Transcript

**Rene:** Hi welcome to QuBites, your bite-sized pieces of quantum computing. My name is Rene from Valorem Reply and today Rene: Hi welcome to QuBites, your bite-sized pieces of quantum computing. My name is Rene from Valorem Reply and today we're going to talk about quantum computing for physical simulation. And that's a topic near and dear to my heart, having myself worked on physical simulation for computer graphics back in the days, right? But not in quantum computing. But you know how you can do physical simulation with quantum computing; we will talk about that today. And for this I'm very honored to have a special expert guest today who works with quantum computing and physical simulation, Professor Eduardo Inacio Duzzioni. Hi Eduardo and welcome to the show! How are you today?

**Eduardo:** Hi, hey. I'm well and thanks for your invitation.

**Rene:** Alright, Eduardo can you tell us a little bit about yourself, and your background as relates to quantum computing and physics and all the things you do?

**Eduardo:** OK. Well, I'm a physicist. I got a bachelor’s degree more than 20 years ago at the Federal University of Santa Catarina in Brazil. I start work on Quantum Optics in my PhD, then I gradually move to the field of quantum information and quantum computation, but I always find quantum computing fascinating because there are very interesting topics. Then in 2018 I decided to open I startup called Quanby and there we develop quantum algorithms to approach commercial problems. And then, I started work on problems like, quantum algorithms to solve fluid dynamics problems and solve partial differential equations and so on yeah.

**Rene:** Awesome. Awesome. Well, that's quite a career here. And you’re also a professor, right? So.

**Eduardo:** Yeah. Yeah.

**Rene:** So, well you should mention it! Anyhow, let's dive into today's topic. And I saw you recently gave a talk at a conference about quantum algorithms for fluid dynamics, or CFD, right? Computational fluid dynamics. Like I said, I have implemented my own kind of fluid dynamics simulation back in the days. But that was a thing called SPH, smooth particle hydrodynamics. And it's been like, oh I don't know, like more than ten years ago. And that was, of course, more for like I said for computer graphics, right? For visualization. And the nice thing is if you're doing physical simulation for computer graphics you have one goal, it has to look believable, right? But it doesn't have to be physically correct, right? And I think that's the main difference if we're talking like fluid simulation for like computer graphics compared to real proper CFD, computational fluid dynamics, right? And I guess for you scenario, it's really about precision and not that it's just looking good right? And, you know, doing smoke and mirrors kind of thing. And so, can you tell us a little bit about how quantum computing actually helps you in the field of fluid simulation and what you are doing there?

**Eduardo:** Exactly. What you know today about quantum algorithms to solve partial differential equations, is that there are some situations in which it's possible to get quantum advantage over the classical counterpart of these problems. For instance, the Navier-Stokes that are equations to solve for fluid dynamic problems, they are partial differential equations. So it's possible in some situations, not all situations at least what we know today, to get some speedups. In particular cases, exponential speedups but in other cases polynomial speedups. So, based on that, we are studying quantum algorithms to solve the solution of partial differential equations. Basically, in quantifying dynamics, motivated initially by the Airbus Quantum Computing challenges that started in 2019. So, since then I am working in these quantum algorithms that are able to be applied in the initial area to solve partial differential equations and basically applied to fluid dynamic problems.

**Rene:** Gotcha. Well that makes a lot of sense and for the audience here, if you look familiar with that kind of stuff, the Navier-Stokes equation for example, is a famous equation basically that describes how you can simulate or how you can compute the behavior of fluid dynamics in the end basically, right? And so that has always been a big challenge to compute that. Like you're saying, it's very complex to simulate and very, very computationally intensive. And the Navier-Stokes is basically based on the mathematical principle of partial differential equations. Which are, well of course, hard to compute. Especially in scale. right? 'Cause you don't just want to simulate like one fluid particle, but like I don't know. millions of them. right? If you want to simulate water or like certain behaviors like smoke and all of that stuff, right? Well, that's impressive. So, basically, you're saying we're using partial differential equations or we can solve partial differential equations with quantum computing and that leads you to the basically the fluid simulation in the end right? What are some other applications and examples you can think of where quantum computing is used to simulate physics? I guess like since you're going with this generic approach about using basically how I can solve partial differential equations with quantum computers, it can be used for a couple of other things. So, I could also think about, you know, classical mass-spring models, right? Which are used for simulating cloth. For example. like cloth simulations are typically based on the good old Newtonian mass-spring model. Of course, there are more fancier ones available. So, I guess that would actually be easy, right?

**Eduardo:** Yeah. OK, well, quantum computers can be used to simulate, as originally proposed by Richard Feynman, maybe in quantum systems. That was the basic idea. But now we know that we can extend the application of quantum computers to other problems. You mentioned that simulation of cloth. As you already mentioned, cloth is described by partial differential equations in which will have masses connected by springs and damping, etcetera. So, I believe that is a special case of partial differential equations so I believe that its possible yes to get speed up in this case.

**Rene:** Yeah. Like you were saying right? Before we talked, I didn't understand you actually are not just solving CFD, like computational fluid dynamics, with quantum computers but an actually more generic approach like how can I solve potential differential equations with quantum computing? And, oh man, there's huge use cases. There's so many things you could do with that. So yeah, totally makes sense what you just said. For us for example at Reply, we're working a lot on and focusing a lot on today's impact and using a lot of quantum inspired computing solutions. Like for example, quantum inspired optimization, right? And with that we're already solving challenging optimization problems for our clients where they can get, for example, a 20% time saving compared to classical optimization solver right? And so there's a ton of stuff even if you use these algorithms on classical hardware, like GPU array, these quantum inspired optimization algorithms are in some way already outpacing classical optimization algorithms. So, this is why for example we at Reply see quite a bit of impact already today with quantum computing. Although the hardware is still a bit in its infancy, but there's also quantum security where you can already see impactful things. Anyhow, my question for you is, in your opinion where are you already seeing the impact with quantum computing these days? Especially in your respective area of physical stimulation, right?

**Eduardo:** Ah, ok. Well, as far as I know, the impact of quantum simulation, impact of quantum computing to simulate physical systems, is not possible today just to simulate atomic physics like spring-systems, and so on. This is quite clear today. And it's possible to find new phase of matter, it is very nice. But more precisely, when you deal with commercial problems, I don't know any quantum advantage today.

**Rene:** Gotcha. Yeah, I mean, there's a ton of stuff. And like you said, like the Airbus Quantum Computing challenge for example, think about aviation and all these things like I said, right? I mean [these are such] complex systems, super complex systems, right? That have tons of attributes. If you put it in equation, it's a huge equation with lots of variables you don't know, right? And you need to use things like partial differential equations and being able to solve those with quantum computing, is providing a ton of impact I think in next couple of years. So, wow, that's impressive. I think we could talk much more about our fun topic of physical simulations and whatnot, but we're already at the end of the show here. Thank you so much Eduardo for joining us today and sharing your insights, it was very much appreciated. Thank you so much.

**Eduardo:** Rene, thank you. Thank you for your invitation and thank you for the opportunity. OK. Thank you. Bye, bye.

**Rene:** Alrighty and thanks everyone for joining us for yet another episode of QuBites, your bite-sized pieces of quantum computing. Watch our blog, follow our social media channels, to hear all about the next episodes when we release them. And you can also of course always watch the old ones, right? Take care, be safe, see you soon. Bye, bye!