## Quantum reservoir computing with Susanne Yelin

Download MP3So I'm joined today by a special guest, Suzanne Yellen, professor of physics in residence at Harvard University. Is that that still accurate in residence?

Susanne Yelin:That is correct.

Sebastian Hassinger:I wasn't the turn you're actually at the University of Connecticut as a professor as well. Yes. Yes. Right. Uh-huh.

Sebastian Hassinger:Very interesting. So your background is more in theoretical AMO. Yes. You're a fellow at the American Physical Society and a fellow at Optica, which I guess is the that's almost the American Optics Society.

Susanne Yelin:It is. It used to be actually.

Sebastian Hassinger:Yeah. Right.

Susanne Yelin:Right. To name.

Sebastian Hassinger:And you've been doing some incredibly interesting work at Harvard. You just gave a talk earlier today here at the Simons Institute, for the theory of computing. Can you tell us a bit about well, first, how you made that transition from sort of the theoretical opt you know, photonics to, working with actually trying to make an application with a quantum computer, and then and then the what the application is you're working with.

Susanne Yelin:So it was actually much less a transition as in phase transition than you might think, Because in quantum optics, we were basically involved in in quantum information early on. A lot of the, a lot of the platforms are AMO based or or quantum optics based. And a lot of the applications that we, for example, kind of use to to justify what we are doing to our funding agencies and our papers, etcetera, was, oh, with this great photon control, we can build quantum computer. Or here, that gives us, in principle, the the possibility to do a quant control, not gate with atoms or something

Sebastian Hassinger:like that.

Susanne Yelin:So the jump wasn't all that bad. For me, the the real transition was a transition from doing relatively application oriented quantum optics to, very theoretical quantum machine learning. And I had a post doc, who who was interested in that. She she came and and she actually she came with with money elsewhere and was funded in order to do quantum machine learning. And I had a couple of people who who were in my group who kind of immediately got interested and started a little bit in their own direction.

Susanne Yelin:And I have to say, my first exploits, I would say, for the 1st year or so, were really highly frustrating in this direction because quantum machine I mean, machine learning, we know that all, you know, chatGPT , large language models, etcetera. We're talking about 1,000,000,000 and billions and whatever.

Sebastian Hassinger:Right? Trillions.

Susanne Yelin:Trillions, of whatever.

Sebastian Hassinger:Of whatever. Yes.

Susanne Yelin:Quantum machine learning, because we don't have any working quantum computers Right. You have to simulate everything.

Sebastian Hassinger:Yeah. Yeah.

Susanne Yelin:And so we could do a quantum machine learning simulation with 6 cubits. If we went really big, we had 10 cubits.

Sebastian Hassinger:Yeah. It's not big data.

Susanne Yelin:It's not not big data and nowhere close. And in addition, and that was not clear, a, the results really not that great. Yeah. I mean, yes, you see some learning, but it's not. Oh, wow.

Sebastian Hassinger:Yeah.

Susanne Yelin:It is yeah. Okay. Yeah. This was one thing. And the second thing is that in order to even get to that point, you have to, already kind of you wouldn't see that in the papers or in the talks, you know.

Susanne Yelin:They always say, oh, we tried that and this gives this great results. You try, like, 7 and a half different models and ansatz and and and kind of loss functions, etcetera, until you hit one that actually works.

Sebastian Hassinger:Right.

Susanne Yelin:And then, if you do quantum machine learning, there is this this so called barren plateau problem, where where, you basically I mean, the the the slope of your evolution is basically at least as far as machine precision goes 0.

Sebastian Hassinger:Right.

Susanne Yelin:And so there is no evolution anymore. So this is this is the more quantum and the more entangled you go, the worse the problem that tends to be. And so my 1st year was like, okay. We have tried this. Now let's see where where we can use this

Sebastian Hassinger:Right.

Susanne Yelin:This experience. And then we started to get to get more into analog systems where we go away from the idea of a of a universal quantum computer. Yeah. And our first model was actually so called quantum reservoir computer. And the and then classically, recurrent neural network is is a network where your where your learning doesn't go only in one direction, but where you can basically circle back and kind of go through any notes any number of time.

Sebastian Hassinger:Right.

Susanne Yelin:A subclass of that is a so called reservoir computer where the where the connections between the nodes inside, you cannot optimize. They are fixed. And typically, they are either on or off, and that's it. And the only learning that you do is basically you look at your outputs, and there is basically a filter function, which for classical typically is classical. And it's more often linear, but not necessarily.

Susanne Yelin:And that one, you can learn on. And other than that, you you just let your let your, evolution run through the computer, and this is usually done. You have an update function. So here, we get very brain like. So every node or every, let's call it neuron, every neuron is is modified, by its direct environment, namely by all the axions or connections that go in there.

Sebastian Hassinger:Plus What's the physical implementation of that reservoir computer?

Susanne Yelin:Exactly. So or So so the the first of it is really the brain.

Sebastian Hassinger:Okay.

Susanne Yelin:Then there is the classical one, and the classical is it it's I I don't know whether how much, honestly, how much classical reservoir computers there are. People just, I think, simulated it and figured this is actually a valleys relatively stable way of learning.

Sebastian Hassinger:Right.

Susanne Yelin:For for quantum, any kind of sort of analog computer that we have is very good for it. So in principle, they they for me, this this in background and AMO, the the obvious wave would be an ensemble of atoms.

Sebastian Hassinger:Mhmm.

Susanne Yelin:And these atoms have some kind of interaction. For example, like, for for the Wittenberg arrays, if they are in the Wittenberg state, they they have a Van der Waals interaction. But it could be also the the normal cooperative interaction, which happens already in in the lower Can be anything.

Sebastian Hassinger:Okay.

Susanne Yelin:And, it's typically it can be completely amorphous. That's one of the things that I really like about it. You have this this basically, you can have a relatively big amorphous set of atoms, of any arbitrary connectivity. You take typically a relatively small part of it and define them as input. And an equally small part of it and define them as output, and all the rest is just a computer.

Susanne Yelin:So because you can go round and round, you have typically quite a bit of redundancy of the way of learning. And I think that's also the big advantage. And if you go quantum, of course, you have the advantage that you have all the typical and cheap quantum advantages like interference. Yeah. You can have various non non, commuting basis, and and true randomness.

Sebastian Hassinger:Right.

Susanne Yelin:And with that, we actually we came up with a couple of simple ideas how one can do use this interference to get basically, fault tolerance or even automatic error correction and so on. And this this turned out of course, we could also not model particularly much bigger systems. Right. But this was much more promising. Yeah.

Susanne Yelin:Yeah. And not only because it worked better and we didn't have to deal with thing something like barren plateaus, so that just didn't show up in this case. But, in addition, this this promise to be much more accessible to present day machines. The the reservoir computer itself is, does have, as I say, fixed connections between the between the nodes or now they are qubits. We can go a little bit further than that because the typical, for example, Rydberg array has global pulse control

Sebastian Hassinger:Right.

Susanne Yelin:Which kind of has an effect on all of these connections. It's the same effect on all the connections as long as the distances are the same.

Sebastian Hassinger:Interesting.

Susanne Yelin:But it it gives you quite a bit of control and it turns out that you and we we showed that subsequently, if you kind of condensed this down on on single nodes, that you can, in principle, actually build a universal quantum computer from that.

Sebastian Hassinger:Amazing.

Susanne Yelin:And, this is still work that we now kind of now I think starts the real

Sebastian Hassinger:work. Right.

Susanne Yelin:And one of one of my goals, for example, with that is I would like to build a machine, for example, a sensor, where they they they kind of assemble that does the sensing. For example, like a, ensemble, optic clock sorry, atomic clock or something like that, is actually the same that is also the quantum machine. Mhmm. So we use that both time as a quantum machine learner or reservoir computer as we use it as for for getting the signal.

Sebastian Hassinger:Is there some relation between what you're describing and and measurement based quantum computing? Because that's often

Susanne Yelin:No. That's different. Because measurement based quantum computer, you need control over everything.

Sebastian Hassinger:Every single one. That's right.

Susanne Yelin:So you measure, then you say where you go on or where where you measure next. And you have to read out every single one. In our case, the readout is depending on what we have. Usually, just a, a projection of the output cubits on the measurement basis. And so we just get this set set of zeros and ones at the end.

Susanne Yelin:That's

Sebastian Hassinger:it. Right.

Susanne Yelin:And then, of course, we can do learning, so we can kind of, make a loss function, do a do a, steepest descent, whatever, and then feed with a little bit different parameters back in. The different parameters will now be, of course, also how we do the pulses for this for this local connections.

Sebastian Hassinger:Okay. Interesting.

Susanne Yelin:So so and and maybe we have done a couple of other things. We also have tried to kind of optimize how one can, take as much of the quantumness, as is still efficiently similar on a classical computer. Do that on a classical computer and leave only the rest for quantum.

Sebastian Hassinger:Right. Right.

Susanne Yelin:That's one direction. And, this talk that I gave today is yet another direction. Here we just, we set out and and we said, okay. We want to do quantum chemistry.

Sebastian Hassinger:Right.

Susanne Yelin:There has to be a way, to do quantum chemistry that quantum chemists actually buy into. Right.

Sebastian Hassinger:Right. Right.

Susanne Yelin:That was for us really the study point. Yeah.

Sebastian Hassinger:Did you start to work on the the rigor device out of Lukens Lab?

Susanne Yelin:I'm not Before?

Sebastian Hassinger:Or or, I mean, have you

Susanne Yelin:I mean, I knew it very well. I mean, it's it's it's half of the people with whom I collaborate. You might not know that I also happen to be married to him. So yes, I know a lot about it, about the Rydberg atom array. I also You're probably

Sebastian Hassinger:sick of hearing it by anybody. No.

Susanne Yelin:And then you I'm actually not.

Sebastian Hassinger:No. It's amazing.

Susanne Yelin:And I also work a lot with the people at QuEra.

Sebastian Hassinger:Yeah.

Susanne Yelin:But that was yes. The the kind of the obvious the the obvious best Yeah. Thing that we had in mind. We are also talking to actually people, Marcus Greiner, who has, an optical lattice Right. And with fermions.

Susanne Yelin:So if if one wants to do anything like fermion Fermi Hubbard model or so, and for for what we do with the quantum chemistry, fermions are next. And for that, we actually will have to probably kind of mix platforms a little bit. But the way how we got to that was, a, we have something that fits very well, a kind of a method that fits very well on the on a experimental platform that that is there and that's being developed in at a very fast pace.

Sebastian Hassinger:Yes.

Susanne Yelin:We saw that people do basically reinvent the wheel of chemistry going back a couple of 100 years.

Sebastian Hassinger:Yeah.

Susanne Yelin:And we thought there has to be a way that we really leverage what they know already.

Sebastian Hassinger:Yeah. Yeah.

Susanne Yelin:And figure out what I mean, they cannot do everything yet. No. So

Sebastian Hassinger:they have to be talking to

Susanne Yelin:you otherwise. Exactly. They have to be there there have to be some things that they are not as good. Yeah. And, of course, naively as we were, Anna Krylov, who is at USC, we had kind of, little bit collaborated on something else.

Susanne Yelin:So she was an obvious person to talk to.

Sebastian Hassinger:And, of course, Martin had mad since.

Susanne Yelin:Martin exact Martin and Martin, is Martin had connection with Anna. So Anna brought in Martin. I see. So we had the 2 of them, and they are both pretty open minded towards quantum computation and so on. Nevertheless, when we ask them, so what kind of problems are hard for you to solve?

Susanne Yelin:The answer is typically, oh, no. Now we can do it.

Sebastian Hassinger:Well, they are scientists. That is sort of the default answer.

Susanne Yelin:I don't blame them. Why why should we idiots who don't know anything about wood chemistry kind of know it better. And so it was actually, I would say, about a 2 year journey to be able to understand what they are doing and what they what they what they are good at, what they are proud of,

Sebastian Hassinger:what

Susanne Yelin:their questions are, etcetera. And similarly, to explain them what we might be able

Sebastian Hassinger:to do.

Susanne Yelin:We, of course, were there in the really in the in the in the beggar's position because they could do all that already. We could not. We could just say, we might be able to potentially do that that. And so, for me, the starting point was actually not what kind it it also what kind of problem. But for me, one of the first things was really how can we get the input output together such that the classical computer and the quantum computer can do can play together very well.

Susanne Yelin:Yeah. And this was somewhat kind of automatically solved by this by this, very effective kind of readout that you can do this kind of because for for the Wiedberg event, you really you do this single shot measurements Right. Where you with one single kind of camera click

Sebastian Hassinger:Yeah.

Susanne Yelin:Get, a projection of all cubits. And by now, this is in the high 100s Yeah. And which tells you whether this is in a 0

Sebastian Hassinger:or in a 1. Right. Right.

Susanne Yelin:And so this can be done relatively efficiently. And, this this project is somewhere it's a little bit of of machine learning, but not really. It's a little bit of simulation, but not really. It's a little bit of computation, but not really. It's really kind of at the overlap

Sebastian Hassinger:also. Sounded also like you had analog time evolution in addition to logical gates.

Susanne Yelin:Yes. Exactly. And our logical gates, of course, are multi qubit gates. And this was by I mean, multi qubit gates was somehow an obvious thing to do with with these Wirtzberger waves because it was clear their gates work just in proximity, but you can bring, way more than 2 of these atoms into proximity.

Sebastian Hassinger:Right.

Susanne Yelin:By now, this is about 8. I think if they work towards it to try to make that higher, they they will be able to make it considerably higher, especially if you go into 3 d, which they don't so far. Yeah. And then there there is, I think this kind of working going away from trying to do things purely digital and trying to say, okay. We are going back to what we know from the reservoir computer and kind of optimize our pulses.

Susanne Yelin:And we now, for this particular we have basically 4 time dependent quantities that we can. These are the strengths of the laser for 2 laser fields. And the detourings of both of the laser fields, all of them are these limits fully time can can make full time evolutions. And so by that time, we had also kind of gotten this the this the quantum chemist and with our trying to understand quantum chemistry papers, etcetera, gotten to a point where we figured, okay. Now we actually we can try to do something.

Sebastian Hassinger:Right. Right. And so you picked, a a a molecule with high correlation. You were talking about

Susanne Yelin:a high correlation.

Sebastian Hassinger:It's a biochemical catalyst. Is

Susanne Yelin:that right? Exactly.

Sebastian Hassinger:And I was wasn't certain from the talk. Are you simulating the whole molecule or just the the manganese, like, just the

Susanne Yelin:the long set of glass? The thing is that the overall kind of large scale, spectrum is known. So the electronic spectrum is known.

Sebastian Hassinger:Right.

Susanne Yelin:The vibrational spectrum is known.

Sebastian Hassinger:Right.

Susanne Yelin:But a lot of the a lot of the the the subtlety, where where really the detail matters comes from the spins because because these are large spins, and they are, after all, relatively close together. This is actually an energy scale that we normally in the typical kind of, whatever kind of, for example, condensed matter Hamiltonians don't necessarily get.

Sebastian Hassinger:Right. Right.

Susanne Yelin:And, and so the this is really I wouldn't say this is the missing link because people understand that already pretty well.

Sebastian Hassinger:But you were demonstrating that, that at those low energy

Susanne Yelin:Yes, exactly.

Sebastian Hassinger:Measures, you potentially are getting sort of higher fidelity simulation

Susanne Yelin:Yes. Yes. Exactly. Than you can do with your class model.

Sebastian Hassinger:Okay. That's what I was thinking.

Susanne Yelin:And I mean, of course, the classical means the thing that you do, you do, for example, a direct diagonalization. So you assume you have a Hamiltonian, you just diagonalize it. For for this, for this molecule that is already a state space, that if you do it fully, so let for example, if you take the the molecular orbitals as s basis functions, you cannot do this classically by by by a large margin already. Right. What people can do still classically is probably up to perhaps a little bit bigger than water.

Sebastian Hassinger:Right. Right. Right. Yeah.

Susanne Yelin:And, so so the thing is, of course, we have also limitations in resolution, etcetera, because our quantum computer, of course, is not error free. So right now Yeah. The quantum computer has an error of of tens of percent. Yeah. And, I mean, we do so faster simulation, but we assimilate everything with this kind of tens of a percent error rate.

Susanne Yelin:And then, of course, it's also the question, I mean, if you, the error bars get smaller and smaller, the more samples you take, you want to stop at some point. The the examples that I showed today is also all a couple of case samples Mhmm. Mhmm. Which is which can be done, relatively quick for the experiment, and and in moderate time if you do the classical simulation.

Sebastian Hassinger:That's really interesting. That's really interesting. I loved the way that it you know, I mean, I feel like we're in this stage right now when, you know, maybe there's a growing realization that, you know, purely NISC approaches have kind of been, you know, run the course and we kind of gotten what we can get out of them. And, you know, we all want logical cubits and doing, large numbers of fault tolerant logical cubits is going to be very hard to do. Yeah.

Sebastian Hassinger:But the way that you're approaching this is in this sort of in between state where you're combining a variety of the the strengths of the platform and avoiding some of the weaknesses of

Susanne Yelin:the platform. Thank you. Thank you for that's actually exactly where I want to be. I mean, there is from this NIST, there are exactly two directions. The one is really going towards fault tolerance.

Susanne Yelin:I mean, error correction. It's full error correction. And people I mean, this this, the the, the the Wirtburg way, they can do

Sebastian Hassinger:this now.

Susanne Yelin:Right? Yeah. The other thing is we are going we we don't do fully error corrected. We go to fault tolerant, robust, whatever you want to call it.

Sebastian Hassinger:Right. Yeah. Yeah. Yeah.

Susanne Yelin:And see how far we can do with that. Exactly. And then, I mean, the point is right now, I think we have, we have circuit depths that are still I think compared to to when people simulate full universal quantum computers, we are doing pretty well.

Sebastian Hassinger:Mhmm.

Susanne Yelin:But for what you would need in order to do a similar quantum chemistry calculation for a universal quantum computer, and we we are orders orders orders of magnitude away.

Sebastian Hassinger:Right. Right.

Susanne Yelin:So but but we can, in principle, do the same thing. And and, we have now just a a combination of of various ways how to do that. The one is, redundancy.

Sebastian Hassinger:Mhmm.

Susanne Yelin:The second is this optimization of the pulses, that really can be tailored for exactly exactly processing. Right. Right. Right. That processing.

Sebastian Hassinger:Right. Right. Right. That's it feels like that is always going to be the case with these these use cases.

Susanne Yelin:There's nothing wrong about that.

Sebastian Hassinger:I don't know. Of course not. Of course not. I mean, as we said, the the, you know, even just on the on the the face of it, the the data bandwidth limitations of a even, you know, a 20,000 qubit quantum computer is not, you know, trillions of of bits like a a classical computer is. So, you know, they each have to be played for their strengths

Susanne Yelin:is what it feels like. Exactly.

Sebastian Hassinger:So you mentioned, you know, you mentioned error correction be one of your next steps. You mentioned moving into dynamics, I think, of chemical reactions.

Susanne Yelin:Yep.

Sebastian Hassinger:And and also you mentioned lithium hydride, as a is that sort

Susanne Yelin:of your next No. So lithium hydride is, of course, ridiculous compared to this to this. So the reason why I showed this and this, you you saw this. I mean, this is very serious spectrum. It's a couple of thousands of lines already.

Susanne Yelin:Yeah. Where we actually and I did not say that that's basically our earliest where we take the the not just the spin, but also the fermionic nature

Sebastian Hassinger:Okay.

Susanne Yelin:Into account. And in principle, it's not better than what other people who kind of do lithium hydride on a quantum computer do. But we do that now with with these particular methods and just see how far we can what we can do.

Sebastian Hassinger:Right.

Susanne Yelin:And one of the things that we want to do, which I haven't seen that much from from other people, is actually calculating this this kind of potential surfaces. That's what I showed for h two. That is something which which, we can, in principle, scale up as much as we want. Yeah. We might lose accuracy for the larger ones.

Susanne Yelin:But it's not that we say, okay. In 10 years, we actually we might be able to do an let's say, a molecule with 10 atoms.

Sebastian Hassinger:Right.

Susanne Yelin:Right. We could do that tomorrow. Right. And probably the accurate we would have to run it a little bit longer. I also should say, so far, these are all simulation results.

Susanne Yelin:And, they have now, just last month, started running the first of these, multi qubits kind of analog ideas on the on the the Ryberg machine at Harvard.

Sebastian Hassinger:Mhmm.

Susanne Yelin:That is, of course, a machine that's much in need right now. Yeah. Yeah. Yeah. Yeah.

Susanne Yelin:But, this stuff, we will try this all out, in certainly before the year is out.

Sebastian Hassinger:Amazing.

Susanne Yelin:And for that machine, there is not really a difference whether we do a molecule that is, like as big as the one that we showed there, this this this catalyst, or something that really uses every single qubit on the machine. Amazing. The thing is, that that, there is a little bit of pre processing work needed. We need to calculate the optimal kind of the optimal pulses for certain gates.

Sebastian Hassinger:Right.

Susanne Yelin:But once we have them, we can just run them. And we run the gate for whatever, 3 cubits, then we run the gate for 4 qubits, etcetera.

Sebastian Hassinger:Right.

Susanne Yelin:And that can be all done in parallel. And there's, as I say, I mean, as long as as it fits in the Yeah. In the present machine, there is no limitation.

Sebastian Hassinger:Right. And is that something that your computational chemists or your quantum chemists, Martin and and Anne are excited about Yes.

Susanne Yelin:I think they're very excited about this. Yes.

Sebastian Hassinger:Well, that's great. It sounds like we're gonna have to have you back once you get those results.

Susanne Yelin:Well Thank

Sebastian Hassinger:you so much. This has been really, really interesting.