Keywords: quantum simulations, path integral Monte Carlo method, electronic structure calculations, parallel tempering algorithm, tensor methods, multi-level parallelization.

In this contribution we focus on HPC aspects of a fully quantum simulation of manyparticle systems at nonzero temperatures and pressures. Our long term intention is to combine the path integral Monte Carlo (PIMC) approach with the fully quantum potentials obtained from electronic structure calculations. Since both of these methods are parallelizable on various levels, the resulting code utilizes multilevel parallelization. If the parallel tempering algorithm is used, the number of parallelization levels can grow up to four. At the top level, the parallel tempering algorithm takes place, running tens to hundreds of simulations in parallel. Each PIMC simulation then calculates in parallel hundreds of evaluations of the density matrix at each Monte Carlo step. Each of these evaluations is done via the electronic structure module which utilizes the bottom level parallelization using hundreds of cores. If the electronic structure module is implemented using the tensor methods, the parallelization of the module can be done in two levels. The main aim of this paper is a) to discuss the scalability of these methods and b) independently estimate the optimal CPU workload under various computational conditions. According to the scalability of the components, the expected scalability of the whole tool can easily reach exascale, utilizing hundreds of thousands of computational cores and more.

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