{"paper":{"title":"Quantum preconditioning method for finite difference discretizations of the Poisson equation via Schr\\\"odingerization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Chuwen Ma, Nana Liu, Shi Jin, Yue Yu","submitted_at":"2025-05-11T06:32:07Z","abstract_excerpt":"We present a quantum preconditioning framework for solving linear systems arising from a finite difference discretization of the Poisson equation. It is based on the combination of the Schr\\\"odingerization technique \\cite{JLY22b,JLYPRL24} and the BPX multilevel preconditioner in order to achieve near-optimal complexity. The Schr\\\"odingerization technique transforms linear partial and ordinary differential equations into Schr\\\"odinger-type systems with unitary evolution in one higher dimension, making them suitable for quantum simulation. A key contribution is a structure-aware construction of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.06866","kind":"arxiv","version":2},"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/2505.06866/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"}