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We present novel algorithmic solutions together with implementation detailsutilizing non-Abelian symmetries in order to boost the current limits of tensornetwork state algorithms on high performance computing infrastructure. In ourin-house developed hybrid CPU-multiGPU solution scheduling is decentralized,threads are autonomous and inter-thread communications are solely limited tointeractions with globally visible lock-free constructs. Our custom tailoredvirtual memory management ensures data is produced with high spatial locality,which together with the use of specific sequences of strided batched matrixoperations translates to significantly higher overall throughput. In order tolower IO overhead, an adaptive buffering technique is used to dynamically matchthe level of data abstraction, at which cache repositories are built andreused, to system resources. The non-Abelian symmetry related tensor algebrabased on Wigner-Eckhart theorem is fully detached from the conventional tensornetwork layer, thus massively parallel matrix and tensor operations can beperformed without additional overheads. Altogether, we have achieved an orderof magnitude increase in performance with respect to results reported inarXiv:2305.05581 in terms of computational complexity and at the same time afactor of three to six in the actual performance measured in TFLOPS. Benchmarkresults are presented on Hilbert space dimensions up to $2.88\times10^{36}$obtained via large-scale SU(2) spin adapted density matrix renormalizationgroup simulations on selected strongly correlated molecular systems. Thesedemonstrate the utilization of NVIDIA's highly specialized tensor cores,leading to performance around 110 TFLOPS on a single node supplied with eightNVIDIA A100 devices. In comparison to U(1) implementations with matchingaccuracy, our solution has an estimated effective performance of 250-500TFLOPS.

Boosting the effective performance of massively parallel tensor network  state algorithms on hybrid CPU-GPU based architectures via non-Abelian  symmetries