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Richter","submitted_at":"2006-06-24T01:09:57Z","abstract_excerpt":"Many classical randomized algorithms (e.g., approximation algorithms for #P-complete problems) utilize the following random walk algorithm for {\\em almost uniform sampling} from a state space $S$ of cardinality $N$: run a symmetric ergodic Markov chain $P$ on $S$ for long enough to obtain a random state from within $\\epsilon$ total variation distance of the uniform distribution over $S$. The running time of this algorithm, the so-called {\\em mixing time} of $P$, is $O(\\delta^{-1} (\\log N + \\log \\epsilon^{-1}))$, where $\\delta$ is the spectral gap of $P$.\n  We present a natural quantum version "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"quant-ph/0606202","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2006-06-24T01:09:57Z","cross_cats_sorted":[],"title_canon_sha256":"45d93ed1d8ba7ef2cf3cce2ffd791d2be26afcb8c887b1ffd2580d992f670750","abstract_canon_sha256":"4bd109ca335c329e25aa4e6870166b1cdef8467e2af75ef8e765628aa86d7c6a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:00:43.099065Z","signature_b64":"NF/4q+fN8FSyorgqjNMxezEJDpRksDd//lSQIMSMMagOWve8SkfJLY/CXTxz6S3SD164cFCNHy+yCKtSPk3zBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f85b6b959ed5974c3fe5f5ba174dce1e6e9407facd71bf217deaa7dde7137f8","last_reissued_at":"2026-07-04T15:00:43.098682Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:00:43.098682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Almost uniform sampling via quantum walks","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Peter C. 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