Wallerberger, M., & Held, K. (2022). Trie-based ranking of quantum many-body states. Physical Review Research (PRResearch), 4(3), Article 033238. https://doi.org/10.1103/PhysRevResearch.4.033238
Ranking bit patterns - finding the index of a given pattern in an ordered sequence - is a major bottleneck in scaling up numerical quantum many-body calculations, as fermionic and hard-core bosonic states translate naturally to bit patterns. Traditionally, ranking is done by bisectioning search, which has poor cache performance on modern machines. We instead propose to use tries (prefix trees), thereby achieving a two- to tenfold speedup in numerical experiments with only moderate memory overhead. For the important problem of ranking permutations, the corresponding tries can be compressed. These compressed "staggered"lookups allow for a considerable speedup while retaining the memory requirements of prior algorithms based on the combinatorial number system.
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Project title:
Adaptive Magnus-Integratoren für Quantensysteme: P 30819-N32 (Fonds zur Förderung der wissenschaftlichen Forschung (FWF)) elektronische Korrelationen auf dem 3-Teilchen-Niveau: P 32044-N32 (Fonds zur Förderung der wissenschaftlichen Forschung (FWF))