{"paper":{"title":"Piecewise Polynomial Tensor Network Quantum Feature Encoding","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Matthias Kabel, Mazen Ali","submitted_at":"2024-02-12T14:26:33Z","abstract_excerpt":"This work introduces a novel method for embedding continuous variables into quantum circuits via piecewise polynomial features, utilizing low-rank tensor networks. Our approach, termed Piecewise Polynomial Tensor Network Quantum Feature Encoding (PPTNQFE), aims to broaden the applicability of quantum algorithms by incorporating spatially localized representations suited for numerical applications like partial differential equations and function regression. We demonstrate the potential of PPTNQFE through efficient point evaluations of solutions of discretized differential equations and in model"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.07671","kind":"arxiv","version":5},"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/2402.07671/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"}