{"paper":{"title":"A Simple GPU-Accelerated Solver for the Schr\\\"odinger Operator with Applications to Ground States and Hamiltonian Simulation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","physics.comp-ph","quant-ph"],"primary_cat":"math.NA","authors_text":"Xiangxiong Zhang, Xinyu Liu","submitted_at":"2026-05-19T20:55:54Z","abstract_excerpt":"We extend the tensor-product direct solver from the Laplacian to the Schr\\\"odinger operator $-\\Delta + V$. When the potential $V_1$ is separable, the operator $-\\Delta + V_1$ is inverted or exponentiated at cost $O(N^{1+1/d})$ in $d$ dimensions via per-axis eigendecomposition. On a single NVIDIA A100 GPU, this costs less than one second for $10^9$ degrees of freedom in 3D. For non-separable potentials $V = V_1 + V_2$, the same solver provides a preconditioner $(-\\Delta + V_1)^{-1}$ for the preconditioned conjugate gradient (PCG) method and a propagator for operator-splitting time integrators. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20491","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/2605.20491/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"}