{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:QT5RKTR2NDE3HPXRTKV7F7VEJY","short_pith_number":"pith:QT5RKTR2","canonical_record":{"source":{"id":"0908.4398","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-08-31T13:40:28Z","cross_cats_sorted":[],"title_canon_sha256":"c9ccb16afa2fdb6489d505994715c89d0a74d082cd2e0a2acf9aa5736e6c6d2f","abstract_canon_sha256":"2b01cccade88477f7ed536ac28602a86e033572bd9a0a93ca2af667a6f0aac33"},"schema_version":"1.0"},"canonical_sha256":"84fb154e3a68c9b3bef19aabf2fea44e040a343da674611aa48939a3c61f834f","source":{"kind":"arxiv","id":"0908.4398","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.4398","created_at":"2026-05-17T23:58:00Z"},{"alias_kind":"arxiv_version","alias_value":"0908.4398v2","created_at":"2026-05-17T23:58:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.4398","created_at":"2026-05-17T23:58:00Z"},{"alias_kind":"pith_short_12","alias_value":"QT5RKTR2NDE3","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"QT5RKTR2NDE3HPXR","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"QT5RKTR2","created_at":"2026-05-18T12:26:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:QT5RKTR2NDE3HPXRTKV7F7VEJY","target":"record","payload":{"canonical_record":{"source":{"id":"0908.4398","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-08-31T13:40:28Z","cross_cats_sorted":[],"title_canon_sha256":"c9ccb16afa2fdb6489d505994715c89d0a74d082cd2e0a2acf9aa5736e6c6d2f","abstract_canon_sha256":"2b01cccade88477f7ed536ac28602a86e033572bd9a0a93ca2af667a6f0aac33"},"schema_version":"1.0"},"canonical_sha256":"84fb154e3a68c9b3bef19aabf2fea44e040a343da674611aa48939a3c61f834f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:00.070300Z","signature_b64":"/7fje3kA9dXhk5F2JQkFJ+UYHmAMOVjBEehXHh31ip+z8oFSjhTwgywPV4gp8dsAe8c2WpDFyOngKJ9R8yxVBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"84fb154e3a68c9b3bef19aabf2fea44e040a343da674611aa48939a3c61f834f","last_reissued_at":"2026-05-17T23:58:00.069693Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:00.069693Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0908.4398","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":"2026-05-17T23:58:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GZwE/HixFWKshK5Hz8suUgD7E0qUY/x0XxNAvn+A3nyr+W3FIkoX/LDspDobR9vgto4sR0pv70sobP+igjm+BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T22:31:42.619583Z"},"content_sha256":"4d2c13c6761a33cddc55201681ce00d845a199ebd52d1008bcffec3719d4c44a","schema_version":"1.0","event_id":"sha256:4d2c13c6761a33cddc55201681ce00d845a199ebd52d1008bcffec3719d4c44a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:QT5RKTR2NDE3HPXRTKV7F7VEJY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Limitations on the simulation of non-sparse Hamiltonians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Andrew M. Childs, Robin Kothari","submitted_at":"2009-08-31T13:40:28Z","abstract_excerpt":"The problem of simulating sparse Hamiltonians on quantum computers is well studied. The evolution of a sparse N x N Hamiltonian H for time t can be simulated using O(||Ht||poly(log N)) operations, which is essentially optimal due to a no--fast-forwarding theorem. Here, we consider non-sparse Hamiltonians and show significant limitations on their simulation. We generalize the no--fast-forwarding theorem to dense Hamiltonians, ruling out generic simulations taking time o(||Ht||), even though ||H|| is not a unique measure of the size of a dense Hamiltonian $H$. We also present a stronger limitati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.4398","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:58:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oVoWYxQbiKJWkE5JBPzXIDCzjpyG3s+CWdNsExt2PsoQGiC7vjVqReoNM2Ud/8s/55OSajQ6/ZMBdwmBoCVjAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T22:31:42.620053Z"},"content_sha256":"175c484aceb035ba8dad88eadb2937682162b0856570b96ff02c94a25e7cb04e","schema_version":"1.0","event_id":"sha256:175c484aceb035ba8dad88eadb2937682162b0856570b96ff02c94a25e7cb04e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QT5RKTR2NDE3HPXRTKV7F7VEJY/bundle.json","state_url":"https://pith.science/pith/QT5RKTR2NDE3HPXRTKV7F7VEJY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QT5RKTR2NDE3HPXRTKV7F7VEJY/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":"2026-06-29T22:31:42Z","links":{"resolver":"https://pith.science/pith/QT5RKTR2NDE3HPXRTKV7F7VEJY","bundle":"https://pith.science/pith/QT5RKTR2NDE3HPXRTKV7F7VEJY/bundle.json","state":"https://pith.science/pith/QT5RKTR2NDE3HPXRTKV7F7VEJY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QT5RKTR2NDE3HPXRTKV7F7VEJY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:QT5RKTR2NDE3HPXRTKV7F7VEJY","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":"2b01cccade88477f7ed536ac28602a86e033572bd9a0a93ca2af667a6f0aac33","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-08-31T13:40:28Z","title_canon_sha256":"c9ccb16afa2fdb6489d505994715c89d0a74d082cd2e0a2acf9aa5736e6c6d2f"},"schema_version":"1.0","source":{"id":"0908.4398","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.4398","created_at":"2026-05-17T23:58:00Z"},{"alias_kind":"arxiv_version","alias_value":"0908.4398v2","created_at":"2026-05-17T23:58:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.4398","created_at":"2026-05-17T23:58:00Z"},{"alias_kind":"pith_short_12","alias_value":"QT5RKTR2NDE3","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"QT5RKTR2NDE3HPXR","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"QT5RKTR2","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:175c484aceb035ba8dad88eadb2937682162b0856570b96ff02c94a25e7cb04e","target":"graph","created_at":"2026-05-17T23:58:00Z","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":"The problem of simulating sparse Hamiltonians on quantum computers is well studied. The evolution of a sparse N x N Hamiltonian H for time t can be simulated using O(||Ht||poly(log N)) operations, which is essentially optimal due to a no--fast-forwarding theorem. Here, we consider non-sparse Hamiltonians and show significant limitations on their simulation. We generalize the no--fast-forwarding theorem to dense Hamiltonians, ruling out generic simulations taking time o(||Ht||), even though ||H|| is not a unique measure of the size of a dense Hamiltonian $H$. We also present a stronger limitati","authors_text":"Andrew M. Childs, Robin Kothari","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-08-31T13:40:28Z","title":"Limitations on the simulation of non-sparse Hamiltonians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.4398","kind":"arxiv","version":2},"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":"sha256:4d2c13c6761a33cddc55201681ce00d845a199ebd52d1008bcffec3719d4c44a","target":"record","created_at":"2026-05-17T23:58:00Z","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":"2b01cccade88477f7ed536ac28602a86e033572bd9a0a93ca2af667a6f0aac33","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-08-31T13:40:28Z","title_canon_sha256":"c9ccb16afa2fdb6489d505994715c89d0a74d082cd2e0a2acf9aa5736e6c6d2f"},"schema_version":"1.0","source":{"id":"0908.4398","kind":"arxiv","version":2}},"canonical_sha256":"84fb154e3a68c9b3bef19aabf2fea44e040a343da674611aa48939a3c61f834f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"84fb154e3a68c9b3bef19aabf2fea44e040a343da674611aa48939a3c61f834f","first_computed_at":"2026-05-17T23:58:00.069693Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:00.069693Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/7fje3kA9dXhk5F2JQkFJ+UYHmAMOVjBEehXHh31ip+z8oFSjhTwgywPV4gp8dsAe8c2WpDFyOngKJ9R8yxVBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:00.070300Z","signed_message":"canonical_sha256_bytes"},"source_id":"0908.4398","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d2c13c6761a33cddc55201681ce00d845a199ebd52d1008bcffec3719d4c44a","sha256:175c484aceb035ba8dad88eadb2937682162b0856570b96ff02c94a25e7cb04e"],"state_sha256":"62a8ba077e8560332f968df0bc072469f87e5939a0eb7b12704b75097105a8de"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4fQAw1B2367tw0cXS4bid3p48WlMGRkjgFrzesKJTWLHGcxhMsVrHKxVbwmf5jTlLHZdqakzwNI0f/mHD0i9Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T22:31:42.623170Z","bundle_sha256":"062f8cfea5258c6eb2340541e83cb65a1820e13cbb1d321641b432bac85be1c1"}}