{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:74E3BP7PFHRLOAVJNZPEX7ELG3","short_pith_number":"pith:74E3BP7P","canonical_record":{"source":{"id":"quant-ph/0407125","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2004-07-16T06:05:02Z","cross_cats_sorted":[],"title_canon_sha256":"008b4e51863396b16c7a36379e38568b3c56768f8983ff8d6e2e3a74f19e899b","abstract_canon_sha256":"13b0861594b8a88b6bb7f9c9d873665715517e5caa281934c73a1b65a11b9f2d"},"schema_version":"1.0"},"canonical_sha256":"ff09b0bfef29e2b702a96e5e4bfc8b36df7c1e7e084cc94b8a3b5fa019cfed24","source":{"kind":"arxiv","id":"quant-ph/0407125","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0407125","created_at":"2026-05-18T01:05:03Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0407125v1","created_at":"2026-05-18T01:05:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0407125","created_at":"2026-05-18T01:05:03Z"},{"alias_kind":"pith_short_12","alias_value":"74E3BP7PFHRL","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"74E3BP7PFHRLOAVJ","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"74E3BP7P","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:74E3BP7PFHRLOAVJNZPEX7ELG3","target":"record","payload":{"canonical_record":{"source":{"id":"quant-ph/0407125","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2004-07-16T06:05:02Z","cross_cats_sorted":[],"title_canon_sha256":"008b4e51863396b16c7a36379e38568b3c56768f8983ff8d6e2e3a74f19e899b","abstract_canon_sha256":"13b0861594b8a88b6bb7f9c9d873665715517e5caa281934c73a1b65a11b9f2d"},"schema_version":"1.0"},"canonical_sha256":"ff09b0bfef29e2b702a96e5e4bfc8b36df7c1e7e084cc94b8a3b5fa019cfed24","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:03.394326Z","signature_b64":"honNFtsC6OJtGRhJpuJ8jbtwBWw4qS7OZRyddZG1IfjEdnuk8bv/racUf3rbDxlzwTp7qFXWgfw68h6Ek2GSAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff09b0bfef29e2b702a96e5e4bfc8b36df7c1e7e084cc94b8a3b5fa019cfed24","last_reissued_at":"2026-05-18T01:05:03.393661Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:03.393661Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"quant-ph/0407125","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:05:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4r/iLUk5DVqoXcEEtr4s9UBRG8lJtKrNbk4dEDd3FtcY6TnRf9fMosswX7ytI/U09xXgEooBYsqcT8lG7qAUAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T01:34:03.355152Z"},"content_sha256":"f492e8dcb61eee5d21342428e4e233de5882b7c6ef58ff9e939f51e8f431aa95","schema_version":"1.0","event_id":"sha256:f492e8dcb61eee5d21342428e4e233de5882b7c6ef58ff9e939f51e8f431aa95"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:74E3BP7PFHRLOAVJNZPEX7ELG3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Implementing fanout, parity, and Mod gates via spin exchange interactions","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Stephen A. Fenner, Yong Zhang","submitted_at":"2004-07-16T06:05:02Z","abstract_excerpt":"We show that, for any n > 0, the Heisenberg interaction among 2n qubits (as spin-1/2 particles) can be used to exactly implement an n-qubit parity gate, which is equivalent in constant depth to an n-qubit fanout gate. Either isotropic or nonisotropic versions of the interaction can be used. We generalize our basic results by showing that any Hamiltonian (acting on suitably encoded logical qubits), whose eigenvalues depend quadratically on the Hamming weight of the logical qubit values, can be used to implement generalized Mod_q gates for any q > 1.\n  This paper is a sequel to quant-ph/0309163,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0407125","kind":"arxiv","version":1},"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":"2026-05-18T01:05:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KXNWdtyj7Be4L2Ulup47lWMlimdS4dTeX2hR76FLMbqvG+g6E7NKrF7f9nsotg2zGoToXE5qCmFn5KPcFzozCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T01:34:03.355499Z"},"content_sha256":"f7efd7b2b7b12d40c24d9ba2e6bb544bd4fed749886cd45f7dd717d879b2d2ae","schema_version":"1.0","event_id":"sha256:f7efd7b2b7b12d40c24d9ba2e6bb544bd4fed749886cd45f7dd717d879b2d2ae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/74E3BP7PFHRLOAVJNZPEX7ELG3/bundle.json","state_url":"https://pith.science/pith/74E3BP7PFHRLOAVJNZPEX7ELG3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/74E3BP7PFHRLOAVJNZPEX7ELG3/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":"2026-06-03T01:34:03Z","links":{"resolver":"https://pith.science/pith/74E3BP7PFHRLOAVJNZPEX7ELG3","bundle":"https://pith.science/pith/74E3BP7PFHRLOAVJNZPEX7ELG3/bundle.json","state":"https://pith.science/pith/74E3BP7PFHRLOAVJNZPEX7ELG3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/74E3BP7PFHRLOAVJNZPEX7ELG3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:74E3BP7PFHRLOAVJNZPEX7ELG3","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":"13b0861594b8a88b6bb7f9c9d873665715517e5caa281934c73a1b65a11b9f2d","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2004-07-16T06:05:02Z","title_canon_sha256":"008b4e51863396b16c7a36379e38568b3c56768f8983ff8d6e2e3a74f19e899b"},"schema_version":"1.0","source":{"id":"quant-ph/0407125","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0407125","created_at":"2026-05-18T01:05:03Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0407125v1","created_at":"2026-05-18T01:05:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0407125","created_at":"2026-05-18T01:05:03Z"},{"alias_kind":"pith_short_12","alias_value":"74E3BP7PFHRL","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"74E3BP7PFHRLOAVJ","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"74E3BP7P","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:f7efd7b2b7b12d40c24d9ba2e6bb544bd4fed749886cd45f7dd717d879b2d2ae","target":"graph","created_at":"2026-05-18T01:05:03Z","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":"We show that, for any n > 0, the Heisenberg interaction among 2n qubits (as spin-1/2 particles) can be used to exactly implement an n-qubit parity gate, which is equivalent in constant depth to an n-qubit fanout gate. Either isotropic or nonisotropic versions of the interaction can be used. We generalize our basic results by showing that any Hamiltonian (acting on suitably encoded logical qubits), whose eigenvalues depend quadratically on the Hamming weight of the logical qubit values, can be used to implement generalized Mod_q gates for any q > 1.\n  This paper is a sequel to quant-ph/0309163,","authors_text":"Stephen A. Fenner, Yong Zhang","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2004-07-16T06:05:02Z","title":"Implementing fanout, parity, and Mod gates via spin exchange interactions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0407125","kind":"arxiv","version":1},"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:f492e8dcb61eee5d21342428e4e233de5882b7c6ef58ff9e939f51e8f431aa95","target":"record","created_at":"2026-05-18T01:05:03Z","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":"13b0861594b8a88b6bb7f9c9d873665715517e5caa281934c73a1b65a11b9f2d","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2004-07-16T06:05:02Z","title_canon_sha256":"008b4e51863396b16c7a36379e38568b3c56768f8983ff8d6e2e3a74f19e899b"},"schema_version":"1.0","source":{"id":"quant-ph/0407125","kind":"arxiv","version":1}},"canonical_sha256":"ff09b0bfef29e2b702a96e5e4bfc8b36df7c1e7e084cc94b8a3b5fa019cfed24","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff09b0bfef29e2b702a96e5e4bfc8b36df7c1e7e084cc94b8a3b5fa019cfed24","first_computed_at":"2026-05-18T01:05:03.393661Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:03.393661Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"honNFtsC6OJtGRhJpuJ8jbtwBWw4qS7OZRyddZG1IfjEdnuk8bv/racUf3rbDxlzwTp7qFXWgfw68h6Ek2GSAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:03.394326Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0407125","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f492e8dcb61eee5d21342428e4e233de5882b7c6ef58ff9e939f51e8f431aa95","sha256:f7efd7b2b7b12d40c24d9ba2e6bb544bd4fed749886cd45f7dd717d879b2d2ae"],"state_sha256":"54d8315f40aace87a242070c2088a0ed9b246181535f1f30255c6ec0454ad571"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YPa7e1EKork8tjeM2mygaGbS6diph6qWBBFx4VechTbu5+6NGwC4KXahe05j3DkkOiE3OjECoGduXoZTsaWdBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T01:34:03.357404Z","bundle_sha256":"be1028a4122c32bfccdb00475518a1143be3ad45d27116a2170ecef5e7ede530"}}