{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:Q45ZBIXTBFNR6D2AMQCM4H6HNY","short_pith_number":"pith:Q45ZBIXT","canonical_record":{"source":{"id":"2604.26865","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-04-29T16:32:48Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"3c83476edb2ec6f1fd530f635605d74022f8095f7f9a743005cdd6c6b6d22377","abstract_canon_sha256":"264fde3c530f5b911977e8c9b45477547c9898bdb36c0ba09684e4931172e11c"},"schema_version":"1.0"},"canonical_sha256":"873b90a2f3095b1f0f406404ce1fc76e375010d77f7fc3d2ea7d802b8a5feb75","source":{"kind":"arxiv","id":"2604.26865","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2604.26865","created_at":"2026-05-20T02:05:44Z"},{"alias_kind":"arxiv_version","alias_value":"2604.26865v2","created_at":"2026-05-20T02:05:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.26865","created_at":"2026-05-20T02:05:44Z"},{"alias_kind":"pith_short_12","alias_value":"Q45ZBIXTBFNR","created_at":"2026-05-20T02:05:44Z"},{"alias_kind":"pith_short_16","alias_value":"Q45ZBIXTBFNR6D2A","created_at":"2026-05-20T02:05:44Z"},{"alias_kind":"pith_short_8","alias_value":"Q45ZBIXT","created_at":"2026-05-20T02:05:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:Q45ZBIXTBFNR6D2AMQCM4H6HNY","target":"record","payload":{"canonical_record":{"source":{"id":"2604.26865","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-04-29T16:32:48Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"3c83476edb2ec6f1fd530f635605d74022f8095f7f9a743005cdd6c6b6d22377","abstract_canon_sha256":"264fde3c530f5b911977e8c9b45477547c9898bdb36c0ba09684e4931172e11c"},"schema_version":"1.0"},"canonical_sha256":"873b90a2f3095b1f0f406404ce1fc76e375010d77f7fc3d2ea7d802b8a5feb75","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T02:05:44.011461Z","signature_b64":"4Y/BsOoLPKMps9mfxHrqpM6OXD9fxMZp8yNa7norLE+AyA3ayNx6WSeN1TkV71lBp0D5EX73meUZBnXKk8ocCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"873b90a2f3095b1f0f406404ce1fc76e375010d77f7fc3d2ea7d802b8a5feb75","last_reissued_at":"2026-05-20T02:05:44.010619Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T02:05:44.010619Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2604.26865","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-20T02:05:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ey2lZvfbJEJkXg0H1DSGUpmj6+gGrsrlNAt2W4OHP72necyXeR5aNqGWHRX7XxRUDSLQLnHxRwBVui6Uc43nBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T22:27:05.770936Z"},"content_sha256":"6ee7ba33993181b1a0c159f52278fd76f2f5638a0847be006909583712a26637","schema_version":"1.0","event_id":"sha256:6ee7ba33993181b1a0c159f52278fd76f2f5638a0847be006909583712a26637"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:Q45ZBIXTBFNR6D2AMQCM4H6HNY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"MLMC-qDRIFT: Multilevel Variance Reduction for Randomized Quantum Hamiltonian Simulation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A multilevel coupling of qDRIFT estimators reduces total gate complexity for observable estimation from O(ε^{-3}) to O(ε^{-2} log²(1/ε)).","cross_cats":["cs.NA","math.NA"],"primary_cat":"quant-ph","authors_text":"Pegah Mohammadipour, Xiantao Li","submitted_at":"2026-04-29T16:32:48Z","abstract_excerpt":"Simulating quantum dynamics is one of the central applications of quantum computing. For Hamiltonians written as a sum of many terms, deterministic Trotter--Suzuki product formulas can require applying a large number of term-wise evolutions at each time step, leading to high circuit costs for large or dense systems. Randomized methods such as qDRIFT offer an alternative: each step samples only one Hamiltonian term, giving a circuit depth with no explicit dependence on the number of terms. However, when qDRIFT is used for observable estimation, high precision requires many independent random ci"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove that the resulting MLMC-qDRIFT estimator reduces the total gate complexity for fixed-precision observable estimation from the standard qDRIFT scaling O(ε^{-3}) to O(ε^{-2} log²(1/ε)), while preserving qDRIFT's lack of explicit dependence on the number of Hamiltonian terms.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The variance of the coupled level differences decays sufficiently fast with increasing circuit depth so that the multilevel estimator achieves the claimed complexity improvement.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"MLMC-qDRIFT achieves O(ε^{-2} log²(1/ε)) gate complexity for observable estimation in quantum dynamics by using coupled multilevel qDRIFT estimators with variance decay across levels.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A multilevel coupling of qDRIFT estimators reduces total gate complexity for observable estimation from O(ε^{-3}) to O(ε^{-2} log²(1/ε)).","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"91731d9f8f00462d191554b363bcc6c44f74620a39ea57d7ca4733f5367d43c8"},"source":{"id":"2604.26865","kind":"arxiv","version":2},"verdict":{"id":"2cc4ac67-1dad-46e1-b01c-c8fdb0e80920","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-07T13:08:12.908237Z","strongest_claim":"We prove that the resulting MLMC-qDRIFT estimator reduces the total gate complexity for fixed-precision observable estimation from the standard qDRIFT scaling O(ε^{-3}) to O(ε^{-2} log²(1/ε)), while preserving qDRIFT's lack of explicit dependence on the number of Hamiltonian terms.","one_line_summary":"MLMC-qDRIFT achieves O(ε^{-2} log²(1/ε)) gate complexity for observable estimation in quantum dynamics by using coupled multilevel qDRIFT estimators with variance decay across levels.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The variance of the coupled level differences decays sufficiently fast with increasing circuit depth so that the multilevel estimator achieves the claimed complexity improvement.","pith_extraction_headline":"A multilevel coupling of qDRIFT estimators reduces total gate complexity for observable estimation from O(ε^{-3}) to O(ε^{-2} log²(1/ε))."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.26865/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_compliance","ran_at":"2026-05-19T19:44:32.237201Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"4a9f2f8274ea782e7f57d549bd6deb576d75fb15b9193e488fb7f4da3ef60237"},"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":"2cc4ac67-1dad-46e1-b01c-c8fdb0e80920"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-20T02:05:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2kHBb7TLNdT7dV+bSccvar4TXa7kl6rTAZkN9bu3CO+mcaxmw5uyLHgYToQjjnTrYGbMcp4D6QYJ1ry6Gf+GCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T22:27:05.771566Z"},"content_sha256":"f10ada832f75b374541320502909ea38b865e30a07898da0d36546cee1d633c5","schema_version":"1.0","event_id":"sha256:f10ada832f75b374541320502909ea38b865e30a07898da0d36546cee1d633c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q45ZBIXTBFNR6D2AMQCM4H6HNY/bundle.json","state_url":"https://pith.science/pith/Q45ZBIXTBFNR6D2AMQCM4H6HNY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q45ZBIXTBFNR6D2AMQCM4H6HNY/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":"2026-06-01T22:27:05Z","links":{"resolver":"https://pith.science/pith/Q45ZBIXTBFNR6D2AMQCM4H6HNY","bundle":"https://pith.science/pith/Q45ZBIXTBFNR6D2AMQCM4H6HNY/bundle.json","state":"https://pith.science/pith/Q45ZBIXTBFNR6D2AMQCM4H6HNY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q45ZBIXTBFNR6D2AMQCM4H6HNY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:Q45ZBIXTBFNR6D2AMQCM4H6HNY","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":"264fde3c530f5b911977e8c9b45477547c9898bdb36c0ba09684e4931172e11c","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-04-29T16:32:48Z","title_canon_sha256":"3c83476edb2ec6f1fd530f635605d74022f8095f7f9a743005cdd6c6b6d22377"},"schema_version":"1.0","source":{"id":"2604.26865","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2604.26865","created_at":"2026-05-20T02:05:44Z"},{"alias_kind":"arxiv_version","alias_value":"2604.26865v2","created_at":"2026-05-20T02:05:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.26865","created_at":"2026-05-20T02:05:44Z"},{"alias_kind":"pith_short_12","alias_value":"Q45ZBIXTBFNR","created_at":"2026-05-20T02:05:44Z"},{"alias_kind":"pith_short_16","alias_value":"Q45ZBIXTBFNR6D2A","created_at":"2026-05-20T02:05:44Z"},{"alias_kind":"pith_short_8","alias_value":"Q45ZBIXT","created_at":"2026-05-20T02:05:44Z"}],"graph_snapshots":[{"event_id":"sha256:f10ada832f75b374541320502909ea38b865e30a07898da0d36546cee1d633c5","target":"graph","created_at":"2026-05-20T02:05:44Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"We prove that the resulting MLMC-qDRIFT estimator reduces the total gate complexity for fixed-precision observable estimation from the standard qDRIFT scaling O(ε^{-3}) to O(ε^{-2} log²(1/ε)), while preserving qDRIFT's lack of explicit dependence on the number of Hamiltonian terms."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The variance of the coupled level differences decays sufficiently fast with increasing circuit depth so that the multilevel estimator achieves the claimed complexity improvement."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"MLMC-qDRIFT achieves O(ε^{-2} log²(1/ε)) gate complexity for observable estimation in quantum dynamics by using coupled multilevel qDRIFT estimators with variance decay across levels."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"A multilevel coupling of qDRIFT estimators reduces total gate complexity for observable estimation from O(ε^{-3}) to O(ε^{-2} log²(1/ε))."}],"snapshot_sha256":"91731d9f8f00462d191554b363bcc6c44f74620a39ea57d7ca4733f5367d43c8"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"doi_compliance","ran_at":"2026-05-19T19:44:32.237201Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2604.26865/integrity.json","findings":[],"snapshot_sha256":"4a9f2f8274ea782e7f57d549bd6deb576d75fb15b9193e488fb7f4da3ef60237","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Simulating quantum dynamics is one of the central applications of quantum computing. For Hamiltonians written as a sum of many terms, deterministic Trotter--Suzuki product formulas can require applying a large number of term-wise evolutions at each time step, leading to high circuit costs for large or dense systems. Randomized methods such as qDRIFT offer an alternative: each step samples only one Hamiltonian term, giving a circuit depth with no explicit dependence on the number of terms. However, when qDRIFT is used for observable estimation, high precision requires many independent random ci","authors_text":"Pegah Mohammadipour, Xiantao Li","cross_cats":["cs.NA","math.NA"],"headline":"A multilevel coupling of qDRIFT estimators reduces total gate complexity for observable estimation from O(ε^{-3}) to O(ε^{-2} log²(1/ε)).","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-04-29T16:32:48Z","title":"MLMC-qDRIFT: Multilevel Variance Reduction for Randomized Quantum Hamiltonian Simulation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2604.26865","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-07T13:08:12.908237Z","id":"2cc4ac67-1dad-46e1-b01c-c8fdb0e80920","model_set":{"reader":"grok-4.3"},"one_line_summary":"MLMC-qDRIFT achieves O(ε^{-2} log²(1/ε)) gate complexity for observable estimation in quantum dynamics by using coupled multilevel qDRIFT estimators with variance decay across levels.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"A multilevel coupling of qDRIFT estimators reduces total gate complexity for observable estimation from O(ε^{-3}) to O(ε^{-2} log²(1/ε)).","strongest_claim":"We prove that the resulting MLMC-qDRIFT estimator reduces the total gate complexity for fixed-precision observable estimation from the standard qDRIFT scaling O(ε^{-3}) to O(ε^{-2} log²(1/ε)), while preserving qDRIFT's lack of explicit dependence on the number of Hamiltonian terms.","weakest_assumption":"The variance of the coupled level differences decays sufficiently fast with increasing circuit depth so that the multilevel estimator achieves the claimed complexity improvement."}},"verdict_id":"2cc4ac67-1dad-46e1-b01c-c8fdb0e80920"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:6ee7ba33993181b1a0c159f52278fd76f2f5638a0847be006909583712a26637","target":"record","created_at":"2026-05-20T02:05:44Z","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":"264fde3c530f5b911977e8c9b45477547c9898bdb36c0ba09684e4931172e11c","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-04-29T16:32:48Z","title_canon_sha256":"3c83476edb2ec6f1fd530f635605d74022f8095f7f9a743005cdd6c6b6d22377"},"schema_version":"1.0","source":{"id":"2604.26865","kind":"arxiv","version":2}},"canonical_sha256":"873b90a2f3095b1f0f406404ce1fc76e375010d77f7fc3d2ea7d802b8a5feb75","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"873b90a2f3095b1f0f406404ce1fc76e375010d77f7fc3d2ea7d802b8a5feb75","first_computed_at":"2026-05-20T02:05:44.010619Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T02:05:44.010619Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4Y/BsOoLPKMps9mfxHrqpM6OXD9fxMZp8yNa7norLE+AyA3ayNx6WSeN1TkV71lBp0D5EX73meUZBnXKk8ocCw==","signature_status":"signed_v1","signed_at":"2026-05-20T02:05:44.011461Z","signed_message":"canonical_sha256_bytes"},"source_id":"2604.26865","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ee7ba33993181b1a0c159f52278fd76f2f5638a0847be006909583712a26637","sha256:f10ada832f75b374541320502909ea38b865e30a07898da0d36546cee1d633c5"],"state_sha256":"526571db3fbc2452375c54aa59bfd55185d3c6515e94021d52392438ef353125"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nHLp3SmVOL2F8PNB8l3sGulQhLERxDCNm4+qRu9a6fMFYBXLVll83aZu/N5YqSjROXNfIQpPuLCcoV1gqwtGAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T22:27:05.774222Z","bundle_sha256":"10212c7555d3d4072a5dacf2fcbe0174bef4ef79c7898a436227bdf2b5f6ebdf"}}