Thanks. Look at that. Look. Okay. Yeah. Thanks. I’m coming here to I guess say something a little different talking about quantum computing for solving aerodynamic problems. And it’s been really nice seeing all the AI talks and kind of how that can kind of revolutionize simulations. And I’m coming here to kind of show where quantum is now. Just I’ll go into some more detail but I want to say not trying to kind of give the hype but kind of just show the data of you know what you could do with a quantum computer on actual hardware today even if it’s not ready at really these you know billions of degrees of freedom or some things that we’ve seen before but I guess also in the second half kind of share some of the key things to think about as you’re going forward so I think part of this as well is that when we come to quantum there’s going to be certain trade-offs or limitations that kind of you as an engineer might not be aware of and kind of my goal is to kind of maybe like make you aware that even when quantum comes with say is hype there’s also going to be some difficulties and how we can work through that.

1:29 So yeah just a little bit myself. My name is William Steedman. I’m a senior algorithm engineer at Quansient. Quient is a multifysics simulation company based in Algra Finland. And yeah we work with a range of companies as shown here doing kind of standard general purpose on multi physics but from the or yeah like finite element analysis but kind of from the start we also had a quantum labs division and that’s kind of what we’re doing and kind of looking as you know step forward how can we bring simulation you know quantity forward where we can put with quantum and so they said the first part is going to be talking about where we are right now so c you motivates inspiration and the results and then the second part is looking forward.

2:19 So not getting kind of into too much detail but just kind of looking at the big picture quantum computing has been you know kind of talked about for a while and we’re kind of going through different phases. So I took this kind of from a report and I would like to kind of highlight three general phases. One is kind of from you know the 80s to about 2000 where theoretical people are coming up with these statements vonoman is like the world is quantum and we have this idea of a quantum computer and then it’s really amazing around 2001 and kind of like say 2020 we actually start seeing people building these and I used to work at a company that modeled back the hardware you know the pulses you would send to control these cubits and it went from you know a theoretical thing to actually we can precisely do them and then around 2020 we have like Google quantum supremacy just kind of this increasing scale you know it’s not just a few cubits we’re talking about hundreds and even now these what we call these neutral atom computers where you can get thousands of cubits and the problem kind of shifts a little bit that we have so many of these cubits when we use them they’re all noisy and so this is kind of going from the physical cubits to what we call the logical cubits this is going forward so it’s not you know certain but kind of this idea we’re going to take all these noisy kind messy cubits and put them together into these error corrected kind of higher quality cubits and we’re going to have to see where this goes.

3:43 Generally I’m just saying it has been kind of impressive that step by step these companies keep building better and you know larger computers. So I claim 025 that 1,00 1 to 3,000. This is about based out of Harvard and there are kind of these promises in the next 2028 to have the first usable of logical cubits and just on the bottom without going into too much this is kind of showing how at least for this was for cryptography and security how kind of step by step we’re making kind of the beginning things of making operations in this case for postquantum security what I think kind of see different fields it’s not say a rush but kind of slowly we’re kind of seeing this maturity So now the motivation kind of more for this audience right we’re trying to find I guess a little different is kind of a problem with you know a big cost and a big reward and so we’ve been focusing on computational fluid dynamics kind of as this idea we know that we want to have these complex numerical simulations and we can kind of show at the bottom here we kind of have this hierarchy of models where you have this simplified models that work at a larger resolution you provide more restrictions and kind of information on the the fluid dynamics onto what we call direct numeric simulation where it’s very there’s no kind of a priority restriction on the physics that you represent in some sens but you just need this huge number in practical number of cells so kind of showing at the top we take the aircraft we have to resolve the scale of the aircraft but we still have this sub millm act where all the turbulence is happening and you know you would need something like 10 to the 18 cells to really scale and it’s very impressive what we’ve seen lately with you know the current models but that’s just not feasible and we do have and this what I’ll talk about is this lattis bulkman method where it is really going on to say 10 to the 12th field but we want to push this further so why the lattis bulman method you know and why do we want to use it for quantum I guess at least from the quantum I won’t be able to kind of get too much into you know how quantum works by all means please ask me afterwards I’m kind of happy to to go into detail but just to say briefly the quantum idea that you have a superp position where you can encode these massive problems.

5:58 The idea is every cubit doubles the space that you can kind of you can address. So with 50 cubits to the 50 you can get about 10^ the 15 point latice for say a single variable. So if we we could impose this whole problem on there but you know what would we do? How would we do that? And that’s where we learn about Boltzman method. It’s a flexible method that works for many particle differential equations and it supports these complex condition boundary conditions and the way it does this is we have kind of this microscopic scale of individual particles you have now stokes your macroscopic physics and the last method is this kind of idea of bridging these two.

6:39 So we have these two status called this collision of propagation where you kind of have these flows on this lapis at this intermediate scale and the they’re capturing the transport and the collision is specifically chosen to match the type of physics. So different types of collisions can represent different physics and so here at the bottom we have some applications. So say subsonic fluid dynamics, acoustics, solid mechanics, combustion, heat transfer dynamics, traffic flow and this is a growing and expanding field.

7:09 So people find new ways to kind of incorporate whatever specific problem within these two operations and in specifically for quantum what’s interesting is we say that the quantum algum is exponentially faster for these two operations. So you imagine you have a huge grid you have to do these flows these calculations on every one of those and that’s where this quantum had its you know best performance I have though an asterk there kind of in two parts I’m not saying that end to end it will be faster or exponentially faster and we have parts where quantum will be slower than you would think and then my last two slide that go a bit about that one thing which I just really want to highlight is this open issue the nonlinearities so quantum computers are very good for linear problems huge linear problems But I think everyone here has sees you know eventually you have this nonlinearity that makes a problem interesting and it’s really the open research of how best to do this.

8:01 So there’s some options of parl linearization. We’re actually looking internally using machine learning kind of a linear approximation you can think of but there are different ideas for how to do that. So, one other thing I want to highlight is there’s not one Latin holdment method. And so, what we’ve been doing and we’re really focusing what we call this one-step simplified method. So, it’s this way to streamline this collision process and it’s to be more efficient.

So, there are other people who are doing quantum lab method but we believe this gives us basically competitive or an advantage. And the way it works is it has these two time levels. So, on the right here you kind of have that standard grid that is 2D. You can also do this in 3D and you have an inner level and then at the second time level this outer level and by combining these two time levels you can simplify the process.

8:50 So this can be done classicalally. It’s there papers for doing this. And we shown also that it’s more numerically stable and it has this efficiency. So one of our goals really is to kind of show that for problems of interest rate if we look at the specific type of model it’s going to be accurate and usable. And so with this combined yeah we can also reduce the the resources and just if you want I’ll have this also at the end we have like a link basically archive this preprint for showing the details of this method that we published recently and in the bottom here is a kind of a plot of how the quantum algorithm would be blocked using these cubits and these kind of different ideas of registers but I don’t have time to go too much into that kind of now you know we have the promise us what’s actually happening.

9:39 So this is why I wanted to get to the hardware as soon as possible. So we’ve run on various different hardware. This was from 2024 on the ion QA1. So this is an ion trap device. And what we want to show first time is multiple time steps of of a simplified problem. It’s that vection by fusion sort of transport problem and really you know seeing what can the current hardware do.

17:33 So you will see in the lower right here these are the different time steps and you can visually see there there are differences right it’s not like we’re at in a perfect and that’s because of all the sources of air and these physical cubits so what we’ve done is we basically use as many tricks as we can so we partnered with high they have ways of doing subcircuit compression and then lots of error mitigation so the idea here is you know you’re trying to measure in say the field output at all the pixels but you know it’s going going to be biased.

You run this, you get a type of error model. And what we’ll try to do is try to use similar circuits that we can predict and kind of build on a library of a noise model for this device and then you use that to filter out the errors. So this is actually shown after a lot of error post-processing. And then kind of another thing which I will get a little bit into later maybe is we also have to approximate the initial conditions.

We can’t actually encode an arbitrary state. That also would be expensive. So we have to do this using these matrix product states to basically start with kind of a simplified but given those limitations we see for a nice large scale time a 64x 64 lice three time steps and this circuit depth of about 800 and just in the upper there again this is this a diagram of these different blocks.

So these cubits at the top that would be the cubits that we use for representing this lattice. So this was 2 6 by 2 6 if I had that right. And then that would be 12 cubits and then we have these additional cubits and they’re representing the different flows that I mentioned before right these these flows and so that together I guess the slower right problem we have the 16 cubits to encode the whole problem.

But we wanted to get to a nonlinear problem. We want to get to aerodynamics. That’s the promise. And so in IBM we ran I would say the very very basic but an air foil like problem. So our air foil it is two pixels but it is an 8×8 grid and we are doing the Na’vi Stokes physics. So to do this we’re actually doing the hybrids method. So what we do is we take the nonlinear fields we encode them on the on the computer and we do one time step.

Then we have to you know take it out of the quantum computer and measure this quantum computer many many times to reconstruct the fields and again it’s expensive. This is one of the bottlenecks of quantum computing. So we actually use some basis functions. This is also with high cube to go and reconstruct these fields with this set of basis functions. And then we can repeat this process and you know see how the errors would build up.

And we can do 15 time steps on this. And yeah, I would not claim that kind of in the lower left here you have this ideal. It’s not 100% perfect, but you see the general, you know, we are representing the general physics here and kind of if we have the densities, the x and y momentum. So it is qualitatively accurate but we have this issue of the errors of these cubits and this gets this interesting point which is the current domain.

So this device I think we used 23 cubits is a device with hundreds of cubits but the problem is as we scale up you know the errors dominate and this is kind of the trade-off of what I said before right every time you add a cubit you double the space so this means that like any time you have an air on one of the cubits it’s not just affecting one of these cells it’s affecting all parts of this you know model that you’re trying to represent.

So if we’re ever really if we’re ever going to get to this 10^ the 15 cells, we need to have these logical cubits with no errors because otherwise any single error will ruin it. So kind of just to give you a little bit of you know where we are and what’s next. We will we’ve shown that we can do the very basic problems on the current hardware.

It’s not something that’s engineeringly useful, but we we run them. And what we want to do is then goes to this trajectory to be, you know, larger and larger problems with more and more accurate details. So on the right here, we have this video. This is a simulation of that same algorithm using these I guess here the yeah the 23 dubits. And with you know we had no errors and we can run for many time steps.

And so what I say is when we get to that transition to logical cubits that’s where these larger simulations become possible you know and saying in that reminder if we get to 50 logical cubits we can do some type of simulation that you wouldn’t do classically. Now the one thing I have to say there is not saying an end to end you know I have the beginning and I can do all of fluid dynamics.

Maybe it’s just one time step. It might be a very limited problem but you can actually represent at least some type of problem that you wouldn’t be able to represent classically and then the ground really is working with people see how can we make this usable right even if I can say I can solve something you know it’s not going to be your whole problem yeah so going forward okay what what can we see so I just want to say on the side quantium we have also a multifysics solver this is all called all solve general purpose multi physics and we use it for a range of applications and I’m going to focus on this micro speaker this nuns micro speaker on the next slide.

So I’m going to kind of show two ways that we want to integrate. So one is just to say we’re going to add lattice bol solver to our to all sol is the way to do fluid dynamics like time domain fluid dynamics and we’ll then mark it across you know standard third party solvers. The idea here is we’ll just do a classical wind solver. And what’s interesting is we have on the one side that we can do these super in principle these super fine grids but quantum can’t represent every type of problem easily.

19:27 So we have to have these like non-quantum features that will be turned off and that might be more complicated handling of your boundary conditions how you add these surface terms. So we’re going to have this trade-off. Our models can resolve and are much finer but they might not be as accurate due to these simplifications. And we want to have is this classical grin basically show that that’s still usable right for your type of problem if we line a very fine grid of the simplified conditions does that actually you know help or you just get non-physical results and so we’re validating against you know the literature right now our lower rentals kind of showing as we increase the the mesh here the reference third party one ours they agree and we’ll build up to higher resolutions and higher rentals numbers the second thing I want to highlight that is on the AI side which we’ve seen already.

So here we have this multi physics problem and basically a speaker where the bottom is fixed and the top is clamped and you know you’re just sending some electrical signals the select statics cause it to vibrate and then you’re getting a speaker for this movement in between the two plates and we’re showing a sweep for different geometry parameters and I’ve shown similar you can kind of do the parametric sweeps and you can find what’s my optimal design.

So blue is basically this training set of these different performance indicators. Basically on the y-axis is my volume. You know how effective is the speaker and on the x-axis is do I get distortion and we from this we can make a an optimization front that’s shown in the the red but using our multifysics we can go and validate it and then we can kind of show that we actually get the best design and the reason I choose this particular example is to also say one things about quantum is we’re going to have to choose specific outputs so you will not necessarily use quantum to run this full sweep and get all these outputs but one way do this use AI, use classical methods to do a general purpose search and really use quantum to investigate a single point.

Yeah, so I’ll come right back to this. I’m going to go very briefly over my two extra slides on kind of some of the trade-offs, but yeah, need me as I say happy to do a pilot and get in touch. So yeah, what are the limitations or the trade-offs? So I said we can do four operations. So this allows whole group very efficiently. But actually in the boundary conditions it’s going to be very hard.

So quantum is very good if you want to do one operation everywhere. It’s very bad at this like I want to do very specific operations at specific points. And so this is one of our open questions is how are we going to represent these air foils? You know you have a very complicated geometry. I remember this like drone of ribs. We have to some way to encode that in the qual computer.

And here I’ve shown kind of two ways and they’re trade-offs. We can do simple polomials but they’re simple polomials or we can also do these matrix product states but visually you can see at the bottom that there’s all sorts of artifacts. So one thing we’re going to have to do and you can really be aware of is it may work but will it work for your geometry and then the second thing very quickly is just as I said we need to get the data out.

And so the way it works on quantum computers is you have these shots you run you have your whole system you run your shot and you get some number out but it’s actually going to be like a binary number one and zeros. So if you want to measure something like acoustic energy your drag coefficient you’re going to run many many shots and you’re going to see some variability unless you use lots and lots of shots.

So I think the other thing I want to say is that we really need to work on and this is what we’re also doing internally like what are sets of parameters that we can extract from the quantum computer because you’re never going to get the full field values but you need to be able to trust this. So we have to come up with not just say the lift and drag coefficients but correlations and so forth that you can use you know you can trust this quantum model.

19:34 So yeah, this was a very kind of rapid and quick but just to kind of show you there where it is right now and maybe what might be interest going forward. So yeah, thanks. Any questions?