{"paper":{"title":"Quantum speedup of classical mixing processes","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Peter C. Richter","submitted_at":"2006-09-26T20:52:12Z","abstract_excerpt":"Most approximation algorithms for #P-complete problems (e.g., evaluating the permanent of a matrix or the volume of a polytope) work by reduction to the problem of approximate sampling from a distribution $\\pi$ over a large set $\\S$. This problem is solved using the {\\em Markov chain Monte Carlo} method: a sparse, reversible Markov chain $P$ on $\\S$ with stationary distribution $\\pi$ is run to near equilibrium. The running time of this random walk algorithm, the so-called {\\em mixing time} of $P$, is $O(\\delta^{-1} \\log 1/\\pi_*)$ as shown by Aldous, where $\\delta$ is the spectral gap of $P$ an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0609204","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"}