# Quantum computing, hype, and CFD: an honest interview with our Chief Scientist

##### There is a lot of hype around the field of quantum computing.

With many companies, especially start-ups working in the space, a big part of the marketing relies on painting a picture of a future where everything has been solved and fault-tolerant quantum computers are chugging away at affordable prices.

As everyone knows by now, this won’t be a reality for a while, which is why we for one want to focus on more tangible, down-to-earth things: milestones we have already achieved, algorithms we have already proven, and results we have already received.

For this article, we sat down with our Chief Scientist, Dr. Valtteri Lahtinen, to discuss exactly this: what have we actually achieved in the past couple of years and what can you expect in the very near future?

*Quanscient Chief Scientist, Dr. Valtteri Lahtinen*

**How did the research in CFD algorithms begin at Quanscient and what kind of algorithms have you developed?**

So starting way back, we started incorporating Quantum lattice Boltzmann type of methods for quantum computing back in early 2022 just when we had founded the company simply because it seemed to be the one truly quantum native method for solving multiphysics problems. We first looked a little bit into different types of methodologies, but this really turned out to be the quantum native method and the way to go for us.

One of the first milestones was to show on simulators (classical machines emulating quantum computers) that it's possible to solve quantum lattice Boltzmann type of simulations with quantum. We came up with advection-diffusion equation and Navier-Stokes equation lattice Boltzmann method and showed on simulators that it's possible to do it. We built an interactive quantum demo to show our stakeholders, customers, and collaborators what we have and what can be done.

When that was shown, we wanted to see how we could solve these on real quantum computers and it was the summer of 2022 when we were able to run our first 1D quantum lattice Boltzmann simulation on a real quantum computer with accurate results.

That was really a breakthrough in the sense that we were the first team in the world to run this kind of multiphysics problem on a quantum computer with accurate results, but also showed ourselves that we can already do something with NISQ (noisy intermediate scale quantum) devices of today and based on the promising results, we wouldn’t have to wait for the fault-tolerant era of quantum computing to achieve quantum advantage.

From there on we wanted to move up the dimension and go to 2D simulations on real quantum computers, but also optimize these algorithms further so that we can run larger scale simulations on the NISQ devices.

During the year 2023, we achieved 2D simulations on real devices of advection-diffusion equation and we've also been able to optimize the Navier-Stokes solver that we have to a degree where we are on the verge of running meaningful Navier-Stokes simulations on a real quantum device.

We have already been able to run a 3D diffusion simulation on a simulator, and are gearing up to run a 3D simulation on a real device as well.

We have also developed imaginary time quantum linear solver as another quantum-native way of solving multiphysics problems. That is a quantum way of solving linear systems of equations, where a linear system is encoded into Hamiltonian and the solution is then found as the ground state of the Hamiltonian. We have also incorporated this into our quantum demo.

Finally, we have researched another lattice-based CFD method, lattice gas automata. We have been able to come up with quantum lattice gas automata algorithms which we have successfully proven to be both quantum native and runnable on NISQ devices using realistic noise models.

##### How do these differ or improve compared to traditional computational methods?

Classically, when you increase the size of the computational lattice that you are simulating (approximating a space with discrete lattice points), the problem complexity increases at least linearly with the lattice size.

With our quantum algorithms, however, with every qubit we add, the size of the lattice grows exponentially. In contrast, the computational complexity, the number of operations required for the simulation, grows only logarithmically.

Therein lies the promise of quantum advantage that we have with our quantum lattice Boltzmann method.

Another advantage of the lattice-based CFD methods is that they are quantum-native by nature.

In the lattice Boltzmann method, we are dealing with probability densities and we are evolving those probability densities over the lattice. There's a clear analogy to probabilities on quantum computers and amplitudes of the qubits which we can use to our benefit, something we couldn’t do if we were solving finite volume method, for example.

###### What are the practical applications of these algorithms?

CFD is quite a vast field with probably the most obvious use cases coming from airplanes and aerodynamics in the automotive industry.

In addition to these, our algorithms can be used to simulate, for example, the spreading of aerosols or viruses in a room with the advection-diffusion equations. Combining the advection-diffusion equation with Navier-Stokes equations allows us to do even more complicated flow-transport simulations.

In geological modeling, for example, groundwater transport is an important application: how groundwater is transported in the soil and how different contaminants travel there, and so on.

Put simply, wherever you have CFD you have the lattice Boltzmann method as a possible solution to that and hence, also the quantum lattice Boltzmann method.

**Have you tested your algorithms in these real-world applications?**

Yes, we actually did a project together with VTT (Technical Research Center of Finland) where we simulated exactly the spread of aerosols in a room with our quantum lattice Boltzmann method.

We had a 2D advection-diffusion model simulating that and they validated our results with their classical simulations.

###### What are the biggest challenges in researching quantum-based CFD and how do you go about solving them?

One of the biggest challenges we are facing with these quantum CFD methods is nonlinearity. When you have nonlinear equations to be solved, it's difficult to deal with them on a quantum computer because quantum computing is inherently linear.

In quantum computing, you are dealing with unitary operations, which are types of linear operators. It's easy to do linear things, but super difficult to do something nonlinear with a quantum computer.

There are different ways of linearizing nonlinear systems which is the most apparent way to deal with the issue of nonlinearity also in classical computing. We've been researching and implementing different types of linearizations into our quantum algorithms.

Another way, where we actually have a very good working Navier-Stokes algorithm, is a hybrid solution where we solve the nonlinear parts on a classical machine and the rest of the problem is solved on a quantum computer.

The lattice gas automata we recently started researching also provides another alternative to addressing this challenge. As opposed to the lattice Boltzmann method, you are not dealing with probability densities, but rather stream and collision of individual particles where the inherent dynamics of the particles are linear.

From these simple dynamics, we can model, for example, the Navier-Stokes equations. In essence, we can emerge nonlinear dynamics of the macroscopic system from these microscopic linear collisions.

###### How have your quantum algorithms impacted the accuracy and efficiency of CFD simulations?

As I mentioned earlier, the promise of quantum computing in these methods lies in the fact that while the problem grows exponentially, the required computational resources only grow logarithmically.

While we haven't achieved quantum advantage in the sense that we have solved something that couldn't be solved with a classical computer, we can already show that our algorithm can do that as quantum computers get better.

###### Anything else to back that up?

We have patented what we call efficient parallelization of quantum basis state shift.

That's a lot of technical terms, but that basically efficiently, in a quantum parallel way, solves the propagation step of the quantum lattice Boltzmann method which beats all the state-of-the-art methods for this type of algorithm.

More specifically, our data shows that in a well-defined CFD problem, we are well on our way toward quantum advantage within two years from now.

We have released a paper about this. Not only can that be used as the propagation step of the quantum lattice Boltzmann method, but that's actually a very important step of the quantum walk algorithm, which is then used in many different quantum algorithms.

That is a key part in, for example, quantum search algorithms and in some linear systems of equation solvers, and in that sense a very important algorithm which we have optimized considerably further than the previous state-of-the-art.

This is really at the heart of the efficiency of our quantum CFD algorithms.

What are the next immediate goals or milestones for Quanscient in quantum computing?

We’re looking to push 3D simulations further, so we’re working towards running a 3D quantum lattice Boltzmann on a real quantum device.

Through our partnership with world-leading quantum computer manufacturers, we want to run large quantum lattice Boltzmann simulations to see how far we can push the envelope with the current devices.

Similarly, we are now running a lot of tests on other machines, looking also to run quantum lattice gas automata simulations on these devices.

###### How close we are to seeing widespread practical applications of quantum Computing in CFD?

Not quite there yet, I would say, but as I said within two years we believe that quantum advantage can be shown in some practical cases, where we are able to do better than a classical computer.

At that point, it does not mean that we have all aforementioned applications of quantum computing, which will still take a number of years, but in terms of what we do I think at that point we will start little by little incorporating these quantum capabilities also to our cloud offering by 2027.

###### Looking ahead, what is the long-term vision for quantum computing at Quanscient?

A lot of the supercomputing resources of the world are being spent on CFD.

A key part of our vision is to move a lot of this CFD to quantum computing. For one, it's much more efficient computationally, but also it's a big factor in reducing CO2 emissions of supercomputing since quantum computers are more energy efficient.

Since our methods are inherently multiphysics, we’re also broadening our quantum algorithms to cover different types of physics such as electromagnetics to enable multiphysics modeling and incorporate our quantum algorithms into our existing simulation product.

That will enable simulations that are simply unfeasible right now, for example, real-time digital twins of complete fusion power plants and airplanes.

How does Quanscient navigate the balance between the potential and the hype surrounding quantum computing?

There's a lot of hype around quantum and for the layman, it can be hard to navigate through that hype.

At Quanscient, we want to be extremely honest about what we have achieved and in terms of how long we think things will take.

We want to educate our customers and have them understand when they can expect our software to have these quantum capabilities – not just saying that you will be quantum-ready when you buy Quanscient Allsolve.

What is the most misunderstood aspect of quantum computing in relation to CFD?

I would say that it's actually the fact that most people think that you need fault-tolerant error-corrected devices to solve CFD problems on quantum computers. You in fact don’t!

As we have proven, you can already do it today in simple cases on the NISQ devices of today, and these are also the devices we’ll achieve quantum advantage on.

Again, to dehype a little bit, it will not mean that we will be able to solve high-speed airplane flow with billions of degrees of freedom and millions of time steps in two years, but given a well-defined case of CFD, we can solve bigger problems than would be possible on a classical device. The other more complex things will then follow.

Can you talk about any significant collaborations or partnerships that have been important in your quantum research?

We have a very good partnership, for example, with Alpine Quantum Technologies (AQT). We are doing a lot of our R&D on their devices.

Through different partnerships, we also have access to other world-leading quantum hardware.

These partnerships are crucial to us since we need prioritized access to these quantum devices to be able to benchmark and test our algorithms. So far, we are super happy about these partnerships and happy that together with these companies we can contribute to the advancements of quantum computing.

What advice would you give to young scientists and engineers interested in pursuing a career in quantum computing and its applications?

First of all, go for it. Quantum is the future and not only the future, it's happening now.

Do your studies and learn the mathematical foundations well. With that strong foundation even though if you at some point figure out that quantum computing is not your career, you can do pretty much anything else as well. But I'd say go for it.