### Speaker

### Description

As the design and mass manufacturing of efficient quantum computers are still subject of intense research, the numerical simulations of quantum systems still rely on classical computation. In this case however the complexity and resource requirements of such algorithms scale exponentially relative to the system size, thus making bigger simulations problematic or even impossible to run.

Our approach focuses on the development of massively parallel algorithms that are not only highly scalable and ideal to use in an HPC environment, but by building on the foundation of theoretical physics and applied mathematics the number of required arithmetic calculations could be reduced by multiple magnitudes. As a result the exponential time cost of the simulations has collapsed into polynomial complexity.

The research program puts an emphasis on one of the subclasses of tensor network state algorithms called density matrix renormalization group, or DMRG for short. In such cases large-scale tensor operations can be substituted with multi-million vector and matrix operations, of which many can be executed independently of one another. Through the exploitation of these (in)dependencies arithmetic operations can be reordered and put into multiple tiers of groups corresponding to specific software and hardware layers ranging from low level CPU and GPU based SIMD execution to high level HPC scheduling. Thanks to the fact that for every tier we can execute all operations contained within the same group independently of all other arithmetics residing outside the group, mass scale parallelism can be achieved at every tier of our multi-tiered grouping. The resulting parallelization is the product of each tier's own massive parallelization, thus with suitable hardware infrastructure exascale computing in the near future might become a reality for DMRG based quantum simulations.