{"paper":{"title":"Quantum Fast-Forwarding: Markov Chains and Graph Property Testing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Alain Sarlette, Simon Apers","submitted_at":"2018-04-06T15:18:11Z","abstract_excerpt":"We introduce a new tool for quantum algorithms called quantum fast-forwarding (QFF). The tool uses quantum walks as a means to quadratically fast-forward a reversible Markov chain. More specifically, with $P$ the Markov chain transition matrix and $D = \\sqrt{P\\circ P^T}$ its discriminant matrix ($D=P$ if $P$ is symmetric), we construct a quantum walk algorithm that for any quantum state $|v\\rangle$ and integer $t$ returns a quantum state $\\epsilon$-close to the state $D^t|v\\rangle/\\|D^t|v\\rangle\\|$. The algorithm uses $O\\Big(\\|D^t|v\\rangle\\|^{-1}\\sqrt{t\\log(\\epsilon\\|D^t|v\\rangle\\|)^{-1}}\\Big)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.02321","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":""},"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"}