{"paper":{"title":"Hamiltonian Simulation by Qubitization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Guang Hao Low, Isaac L. Chuang","submitted_at":"2016-10-20T19:19:57Z","abstract_excerpt":"We present the problem of approximating the time-evolution operator $e^{-i\\hat{H}t}$ to error $\\epsilon$, where the Hamiltonian $\\hat{H}=(\\langle G|\\otimes\\hat{\\mathcal{I}})\\hat{U}(|G\\rangle\\otimes\\hat{\\mathcal{I}})$ is the projection of a unitary oracle $\\hat{U}$ onto the state $|G\\rangle$ created by another unitary oracle. Our algorithm solves this with a query complexity $\\mathcal{O}\\big(t+\\log({1/\\epsilon})\\big)$ to both oracles that is optimal with respect to all parameters in both the asymptotic and non-asymptotic regime, and also with low overhead, using at most two additional ancilla q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06546","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}