{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:HY2KRUTZJLR4VOSUWAYEE4L7MQ","short_pith_number":"pith:HY2KRUTZ","canonical_record":{"source":{"id":"1504.06987","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-04-27T09:23:02Z","cross_cats_sorted":[],"title_canon_sha256":"ea159562af5889d78fcf3d277ec262e2198bbfd4f89a8a48ddcfc03b6c62ae17","abstract_canon_sha256":"3d2a35010ef76f79c8bdd6548294edfdd8b3d905d6446a6a4a6aad9a3ba0cdde"},"schema_version":"1.0"},"canonical_sha256":"3e34a8d2794ae3caba54b03042717f64387fb1e3871460d991bc4ac020fe829a","source":{"kind":"arxiv","id":"1504.06987","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.06987","created_at":"2026-05-18T00:40:33Z"},{"alias_kind":"arxiv_version","alias_value":"1504.06987v3","created_at":"2026-05-18T00:40:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06987","created_at":"2026-05-18T00:40:33Z"},{"alias_kind":"pith_short_12","alias_value":"HY2KRUTZJLR4","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HY2KRUTZJLR4VOSU","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HY2KRUTZ","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:HY2KRUTZJLR4VOSUWAYEE4L7MQ","target":"record","payload":{"canonical_record":{"source":{"id":"1504.06987","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-04-27T09:23:02Z","cross_cats_sorted":[],"title_canon_sha256":"ea159562af5889d78fcf3d277ec262e2198bbfd4f89a8a48ddcfc03b6c62ae17","abstract_canon_sha256":"3d2a35010ef76f79c8bdd6548294edfdd8b3d905d6446a6a4a6aad9a3ba0cdde"},"schema_version":"1.0"},"canonical_sha256":"3e34a8d2794ae3caba54b03042717f64387fb1e3871460d991bc4ac020fe829a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:33.917971Z","signature_b64":"nlZny/ZckD72wIJlM7B++IdxPViPCovowE51e2kNuNqJlH/4ySDkYM9vYvCu1/7ze4wPII9CAPk5/M9MMfgKAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e34a8d2794ae3caba54b03042717f64387fb1e3871460d991bc4ac020fe829a","last_reissued_at":"2026-05-18T00:40:33.917338Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:33.917338Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.06987","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:40:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ke3O9UAiGCgWoHcZBtAWTcLM0Z6zaBWc9ObS8lJPjAloDKgoEvd6be806XRVUoJn9F6UJ57poQ33rRMuFVhYBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T08:37:37.216513Z"},"content_sha256":"ecbd04ab6b069f626ddc5b239c058e5bbcd5b78a97232f1fb6034b5ff77821c3","schema_version":"1.0","event_id":"sha256:ecbd04ab6b069f626ddc5b239c058e5bbcd5b78a97232f1fb6034b5ff77821c3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:HY2KRUTZJLR4VOSUWAYEE4L7MQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum speedup of Monte Carlo methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Ashley Montanaro","submitted_at":"2015-04-27T09:23:02Z","abstract_excerpt":"Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition functions. In this work we describe a quantum algorithm which can accelerate Monte Carlo methods in a very general setting. The algorithm estimates the expected output value of an arbitrary randomised or quantum subroutine with bounded variance, achieving a near-quadratic speedup over the best possible classical algorithm. Combining the algorithm with the u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06987","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:40:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yPCq1R/CCJ2CBy7tVLWDqgcQBlRFdsMV7aZO6279m275nKTbVHm0v/6WG9H3BvJZg9IwbjEKLsgk0DxVzLURDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T08:37:37.216858Z"},"content_sha256":"20301e04256c32103ac76a6f07a8fb4182e43ede7553a7718fe6d4649679305b","schema_version":"1.0","event_id":"sha256:20301e04256c32103ac76a6f07a8fb4182e43ede7553a7718fe6d4649679305b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HY2KRUTZJLR4VOSUWAYEE4L7MQ/bundle.json","state_url":"https://pith.science/pith/HY2KRUTZJLR4VOSUWAYEE4L7MQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HY2KRUTZJLR4VOSUWAYEE4L7MQ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-05T08:37:37Z","links":{"resolver":"https://pith.science/pith/HY2KRUTZJLR4VOSUWAYEE4L7MQ","bundle":"https://pith.science/pith/HY2KRUTZJLR4VOSUWAYEE4L7MQ/bundle.json","state":"https://pith.science/pith/HY2KRUTZJLR4VOSUWAYEE4L7MQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HY2KRUTZJLR4VOSUWAYEE4L7MQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HY2KRUTZJLR4VOSUWAYEE4L7MQ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"3d2a35010ef76f79c8bdd6548294edfdd8b3d905d6446a6a4a6aad9a3ba0cdde","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-04-27T09:23:02Z","title_canon_sha256":"ea159562af5889d78fcf3d277ec262e2198bbfd4f89a8a48ddcfc03b6c62ae17"},"schema_version":"1.0","source":{"id":"1504.06987","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.06987","created_at":"2026-05-18T00:40:33Z"},{"alias_kind":"arxiv_version","alias_value":"1504.06987v3","created_at":"2026-05-18T00:40:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06987","created_at":"2026-05-18T00:40:33Z"},{"alias_kind":"pith_short_12","alias_value":"HY2KRUTZJLR4","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HY2KRUTZJLR4VOSU","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HY2KRUTZ","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:20301e04256c32103ac76a6f07a8fb4182e43ede7553a7718fe6d4649679305b","target":"graph","created_at":"2026-05-18T00:40:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition functions. In this work we describe a quantum algorithm which can accelerate Monte Carlo methods in a very general setting. The algorithm estimates the expected output value of an arbitrary randomised or quantum subroutine with bounded variance, achieving a near-quadratic speedup over the best possible classical algorithm. Combining the algorithm with the u","authors_text":"Ashley Montanaro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-04-27T09:23:02Z","title":"Quantum speedup of Monte Carlo methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06987","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ecbd04ab6b069f626ddc5b239c058e5bbcd5b78a97232f1fb6034b5ff77821c3","target":"record","created_at":"2026-05-18T00:40:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"3d2a35010ef76f79c8bdd6548294edfdd8b3d905d6446a6a4a6aad9a3ba0cdde","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-04-27T09:23:02Z","title_canon_sha256":"ea159562af5889d78fcf3d277ec262e2198bbfd4f89a8a48ddcfc03b6c62ae17"},"schema_version":"1.0","source":{"id":"1504.06987","kind":"arxiv","version":3}},"canonical_sha256":"3e34a8d2794ae3caba54b03042717f64387fb1e3871460d991bc4ac020fe829a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e34a8d2794ae3caba54b03042717f64387fb1e3871460d991bc4ac020fe829a","first_computed_at":"2026-05-18T00:40:33.917338Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:33.917338Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nlZny/ZckD72wIJlM7B++IdxPViPCovowE51e2kNuNqJlH/4ySDkYM9vYvCu1/7ze4wPII9CAPk5/M9MMfgKAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:33.917971Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.06987","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ecbd04ab6b069f626ddc5b239c058e5bbcd5b78a97232f1fb6034b5ff77821c3","sha256:20301e04256c32103ac76a6f07a8fb4182e43ede7553a7718fe6d4649679305b"],"state_sha256":"6affb1fc9d858ca3dd3fea3f16a467571de6d8ad0ed8ba5c04d70323cc04fdbc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I6nVBM2Z8vomVOdDCB9oAb6yC+3WyAtHBRWyExDcoSbUUoCaBrkUtO0spSftLIDmKt1RaYJPbtraj4W45tIvBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T08:37:37.218787Z","bundle_sha256":"c62355f645e10074f1b9a1a4438399d4c76d7bc537137b7395a688b6c71f1d1e"}}