##### 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. ###### 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.