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Successful Polish LUMI pilot project in the field of quantum mechanics

One of the projects submitted by Poland for the LUMI GPU pilot phase in late 2022 was a project called Turbulent Dynamics in Superfluid Fermi Systems, which researched complex quantum mechanical problems with a particular focus on quantum turbulence occurring in superfluids. Although such a phenomenon has been extensively studied in the last years if bosons are considered, the research on fermions is comparably new. It may, among others, shed new light on processes taking place inside neutron stars.

Principal investigator Prof. Gabriel Wlazłowski (Warsaw University of Technology) shares some preliminary results and a general overview of using the LUMI infrastructure resources.

– Bosons like to condensate in a single state at low temperatures, and knowing the properties of this single state is sufficient to understand the whole system. The emerging Bose-Einstein condensate is a prime example of a superfluid. Similarly, fermions can also create superfluids at low temperatures; however, the underlying mechanism differs. The Pauli principle forbids two fermions to occupy the same quantum state, and to understand the behaviour of the whole system; one needs to track all quantum states. This generates a substantial computational demand, which was the main bottleneck for researchers in this field. For example, we still lack a clear answer to what extent quantum statistics impact the dynamics of quantum systems. Understanding the dynamical properties of superfluids and the conditions at which the flows change nature from laminar to turbulent is essential in the context of future applications – explains prof. Wlazłowski asked to characterise the subject of the research synthetically. The team also wanted to demonstrate, test, and optimise the performance of the ELPA library on HPC systems with AMD MI250x GPUs.

ELPA, ”Eigenvalue Solvers for Petaflop Applications,” is a publicly available library that provides highly scalable direct eigensolvers for symmetric (hermitian) matrices. The library has been being developed since 2008. It is used for solving large problem sizes on massively parallel supercomputers – such as LUMI, which, as it turned out, gave the possibility to obtain promising research results.

– As preliminary results concerning the porting of the ELPA library, we can report that we were able to run the ELPA library with good performance on LUMI. Furthermore, we solved eigenvalue problems with matrix sizes of 3,000,000, which, as far as we know, has never been possible before with a direct eigenvalue solver – informs Dr. Andreas Marek (MPCDF), one of the project researchers. And Prof. Wlazłowski follows that the team was able to evolve in time quantum states extracted by the ELPA library:

– Technically, this process means solving more than 1 million coupled, nonlinear partial differential equations in space and time. From the physical point of view, we can simulate quantum systems consisting of thousands of particles that obey the Pauli principle. The obtained results are still under analysis, but we can already say that we have managed to study systems that were not accessible to us before.

Prof. Wlazłowski is satisfied with using the LUMI infrastructure and focuses on the possibility of operating on dense matrices whose sizes are of the order of millions and solving coupled sets of partial differential equations of the same order in size, which, in his opinion, makes a natural step forward for quantum mechanical simulations. Prof. Wlazłowski also comments that the process of applying for the LUMI resources was effortless:

– Everything is done digitally, and we had no problems with this part. However, we understand that the LUMI is one of the best computing systems in the world. Naturally, it sets scientific competition to be at a very high level.

At the same time, Dr. Marek evaluates the system availability and software stack very well and expresses contentment with the cooperation with the LUMI User Support Team.

As soon as the preliminary results are developed, a question emerges about the possibility of continuing research on their basis and the future challenges. Prof. Wlazłowski notices the current potential of providing solid benchmarks or guidance for groups that develop quantum devices based on ultracold Fermi gases and supporting astrophysics research.

– According to present knowledge, neutron stars are filled with superfluid and strongly interacting fermions, like neutrons. Among many open questions in this field, one is whether such matter flows inside the star in a laminar or turbulent fashion. This can be answered only by utilising numerical modelling. Nuclear systems are more challenging than ultracold atomic gases, as considered within this project. However, the same methods can be extended to such cases, and it is the direction that is intensively developed presently. In the long term, we would like to construct a reliable microscopic simulator of processes that take place inside neutron stars – systems that are not directly accessible. Then large-scale simulations will play the role of “numerical experiments” that can drive the field forward – concludes Prof. Wlazłowski.

After a successful pilot project period, LUMI entered the regular access phase. European researchers and researchers from the countries participating in the LUMI consortium, including Poland, can apply for the LUMI resources.

Visualisation of a Polish LUMI GPU pilot project's results

Image: Preliminary result: Visualisation of quantum turbulence state in ultracold Fermi gas. The lines inside the simulation domain indicate quantum vortices. Around these lines, the gas circulates, depicted by a vector field (currents) on one of the sides of the domain. Isosurfaces show the sizes of the vortex cores. To some extent, one can imagine these objects like a chaotic tangle of tornados but in the quantum world.

Author: Kamil Mucha, Cyfronet