Generative Quantum Eigensolver with Alán Aspuru-Guzik

We've got a bunch of incredibly fun and interesting things planned for the year, which we'll be sharing more about as the year progresses. And today's episode is one that I've been working on for quite a while now. I've been wanting to interview our guest today for quite some time. He's a pioneer in the field in the true sense of the word. He's been working for quite some time in quantum computing.

His name is Aspuru-Guzik. He is, was a an author of the foundational paper, the Variational Quantum Eigensolver Technique. If you haven't heard of it, the, Variational Quantum Eigensolver or VQE is a a technique for combining classical computing with quantum computing to try to come up with approximations, particularly of the ground state of chemical systems. It's really interesting because I I thought it was very innovative. The paper came out in 2013.

It was the first, along with, QAOA, the first two hybrid approaches to try to get some practical results, something useful out of the NISQ devices that have been sort of the typical, output of the hardware vendors for the last 10 years, noisy intermediate scale quantum devices. Variational techniques are actually, they're mathematical techniques that are quite familiar both in mathematics themselves that they were initially for solving partial differential equations and boundary value problems. They've been adopted in machine learning, and they're used in physics before quantum computing as well just to, to in quantum mechanics to to get those approximate ground state energies and wave functions. So, you know, it was very much an off the shelf kind of technique, but adapted very cleverly for quantum computing. The reason that it, you know, that I find it clever is that it takes advantage of the inherent strengths of qubits and, of course, the the linear algebra that that, is native to quantum computers, but manages to or or attempts to sidestep the limitations of the devices we have today by only running very short circuits, on the device before returning the result back to the classical code that then, can take another pass at another, iteration of the the approximation to get closer to your your eventual end answer.

The as I mentioned, the the mathematical approach is also familiar to machine learning, and therefore, this type of, of hybrid, variational approach is also core to a lot of what is considered quantum machine learning, early research into quantum machine learning. And so the topic today is work that Alain has been carrying out over the last couple years to update the variational quantum eigensolver technique with, sort of more cutting edge machine learning techniques. Really exciting stuff, and I think you'll enjoy the interview quite a bit. Welcome back to the podcast. I'm here today with yet another very special guest.

Super excited to be speaking with him, Alán Aspuru-Guzik from the University of Toronto. He's a professor of chemistry and computer science and really a leading pioneer in the field of quantum computing from way back when. I actually first saw you speak, Alán, at, IBM's Think Summit in 2017, when they were announcing the 53 or 54 qubit system was coming out the next year. And you presented on stage your variational quantum eigensolver, eigenvalue solver, which was a really interesting, I mean, since it was my first exposure to quantum, it completely, steamrollared my brain. I don't think it even blew my brain.

It just completely flattened me. But it was really exciting because it it was something potentially practical we could do with near term noisy quantum devices. And that was 2013, I think, that paper came out. So 4 years earlier and more recently, you sort of revisited the variational space, with an updated kind of approach. So first of all, thank you for joining us. And, can you can you give a little bit of background on the work that led to that that first VQE paper?

But, just to give you, like, a 2 1 minute and a half introduction, when I was finishing my PhD, I joined the group of Martin Head-Gordon as a postdoc. There, D Wave Systems, at the time, was thinking about gate model quantum computers. And cofounder, Geordie Rose, handed me over 5 papers that he found were interesting and funded my advisor to think about quantum computing for chemistry. Me as a postdoc said, oh, this is really cool. And collaborating with Peter Love and Tony Dutoi and, of course, Martin, we looked at those papers, and I found out kind of an easy mapping to do chemistry on quantum computers.

And, basically, that paper simulated quantum computation of molecular energies in 2005. Got got me you know, published in science, got me like a like a door at Harvard where I started my research group. But the VQE comes from that pressure because at Harvard, they said I said, look. I'm gonna do all the things that are not quantum computing because quantum computing for chemistry is not a new field. And I said, what are you talking about?

We hired you to create a new field. Go and just create a field. Create the field of quantum computing for chemistry.

And we met and we said, like, why don't we try to build a minimalistic, phase estimation algorithm for molecules? And we published a paper in Nature Chemistry in 2010. That is the first time, actually, due to a quantum chemistry calculation on a quantum computer with quantum optics. There was a group in China that got it, like, a couple weeks later after I was in the archive or, you know, like, around the same time. I forget if it's before or after, but I'm traumatized by that scoop because we put it together around the same time.

And one in NMR, one in one in quantum optics, and then we just suddenly, did that. And you know, it was really cool because we even had error correction. With 2 qubits, you can actually do majority voting error correction. So we got the potential in your surface of the hydrogen molecule. And that's a very interesting paper.

It's, I think, one of the first applied papers in quantum computing ever. Right. And what we did is that paper that was really cool, obviously, besides doing showing error correction and showing that a molecule can work. It's showing the most explicit diagonalization of a 2 by 2 matrix ever done in history because, really, that's what he was doing. Right?

I mean, like, a quantum optics table about these size just diabolizing a matrix. Okay. So it is in that context now I need to get tenure that VQA is born. Okay? So don't underestimate the precious academia.

And there's a moment where, you know, like, we were thinking about why is phase estimation really measuring energy in such a complicated way? Why don't we just measure the energy directly? So, I went to to Jarrod McLean and to Man-Hong Yung, and I told him, like, why don't we measure the energy directly for Hamiltonian? And then the next day, Jarrod came to my office with Man-Hong and said, we figured out how to do it. This is how we do it.

You just write the Hamiltonian, map it into spins, and, you know, you measure it. And and I said, let's write a paper. But you know what? At the time, it was very hard to get a very high profile paper if it's only theory. Right. They said, let's work with, let's work with with Jeremy O'Brien, to do a because he was a great guy. I met, you know, very energetic professor of my same age from Bristol at the time. And he's a guy now. He's the CEO of PsiQuantum.

Let's actually do what people do in quantum chemistry. Right. And and that's how VQE was born. It was together with QAOA, which was presented at the same conference in Aspen. Eddie Farhi stands up and persist QAOA. Then I stand up and present VQE. We were like, dude, this the same thing almost. That was the beginning of the that was the beginning of the the the variational algorithms finally. Well, and I

But, in in my around my closer circle, I think the person that I recall around the same time, really thinking heavily about machine learning was Seth and Patrick. And they were they were rocking at that as well. So Peter Wittek, the the late Peter Wittek, also wrote a textbook on quantum machine learning.

And we're like, oh my god. Maybe we can do a quantum out of color. And then with, Johnny Olson and many other people in my group, Jonathan Romero, we published the quantum out of color, which is also one of the seminal papers in quantum machine learning. Right. That's our contribute our contributions, we also worked a lot in the quantum. So that's that's kind of the era. Right? So Yeah. Yeah. That's that's kind of what I can tell you about the VQE.

I guess you wanna talk more about the GQE, but now people saw history too.

So, and obviously, generative AI has become this incredibly huge topic, over the last couple years. Speak to me, like, how did you apply, sort of generative techniques to the to the variational foundation of of of VQE? Or is that is that an accurate depiction for one thing?

Right? This that just has to do with just the statistics of how you do quantum measurements. And that means that without, like, previous knowledge of the of the problem initialization of what your tricks, you might get lost in the optimization. And, that seemed like the tool most of ourational algorithms. Yeah. And is that

You can always do gradient less optimization, but if you have too many, many parameters, right, maybe even there, you you have issues with the noise of your measurements. And so then a mantra in my group became I mean and and people in my group know how it works. Like, in my group, basically, I kinda like to set challenges and then keep barking at my students with a challenge and then, see who drives us up to the challenge. And a lot of interesting algorithms have come out of that. So I told them once, like, hey, guys.

We don't want radians. So there was an algorithm that I proposed to my group. We call it quantum Angry Birds. I'm not gonna tell you what it is, but if you remember the video game Angry Birds. Yeah. Right? It had to do with initial conditions and quantum dynamics, and we we call it quantum Angry Birds. Can you aim at something by, like, initial conditions? And we start to thinking about algorithms. We never publish quantum Angry Birds, but we started thinking about this type of algorithm.

It's like, we're an anarchist collective, as Peter Love likes to call, so it's call us. Right? So so then I I kept telling them, like, I want an algorithm without gradients. Like, we need to think about a way of, like, having a variational algorithm where you don't need the gradients in the quantum computer. I want to calculate the gradients outside of the quantum computer.

And then this brilliant scientist, which now works at NVIDIA, spent a couple years in my group, Kohei Nakaji, has all the credit of taking that idea and coming back to me one day and says and he he's very humble and very smart. He just comes and, you know, tells me a lot. Like, I found a way of doing this. And he says, like, I'm gonna use a generative model to generate the variation of trials. Mhmm.

And then I'm gonna optimize the gradients in that generative model. Right? Like, so the gradient is pushed out to the quantum computer into this thing. Mhmm. This thing prepares the quantum states in the quantum computer. And that thing, I would tell you what I call it, that thing. It can be any machine learning model. We use a transformer, but it can be anything that generates generatively. Mhmm. You like GaN? GaN. It can be an autoencoder. You can do an autoencoder.

Mhmm. But then the quantum circuit, based on that ensemble of energies, feeds the fits its parameters to generate tokens, which in turn would generate lower energies.

So what

And and we told the reviewers, like, you know, come on, guys. Like, this is a new algorithm. Like, we don't care too much about running it into a supercomputer. I'm just showing you that it can run larger. So we started, like, 3 or more VQE papers that are so VQE papers that are being written.

And then, well, Kohei and I just corresponded. We'll revise the prepping very soon and resume to another journal. So this paper is it's been there in the archive because we started so many collaborations. I think, okay, Kohei has about 10 or so going on. Right.

On the on the GQE, but the paper is kind of like there. We're gonna revise it with all our new knowledge. Right. So but, anyway, the point is that the the point is that, that that preprint, right, shows that we can do that. We can generate with the you can even start random, for example, and then slowly, the algorithm learns, which is important to know.

Now this uses GPT, pretrained. That's when things get really interesting. Okay? Because we could generate large quantum mechanical models. Right?

Models that could be could be pre trained. And what we know how to do now nowadays, at least what we are publishing so far, You could remind our collaborations to stand this in a lot of ways. But what we're doing is okay. So if I have the same number of electrons at this point and I have, for example, the same molecule, which is different geometries. If we have data on a few geometries, we can always learn predict the other geometries way faster.

So it learns the parametrization of the Hamiltonian, and we have done a lot of work on that. Even our first paper in the outer corner showed that if you learn across a potential energy surface, you can't predict the rest. Our quantum autoencoder paper originally did that. We did it also, with a paper with Alvar Severa Alerta that combines quantum machine learning with out encoders with variation sorry. Variational ligandsolver.

That shows also that we can do that. Like, it's called the meta variation ligandsolver. That's an interesting paper we published along the way called metaVQE. So so learning across a potential in the surface has been done before. We did it in metaVQE.

We did it in the autoencoder. Now we're doing it here again. It's kind of like, we know it's gonna be done, but what is nice about it is that then you can imagine, okay, this is VPT. GPT can read the entire Internet. So in principle, can I generate a big data set of molecules? And then the question is how to learn across molecules, and that's where the work is happening.

We have this error, and then we have the error corrected error. So if we extrapolate to the error corrected error of course, eventually, of course, all these algorithms that we also have worked on, but now here I'm gonna say, like, Dominic Barry and my former student, Jarrod McLean and also Ryan Babbush Actually, more Ryan Babbush than Jarrod, I think, in that case, have been working very, very hard on on this, you know, long term algorithms. My group also works in that. Recently, we have new work, by most and by anybody that I I wanna I wanna promote on on new ways of doing quantum simulation as well.

So we also work on that my colleague Nathan Wiebe. So we're also working by loop a little bit less focus, but also on the long term vision. Right. But I think, eventually, we wanna know my prediction in what would you wanna run a quantum computer in the future? You might run. I mean, this is speculation. But you might run a GQE to get started.

It'll be, you know, tens of logical cubits to begin with. But I I wonder, you know, if that speaks to exactly what you're saying. It's to to get the value out of, you know, a dozen, 2 dozen, maybe 50 logical qubits, you'll need these really sophisticated sort of hybrid architectures, solution architectures that that leverage the power, the best powers of classical computing and the best that we can deliver in quantum computing to to get to something that's together, the sum of the parts is more than, you know, than individually. Right? Like, that seems to be the direction we're going in.

Somebody can correct me if I'm wrong, but I think we are the first ones to call a QPU a QPU. Obviously, we were inspired by the GPUs. My group was also working on GPUs at the time. But QPU and the reason that VQE is very appropriate to call these things QPUs because they're like the GPU. They they they depend on the CPUs.

And, therefore, the quantum computer really has to be called a g a QPU. They will never be independent, and they are gonna be connected they are reconnected to, like, a massive supercomputer as we know or or the cloud or whatever. So so that's kind of gonna be the future, I think, for the from near time. And that's why, yeah, I think regardless of the era that we are on, if we're still in the relational era or new era that that that my friend John is is pushing, I am a I am a believer that and and some people are not. Sabrina Maniscalo just put out a paper in the archive with a bunch of colleagues about needs and tools about quantum computing.

And I paid attention to the one that says, we're gonna be able to do something before error correction. Yes or no? And most people believe no.

Yeah. In the University of Oxford. So, so he's in Germany. Okay? So, anyway, Jakob, which is a rock star, he still is maintaining mostly, tequila.

So tequila, just advertising here in the podcast, is still a a a a mundane package with dream new stuff. We don't have the GQE connected to tequila, but, obviously, it should be a it should be a necessity to do that soon. And and, yeah, I think you correctly told me that people have not got on to the GQE yet. I get this from my friend, Shaul Mukamel, very famous theoretical chemist, that told me, Alan, you you kinda wanna work 10 years ahead of everybody. Yes.

20 years ahead is too much because then people don't know what to do. Yeah. But 10 years ahead is kind of what you should do. And, you know, like, if you actually look at my publications now in my scholar, Google Scholar, the VQA paper keeps keeping up steam. And 10 years ago, it was not that much cited.

And I think the GQE will be the same once people realize, and thank you. Thanks to your post podcast, Sebastian. Maybe some of your listeners will be like, oh, what is GQE? And I didn't see this paper in the archive. Obviously, there's so much stuff coming up, but Links in the show notes, people.

Exactly. You just you just, you just figured it out that you know, it's helped me out to kinda popularize this. And and yeah. So I am working on it in my lab, in collaborations with Kohei at NVIDIA and, collaborations across companies and across institutes, across, academic and national labs. And so it's it's it's gonna be fun to see what comes out of the of the GQE era. But, yes, as you say, right now, the GQE is one paper and a bunch of little mini eggs that are about to hatch.

People right now haven't seen it yet, but it's okay. You're always gonna be 10 years ahead of the of the of the curve.

So that's fantastic. I I really appreciate your time. This is super interested. I interesting. I I'm absolutely agree with you that there won't be quantum computing without, you know, sort of that preprocessing that'll be machine learning based. I think there's, you know, AI for quantum as a category is going to be an increasingly important topic and important area for exploration. I think this paper will turn out to be foundational in in all of that area. So thank you so much for joining us.

And even consider, if you like what you've heard today, reviewing us on iTunes and or mentioning us on your preferred social media platforms. We're just trying to get the word out on this fascinating topic and would really appreciate your help spreading the word and building community. Thank you so much for your time.