{"paper":{"title":"Parallelized contraction of tensor trains or matrix product operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.comp-ph","authors_text":"Hiroshi Shinaoka, Jan von Delft, Marc K. Ritter, Simone Foder\\`a","submitted_at":"2026-06-22T12:52:56Z","abstract_excerpt":"Tensor Trains (TT), also known as Matrix Product States (MPS) and Matrix Product Operators (MPO), provide a compact and structured representation for high-dimensional data and operators. One of the most expensive manipulations involving tensor trains is the contraction of two MPOs. A popular and accurate method for mitigating this cost is the fit algorithm. However, it is still comparatively costly since it involves 2-site updates. Moreover, the parallelization of the fit algorithm when used for MPO-MPO contractions has received comparatively little attention. In this work, we present two stra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.23274","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.23274/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}