense, a lot of things come full circle in that a lot of the classical complexity theory things that I learned at the beginning, sort of fed back into my research later on. And it’s all sort of connected and it’s all one thing, whichβ¦

π’ **Yihui Quek** (09:24):
Well, that is super interesting. So for our viewers who may not have heard of these concepts before, you mentioned probabilistically checkable proofs, and what was the other thing that you mentioned?

π£ **Henry Yuen** (09:34):
Hardness of approximation.

π’ **Yihui Quek** (09:35):
Hardness of approximation, yeah. Could you maybe give a short explainer of these concepts to our viewers? Uh, our listeners, sorry.

π£ **Henry Yuen** (09:43):
Sure. So hardness of approximation is a field that studies how hard is it to approximately solve NP hard optimization problems or NP hard problems. So there’s a lot of problems that are famously NP complete, like solving 3SAT or travelling salesman or other things. And it was known for a very long time that these problems are NP complete, so probably we won’t have a polynomial time algorithm to solve them. But then people started asking, well, how hard is it to get approximate answers to these problems? And the field of hardness of approximation is, as the name suggests, is it’s still NP hard to even get approximate answers, but proving this is much harder than proving that the exact problem is NP hard. And in fact, this is where probabilistically checkable proofs or PCPs, that’s where they come in. It turns out that if you show that a problem like 3SAT is hard to approximate, this is equivalent to coming up with what’s called the PCP. And in just a short summary of what a PCP is, it’s a way of formatting proofs such that you can check their correctness with high probability by only examining a few locations in this proof. You know, pick three random bits in the proof. And by looking at these three bits, you can determine with high confidence whether the proof is a correct proof or not.

π’ **Yihui Quek** (11:12):
That’s really lovely. That’s a really lovely explanation and also very fascinating concepts.

π£ **Henry Yuen** (11:17):
It’s amazing, it’s beautiful stuff.

π’ **Yihui Quek** (11:18):
Yeah. There was something very interesting that you said just now, which is that you ended up using concepts from classical complexity theory to help you in your quantum research. So could you give some examples of that?

π£ **Henry Yuen** (11:30):
Yeah. So a lot of the research that I’ve worked on in the quantum complexity area are really taking questions that people considered in classical complexity theory, classical cryptography, and asking what happens when we add quantum to this? How do things change or do things change? And so for example, a big part of what I worked on in grad school is to prove what’s called a quantum parallel repetition theorem. Okay, so what is that? So the idea is you take what’s called a non-local game or a Bell inequality. So you know, have a referee who’s playing with two separated players, Alice and Bob. Alice and Bob can’t communicate, but they share entanglement so they can generate quantum correlations via measurements on their entangled state. So there’s many famous non-local games that people studied in quantum physics and quantum information, for example, like the CHSH game or the Magic Square game.

(12:36): Maybe the people who are listening have heard of these. And in these games, Alice and Bob, they’re trying to win this game with as high a probability as possible using their entanglement. So the parallel repetition question asks, suppose I give you a non-local game, maybe CHSH, where the maximum success probability of the players, of Alice and Bob is less than one, they can’t win perfectly, maybe they can win…in the case of CHSH, they can win with probability 85 point something percent, right? So now imagine you play many instances of this game with the same two players, Alice and Bob. So you say, I’m not going to play one game, but instead I’ll play like a hundred games all at the same time. Alice and Bob will see now not just what are called questions or measurement settings, they see a hundred measurement settings, which are given by the referee, all at the same time.

(13:32): And Alice and Bob, they’re supposed to just have a hundred copies of their entanglement and perform the strategy that they did in the single game a hundred times and try to win all of them at the same time, but maybe they can do something different. The parallel repetition question asks, what is their maximum success probability now with if they’re playing a hundred of these, can they win all hundred with what probability? And so it, it’d be very tempting if you haven’t thought about this question before to say, well, it’s obviously 85% raised to a hundred, so that should be a very, very small number. But in general, it’s not quite clear that this is the correct answer. And the reason is because Alice and Bob don’t necessarily have to treat each of these games or experiments independently. They can somehow correlate their answers for one game with answers in another game, they can do things like that and the whole task of parallel repetitions is to understand the extent to which they can do this.

(14:38): Okay. So that’s the setup. Now in classical complexity theory, people looked at the very same question back in the nineties, but without any quantum. They thought about Alice and Bob where they are classical players now they don’t share entanglement. And the reason they were interested in understanding the success probability of these many repeated games is precisely to understand the behavior of PCPs and hardness of approximation. That was the whole reason for them to think about this. And it actually took quite a lot of work to prove that if you have a game whose maximum success probability is less than one, if you repeat it many times the success probability is going to go down exponentially. It’s not going to be the original probability raised to the number of times you repeat it. It’s some more complicated function than that. But there still is some exponential decay, and this is known as Raz’s parallel repetition theorem, and it’s actually, it’s not so easy to prove, it takes some work. So that was proved in the nineties, but then people had the question, okay, well what about when Alice and Bob share entanglement, is there a quantum analog of Raz’s parallel repetition theorem? And something I worked on in grad school a lot was to try to prove a quantum analog.

π’ **Yihui Quek** (16:00):
And did you succeed?

π£ **Henry Yuen** (16:02):
In some ways. So an exact analog of what he proved is still not known. It’s still an open question and I think a lovely open question, but I was able to show that if you have a non-local game and you repeat it N times the success, the maximum success probability of this non-local game decays at some rate related to N. It’s not known to be an exponential rate, but it’s an inverse polynomial rate. So that’s the best we know so far. So that’s sort of the connection between classical complexity theory and some of the stuff I’ve worked on in the quantum space.

π’ **Yihui Quek** (16:43):
I see. Also, I wanted to know, what do you think is the most beautiful thing about your research or the field that you’re in right now – maybe give a short spiel to our listeners who might be considering what fields to go into for their PhDs?

π£ **Henry Yuen** (17:01):
So I guess there’s – it’s hard for me to point to any one thing at the moment that I would hold up as an example of a particularly beautiful thing because I just find so much in complexity theory absolutely wonderful and fascinating and enthralling to me. But maybe the reason I’m interested in complexity theory and cryptography in quantum is because I feel like it’s a beautiful way to try to understand what makes quantum information and the quantum world different from the classical world. It’s a way of asking questions and thinking about things that’s just so different from anything else I’ve seen. And it’s just so fun to think about. So for example, in cryptography, there’s all these fascinating concepts like encryption or interactive protocols where you want to hide pieces of information from one party but reveal it to another party. And you have all these interesting scenarios.

(18:05): And what theoretical computer science and cryptography has shown is that there is a way of achieving these weird scenarios or situations or protocols to do these really cool things. For example, I can have you perform a computation without you knowing what exactly you’re computing, but I can know, even though you’re doing the computation, this is an example of homomorphic encryption, right? This is just something from cryptography. Who would’ve thought that this was possible? But the fact is, you can mathematically construct schemes to do this and people are implementing it. So that’s all stuff in classical crypto and complexity. It’s all already fascinating. But then you add quantum to the mix, then this unlocks a whole new dimension to things and it really forces you to understand what exactly makes quantum information different from classical information. So just to give an example, in quantum cryptography, you can perform information theoretically secure key distribution, which isn’t possible classically.

(19:12): And you can ask, well, why is it possible in the quantum world, which is the world we live in? And so that’s a base example that’s been known for a very long time, but something that people have been thinking about more recently, stuff like quantum zero knowledge proofs, which is, you know, can have an interaction with someone and you can learn whether a statement is true or false without knowing anything else other than the fact that it’s true or false. And in the quantum world, this notion of zero knowledge is also possible, but things get so much trickier because information can’t be cloned. If you measure something it collapses. And so how do you deal with that? And all these issues come up when you’re thinking about all these concepts and it’s just a wonderful mix of things to hold in your mind all at once and play around with them.

π’ **Yihui Quek** (20:06):
Yeah, something…I mean, I agree very much with everything you’ve just said. And I also wanted to add that something that’s always fascinated me a lot about theoretical computer science as compared to physics is that somehow it’s always very easy to communicate the problems to people who have never heard of them before. But to actually find a solution requires a lot of very sophisticated and very beautiful math – and that really draws me to this field, actually.

π£ **Henry Yuen** (20:31):
Right. Yeah. I have a similar feeling when it comes to comparing theoretical computer science to maybe pure mathematics or something. Like I mentioned earlier, I was a math major in…I ended up as a math major in college, but I don’t think I would’ve wanted to pursue pure math as graduate studies. I mean, it’s beautiful stuff, but somehow it’s just so abstract and somehow, you know, require many years of study before you can even understand the problem. Whereas in theoretical computer scienceβ¦

π’ **Yihui Quek** (21:09):
I feel the same way about physics!

π£ **Henry Yuen** (21:10):
In physics? I see. Whereas in theoretical computer science, somehow there’s a culture or tradition of making things as concrete and as operational as possible. There’s always a story or a movie that you can play in your mind about one person is trying to do something else with this other person, but can they accomplish it? It’s somehow much more tangible and concrete.

π’ **Yihui Quek** (21:34):
Exactly. Okay. So pivoting a little bit to the current focus of your research. What is the big picture goal of your field and where does your work fit into this picture?

π£ **Henry Yuen** (21:43):
Yeah, I guess it depends on where you draw the outlines of what my field is. I guess I feel like I live in different intersecting circles. I see myself as a theoretical computer scientist, so I belong to that community, but also as a quantum computing scientist. And so I also belong to that community. And the goals are somewhat different. They’re closely related. So from the theoretical computer science point of view, I want to understand what is the nature of computation in this world? And since we live in a quantum world, you have to think about quantum physics and quantum information and try to understand just what, like I said, what makes quantum information different from classical information. And there you want to understand, can we have a theory or some kind of understanding of when and why some problems are easier to solve on a quantum computer than others, and also understand what quantum computers can’t do.

(22:49): That’s maybe the biggest question there. But in the quantum computing community, of course there’s a big question, can we build these things and what sort of interesting things can we do with them? What are practical things that we can do with them? When can we achieve it? Of course, that’s a huge question. Lots of people are working on it, but it’s not too hard to see that these two goals are very tightly intertwined. If someone proves that you can actually simulate quantum computations with a classical computer, that would just completely, I think take a lot of wind out of the sails of people who want to build a quantum computer. What’s the point? On the other hand, I think people who are actually trying to build quantum devices and run cool experiments with them and build cool quantum technologies, by doing so, you open up new questions that the theorists can ask. And so there’s a very close interplay between these two.

π’ **Yihui Quek** (23:54):
So what do you think is the biggest challenge in your field at the moment? I guess here your field means complexity theory or quantum complexity theory.

π£ **Henry Yuen** (24:04):
Well, there’s the ultimate ultimate challenge, which is to definitively prove that there is a problem that quantum computers can solve efficiently that classical computers cannot, right? That’s the holy grail. But to actually do that, that’s on the same level as proving essentially…it’s kind of proving P not equals to NP. I mean, it’s not the same question, but we feel like we’re as far away from proving a separation between quantum computation and classical computation as separating P versus NP. And these…it feels like we’re nowhere close to that. Okay. So anyways, what about more near term goals…would be to come up with evidence that they are different. So how can we come up with more mathematical evidence or more of a structural understanding of what types of problems admit a quantum speed up? So yeah, I’d say that’s one of the biggest problems. Another one I think that’s very interesting, which is separate from understanding the separation, is to apply concepts from complexity theory to things like condensed matter physics.

(25:16): So there’s a huge open question called the quantum PCP conjecture, which is related to the PCPs that I mentioned from before. And I guess in a short summary of it, it’s trying to understand how hard is it to approximate ground energies of local Hamiltonians? And somehow it’s not just a question about computational hardness. I mean, we know this problem is already hard for polynomial time algorithms. Really what the question is asking is can we embed quantum computations in a robust way in low energy sub spaces of local Hamiltonians? And this question is beautiful because it connects with ideas from quantum error correction and proof checking from classical complexity theory and hardness of approximation and all these things sort of swirled together and it’s all in one place, all in one question. And so I would say this quantum PCP conjecture is one of the most interesting guiding open questions in our field, and it connects things from computer science, condensed matter physics, information theory and so on.

π’ **Yihui Quek** (26:23):
And what would be the consequences of proving the quantum PCP conjecture?

π£ **Henry Yuen** (26:27):
There are a few, and probably there’s more to come, but we…it’s an active field of research. So from the condensed matter physics point of view, it would sort of say that one consequence is that there exists families of local Hamiltonians where if you take states that aren’t necessarily the ground state, but actually have pretty…they’re low energy states, but still have relatively high energy, the energy sort of a constant fraction of the total norm of the Hamiltonian, that any such state must be highly entangled and cannot possess an efficient classical description. I think one, a sort of cartoonish way of talking about it is, say there’s robust entanglement at room temperature. So we know that ground states of local Hamiltonians can be very highly entangled, but this is sort of in a very zero temperature regime. But if you crank up at the temperature to something more like room temperature, whatever that means, does entanglement still persist?

(27:30): And if the quantum PCP conjecture is true, then this would provide constructions or strong evidence that you can construct local Hamiltonians where the entanglement doesn’t go away no matter if you crank up the temperature to room temperature. So from a condensed matter physics point of view, this would be very interesting, and I think physicists are looking for these exotic local Hamiltonians from the computer science angle. This would be super interesting because one, it’d be an analog of this beautiful PCP theorem that’s very important and central in computer science. And so it’s just interesting by itself to ask whether there’s a quantum analog. I mean technically speaking it would have some complexity implications. It would imply that the local Hamiltonian problem with a large promise gap, whatever that means, is a QMA complete problem. Okay. What are the consequences of that? It would say local Hamiltonians are harder than we thought. I mean, they’re already hard, but even harder than we thought. But I’m sure this would actually have – just like the PCP theorem in classical computer science had lots of applications and implications – I’m sure the same would happen also if a quantum PCP conjecture were also proved.

π’ **Yihui Quek** (28:45):
Excellent. I find it remarkable that you managed to explain all of that with using almost no acronyms at all – except PCP, maybe QMA, NP, P. I think that can also be very surprising and off-putting for someone who hasn’t really studied complexity theory before. But yeah, I think it’s very instructive to be able to see the big picture goals of complexity theory without going into the weeds of these acronyms.

π£ **Henry Yuen** (29:13):
Right. Yeah, I guess, well, this is both a reason to love and also hate complexity theory is because it’s just an alphabet soup of different complexity classes and acronyms that…I mean, oftentimes I can’t even keep track of it myself, but I think once you realize what the concepts these acronyms are referring to, then you realize they’re such beautiful concepts. Amazing concepts.

π’ **Yihui Quek** (29:39):
Exactly. You really have to stall your impatience and look past the initial obstacle. I also wanted to ask some questions about maybe your personal working style. If you could go back in time and give your younger self a piece of advice, what would that be?

π£ **Henry Yuen** (29:58):
I’m going to just pick a specific period of time. I’m thinking of myself as when I was going through grad school. So I started grad school in 2011, and it…you know, grad school is a very long period of time. I’m sure you can relate. And it’s not smooth, I don’t think for most…very few people. I don’t know of anyone who had a very smooth ride. And so there were definitely ups and downs, and there were definitely parts in grad school where I was just very anxious about being able to do research. I wasn’t sure that I could produce anything worthwhile or anything.

π’ **Yihui Quek** (30:36):
Interesting. Yeah, I can definitely relate to this.

π£ **Henry Yuen** (30:38):
So I think one thing that I would’ve told myself – but I wouldn’t have listened – I would’ve told myself to just relax and not worry about the future so much and really just focus and be present and focus on learning and enjoying the process. I wouldn’t have listened to myself. I’d be like, you know, you might as well just have asked me to walk to the moon or something. So that’s one piece of advice I would’ve given, but I would’ve disregarded it. I think a turning point for me in grad school was when I did other things other than research. So I think it was three years into grad school and everyone around me just seemed to be very productive and doing wonderful things and marvelous things. And I was like, why am I not doing as well as these other folks? And so to take my mind off of things, I took up some hobbies, sort of the biggest one was I got really into swing dancing.

(31:40): And that was such a breath of fresh air because one, it was just a completely different thing. It’s just, it’s so different from research or science or anything. And it was a different community. So I got to meet other people. I mean, I love the people in our community. They’re great people, but it’s also helpful to broaden the types of people you interact with. And two, I was able to get better at something and see some results. I would go take swing dancing lessons at MIT or at the other places in Boston, and I would get better at it. And that, that’s something that I did not encounter when doing research, at least for a very long time. And so that was sort of a breath of fresh air, and it was so fun. And so I got really into that. And I think that did wonders for my mental health and happiness, but also reminded me or made me realize that okay, there’s a world outside of research and academics and stuff. So one piece of advice to myself would be to just, there’s a bigger world out there and you know, you can enjoy other things other than doing well academically. So I would’veβ¦

π’ **Yihui Quek** (32:53):
Take the broader perspective.

π£ **Henry Yuen** (32:54):
Take the broader perspective, and it’sβ¦

π’ **Yihui Quek** (32:55):
Better for your mental health in the end.

π£ **Henry Yuen** (32:56):
…and do other things. And I think, yeah, I would’ve maybe been happier in those beginning phases of grad school or at least have a more balanced outlook on things. I think overall, I feel like I had a pretty good grad school experience. I enjoyed most of it, but there are definitely rough patches and I think doing other things would’ve helped with the rough patches.

π’ **Yihui Quek** (33:19):
That’s really useful advice. And in regards to maybe finding the next thing to work on, how do you decide whether something is a good problem or how do you find good problems or what is even a good problem to you?

π£ **Henry Yuen** (33:33):
Oh, that’s a very complex question. Yeah, that itself is a problem. I think about that a lot. I don’t think there’s a universal answer. I think it really depends on every researcher’s style and strengths and personality. And so I think a very important part of that is to really have a good understanding of yourself. So for me, the way I approach finding questions is it’s…you know, you’re trying to achieve several things, and one is, okay, first of all, the problem has to have some level of tractability. I’m not going toβ¦

π’ **Yihui Quek** (34:09):
Definitely. It has to be a good fit for your skills as well.

π£ **Henry Yuen** (34:12):
Yeah. First of all, I have to have some belief that I can solve it in some reasonable amount of time. So I’m not going to say I want to work on P vs NP, but it also has to address a question that I think at least resonates with me and I feel like will resonate with other people and gets at the heart of what people are really trying to understand. And in order to figure that out, it requires some sort of understanding of, well, what are people thinking about? So I don’t know, just to give a concrete example. So something I’m super interested in these days is understanding the foundations of quantum cryptography, right? Cryptography, where not only the adversaries have quantum computers, but the honest users also have quantum capabilities, they have quantum computers, they can send quantum information to each other.

(35:06): What sorts of things can you do in this world? And a really exciting thing now is to understand, say for example, the complexity theoretic foundations of quantum crypto. If you have a quantum cryptographic protocol and it relies on some computational assumptions, what’s the minimal assumption you need? You need to assume something is hard for the adversary, but what is that? This sort of thing has been pretty well understood in the classical setting, but it’s a wild west. It’s totally, completely open right now in the quantum case, which I find very exciting. I find this question super fascinating because it’s a) timely, because a lot of people are thinking about quantum crypto now. People are coming up with all sorts of really interesting protocols and objects like pseudo random states, which you know about, or other things like quantum money schemes or copy protection or certified deletion and all these things that we didn’t know about a couple years ago.

(36:05): And you can ask, is there something that ties all these things together? Is there a way that we can have a coherent framework of understanding this? And when you think about this question, then you realize it sort of leads you into saying, well, we actually don’t understand some basic questions about the complexity or the hardness of tasks where the inputs and outputs are quantum states. This is a very natural setting. If we’re going to have quantum computers, we want to do computations where you input a quantum state into the quantum computer and maybe it does some transformation and outputs a quantum state. How hard was it to do that transformation? And it’s sort of a very natural question, but you know, realize that we actually don’t have a framework or a theory of thinking about this. So then you say, well, okay, we have to come up with a complexity theory for this, and this is something that I’m super interested and super gung-ho about these days, but it also feels like it’s sort of the right time to think about these questions because people are thinking about related things. And sometimes it just feels like the time is ripe. It’s the right time to do it.

π’ **Yihui Quek** (37:06):
I think that’s a very important judgement as well to make whether the field is ripe for the question that you want to answer, or whether the tools have been developed already.

π£ **Henry Yuen** (37:16):
Exactly. Yeah. And that part, it’s like how do you know when the time is ripe for something? I think a lot of that just comes from experience. You spent some time in the field and you sort of see how questions come and go, and you definitely see cases of when people looked at questions and they’re the right questions, but just at the wrong time, they’re maybe a little too early. And so maybe they write a paper on something and people are like, oh, that’s interesting. But it doesn’t necessarily connect to anything else. So it becomes forgotten until when it is the right time. People do Google Scholar search and are like, oh wait, someone looked at this question or created this model back then. And back then it was weird, but now it’s, you realize it’s the right thing. So it requires hindsight and some understanding of context to get a feeling for when it’s the right time. And I’m not saying I have a good feeling for that, but I’m realizing over time this is actually a really important aspect to choosing questions.

π’ **Yihui Quek** (38:18):
Also I think talking to more people can help you get more of a sense of what people have been thinking about in the past and what they’re currently interested in.

π£ **Henry Yuen** (38:25):
Absolutely. Yeah, that’s right. Yeah, without that, you know, can’t really do research in a vacuum.

π’ **Yihui Quek** (38:36):
Okay, so my last question for today, and the question is, physics has historically been a field dominated by white cisgender men, and there’s still a long way to go before we reach a level playing field. So in your experience, are things changing at all for the better?

π£ **Henry Yuen** (38:52):
Yeah, thanks for the question. I’ll offer what I feel like is my own very narrow perspective on things, and it’s narrow because one, I’m just an individual, but also haven’t been around the block. I’ve only been in the field for not that long. I mean, I started grad school 2011, but a couple observations. One is that on one hand I do think some things have gotten better. The sense of…I feel like there’s a much higher level of awareness about the issues of inclusivity and diversity and representation in the sciences and just more in society more broadly. There’s a higher level of awareness, there’s a higher level of willingness to talk about these issues and comfort levels, which I don’t think was there when I started grad school. So I think it’s gotten better in some regards in that sense. But my impression is that I think we’re really far from where we would like to be ideally.

(39:57): And I think just sort of look around us. I mean, it’s kind of obvious that we haven’t built the best possible environment that is as welcoming to everyone who wants to be in it and who has something to contribute. I mean, I think that should be the bottom line. We’re all in this enterprise of just trying to learn more about quantum computing or theoretical computer science or mathematics or the universe. And we’re all super interested and passionate about learning about this. And it’s a hard journey. It’s a hard enterprise and there’s many people who are passionate about it and want to contribute and have something to contribute. But we just haven’t made a great environment to welcome people. And I mean, I love the community that I’m in. I feel like I’m very lucky to be in this field of theoretical computer science and quantum computing where I feel overall the level of friendliness and fun and passionate people is pretty unique and special from what I can tell.

(41:06): But it’s…I don’t think everyone necessarily shares this view. And so I think we have a ways to go and I don’t know, I don’t think I know what is the best way to fix these issues. But I think for starters, one thing is it, it’s important to have a more diverse set of role models and mentors. Because I think that actually makes a huge difference for people. Yeah, actually, just not to turn the tables on you or something, but I’m just curious, what’s your impression of the perspective of where things are in our field?

π’ **Yihui Quek** (41:48):
I think I would firstly say that it’s better in theoretical computer science than in theoretical physics. And I think this has something to do with the fact that theoretical computer science is a younger field as compared to theoretical physics, which traces its lineage back to the days of Pauli and Einstein and the days when gender diversity was not an important topic at all. Right?

(42:09): So I think the fact that younger fields tend to have a better gender balance suggests that our society as a whole is viewing these diversity issues as being more important now. So I think that we are heading in the right direction, but I mean, growing up it was also hard for me to find good female role models in the various fields that I was interested in. So definitely there’s more that could be done, but I think theoretical computer science is heading in the right direction. But I did want to also give a shout out to a certain – to I think the organizing committee of QIP 2021 in Munich, because I remember that there was a gender diversity panel there. And I think there had been similar panels in future QIPs, but they haven’t been as well publicized for it. For instance, I think there actually was such a thing at this year’s QIP as well, but I recall tuning into the gender diversity panel at QIP 2021, and it was such a breath of fresh air, the fact that there were so many other people there. And you could also see that there were not just women, there were also men who were interested in these issues.

π£ **Henry Yuen** (43:19):
I see. If you don’t mind me following up on that…so was there a particular thing that felt like a breath of fresh air?

π’ **Yihui Quek** (43:33):
I think it was mostly just the fact that these female role models were highlighted and they were very visible because I think really an issue is that in our daily lives, or at least in my daily life, I don’t have that many other opportunities to see role models, as you mentioned. And so the fact that these people were very publicly identified and there was kind of an exchange between the participants of the panel and them, felt like public affirmation to the fact that the lack of gender diversity is a problem and that we must work to solve this problem.

π£ **Henry Yuen** (44:09):
This resonates a little bit with something I’ve been thinking about. So I think maybe to sometimes the way I think about it or to try to understand…I’m male and I only have that particular perspective and my particular experiences, but I guess drawing a lesson from just doing research, one of the most important things that I’ve found when doing research is that confidence and somehow a belief or a visualization that you will succeed at the thing you’re doing is so important.

π’ **Yihui Quek** (44:43):
Absolutely.

π£ **Henry Yuen** (44:46):
And whether it’s just the belief that I can solve this equation or prove this theorem, whether or not you can actually do it, but somehow the belief or visualization that you can β

π’ **Yihui Quek** (44:56):
Being able to see the end point β

π£ **Henry Yuen** (44:57):
To see the end point makes a huge difference in whether you actually make progress on something, even if you’re actually going down a wrong angle, but at least it keeps you going. And I found that having this belief has really been the difference between when I complete a project or not. And so just drawing a parallel to that, I can also understand if you’re coming in as, let’s say a sort of an underrepresented minority or something and you know, come in and you’re not sure whether you necessarily belong and it’s harder for you to visualize yourself belonging in this community or making contribution, that’s a huge barrier, a huge impediment for one to continue and can…it’s easy to tell someone like, oh, well, don’t worry about it, just keep at it. But again, that’s just such an abstract thing to tell someone, right? And so having people who you feel like you can relate to, or mentors who are supportive, or colleagues who are peers who are supportive, that I can totally understand how that could make a big difference. And whether someone wants to continue being in a field or whether they enjoy being in a field and doing this research activity. So that’s one of the reasons why I really strongly believe it’s really helpful to have a diverse cast of people that we have in our field.

π’ **Yihui Quek** (46:24):
I think that’s a very nice observation, and you really put your finger on the thing that makes it so important to ensure diversity. I think we should conclude. So if our audience wants to learn more, where can they find you on the internet?

π£ **Henry Yuen** (46:39):
Oh, well, I – just look up my name on Google and then I have a personal homepage.

π’ **Yihui Quek** (46:43):
Which we will link. Okay. So thank you very much to Dr. Henry Yuen for their time today. Thanks also to the Unitary Fund for supporting this podcast. And if you’ve enjoyed today’s episode, please consider liking, sharing and subscribing whenever you listen. It really helps to get our guest stories out to as wide an audience as possible. I hope you’ll join us again for our next episode. And until then, this has been insideQuantum, I’ve been Dr. Yihui Quek. And thank you very much for listening. Goodbye.