{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ZBYUZV3APLPXLQ33WPCS6DRQXI","short_pith_number":"pith:ZBYUZV3A","canonical_record":{"source":{"id":"1311.3599","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-11-14T18:28:37Z","cross_cats_sorted":[],"title_canon_sha256":"aa3c45498e241ba637ca707774caf5a3e7aea9aa180b458303ebff6bbe330b56","abstract_canon_sha256":"ce48e2d65d718cbd0978ca5b5f17e97c7cd00f79be95c391ec3c2ea3d10de349"},"schema_version":"1.0"},"canonical_sha256":"c8714cd7607adf75c37bb3c52f0e30ba252c6f650daf2d43cf5bec9b5c69fda2","source":{"kind":"arxiv","id":"1311.3599","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.3599","created_at":"2026-05-18T03:05:27Z"},{"alias_kind":"arxiv_version","alias_value":"1311.3599v2","created_at":"2026-05-18T03:05:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.3599","created_at":"2026-05-18T03:05:27Z"},{"alias_kind":"pith_short_12","alias_value":"ZBYUZV3APLPX","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZBYUZV3APLPXLQ33","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZBYUZV3A","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ZBYUZV3APLPXLQ33WPCS6DRQXI","target":"record","payload":{"canonical_record":{"source":{"id":"1311.3599","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-11-14T18:28:37Z","cross_cats_sorted":[],"title_canon_sha256":"aa3c45498e241ba637ca707774caf5a3e7aea9aa180b458303ebff6bbe330b56","abstract_canon_sha256":"ce48e2d65d718cbd0978ca5b5f17e97c7cd00f79be95c391ec3c2ea3d10de349"},"schema_version":"1.0"},"canonical_sha256":"c8714cd7607adf75c37bb3c52f0e30ba252c6f650daf2d43cf5bec9b5c69fda2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:27.727432Z","signature_b64":"HEWWAVfZ/z7IzUnv+yYM+iZA9wTk95BDbyirdccvxZcw+1vlu4lEvKs2J+e3pC9r5mbTCcJeSpPoB+28/mE9Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8714cd7607adf75c37bb3c52f0e30ba252c6f650daf2d43cf5bec9b5c69fda2","last_reissued_at":"2026-05-18T03:05:27.726825Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:27.726825Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.3599","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":"2026-05-18T03:05:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5cC26S3ZjNKRnWtVQ62Pwxx97I/nY7j688iX2IKanR+WIquU7H3SxymtAexRyOgxdBHInKVDlgl11HA87ssMDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T12:42:23.167539Z"},"content_sha256":"1828242982468ff8293e4e8fcc148e6e034f088821387a452acfd7e0cc884711","schema_version":"1.0","event_id":"sha256:1828242982468ff8293e4e8fcc148e6e034f088821387a452acfd7e0cc884711"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ZBYUZV3APLPXLQ33WPCS6DRQXI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Decomposition of quantum gates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Chi-Kwong Li, Diane Pelejo","submitted_at":"2013-11-14T18:28:37Z","abstract_excerpt":"A recurrence scheme is presented to decompose an $n$-qubit unitary gate to the product of no more than $N(N-1)/2$ single qubit gates with small number of controls, where $N = 2^n$. Detailed description of the recurrence steps and formulas for the number of $k$-controlled single qubit gates in the decomposition are given. Comparison of the result to a previous scheme is presented, and future research directions are discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3599","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":"2026-05-18T03:05:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C/owsI7jgZvoWPbhhuCvmmKOup/gBgPn88ncP/sPoIPSRunK1C7YVM0C5VwkID28rZZChZkhUNPvfvq8N0VECw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T12:42:23.168181Z"},"content_sha256":"6778e5b5c54e2697d90f6553a42058e6633765245d9fa24f4b4984bd3a28c5f9","schema_version":"1.0","event_id":"sha256:6778e5b5c54e2697d90f6553a42058e6633765245d9fa24f4b4984bd3a28c5f9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZBYUZV3APLPXLQ33WPCS6DRQXI/bundle.json","state_url":"https://pith.science/pith/ZBYUZV3APLPXLQ33WPCS6DRQXI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZBYUZV3APLPXLQ33WPCS6DRQXI/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":"2026-05-25T12:42:23Z","links":{"resolver":"https://pith.science/pith/ZBYUZV3APLPXLQ33WPCS6DRQXI","bundle":"https://pith.science/pith/ZBYUZV3APLPXLQ33WPCS6DRQXI/bundle.json","state":"https://pith.science/pith/ZBYUZV3APLPXLQ33WPCS6DRQXI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZBYUZV3APLPXLQ33WPCS6DRQXI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ZBYUZV3APLPXLQ33WPCS6DRQXI","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":"ce48e2d65d718cbd0978ca5b5f17e97c7cd00f79be95c391ec3c2ea3d10de349","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-11-14T18:28:37Z","title_canon_sha256":"aa3c45498e241ba637ca707774caf5a3e7aea9aa180b458303ebff6bbe330b56"},"schema_version":"1.0","source":{"id":"1311.3599","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.3599","created_at":"2026-05-18T03:05:27Z"},{"alias_kind":"arxiv_version","alias_value":"1311.3599v2","created_at":"2026-05-18T03:05:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.3599","created_at":"2026-05-18T03:05:27Z"},{"alias_kind":"pith_short_12","alias_value":"ZBYUZV3APLPX","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZBYUZV3APLPXLQ33","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZBYUZV3A","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:6778e5b5c54e2697d90f6553a42058e6633765245d9fa24f4b4984bd3a28c5f9","target":"graph","created_at":"2026-05-18T03:05:27Z","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":"A recurrence scheme is presented to decompose an $n$-qubit unitary gate to the product of no more than $N(N-1)/2$ single qubit gates with small number of controls, where $N = 2^n$. Detailed description of the recurrence steps and formulas for the number of $k$-controlled single qubit gates in the decomposition are given. Comparison of the result to a previous scheme is presented, and future research directions are discussed.","authors_text":"Chi-Kwong Li, Diane Pelejo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-11-14T18:28:37Z","title":"Decomposition of quantum gates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3599","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":"sha256:1828242982468ff8293e4e8fcc148e6e034f088821387a452acfd7e0cc884711","target":"record","created_at":"2026-05-18T03:05:27Z","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":"ce48e2d65d718cbd0978ca5b5f17e97c7cd00f79be95c391ec3c2ea3d10de349","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-11-14T18:28:37Z","title_canon_sha256":"aa3c45498e241ba637ca707774caf5a3e7aea9aa180b458303ebff6bbe330b56"},"schema_version":"1.0","source":{"id":"1311.3599","kind":"arxiv","version":2}},"canonical_sha256":"c8714cd7607adf75c37bb3c52f0e30ba252c6f650daf2d43cf5bec9b5c69fda2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c8714cd7607adf75c37bb3c52f0e30ba252c6f650daf2d43cf5bec9b5c69fda2","first_computed_at":"2026-05-18T03:05:27.726825Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:27.726825Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HEWWAVfZ/z7IzUnv+yYM+iZA9wTk95BDbyirdccvxZcw+1vlu4lEvKs2J+e3pC9r5mbTCcJeSpPoB+28/mE9Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:27.727432Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.3599","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1828242982468ff8293e4e8fcc148e6e034f088821387a452acfd7e0cc884711","sha256:6778e5b5c54e2697d90f6553a42058e6633765245d9fa24f4b4984bd3a28c5f9"],"state_sha256":"1bc63efc98e6bf59aba5b7ae342cf1e2203e1a6a60ac2d59287eacb11a628110"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZYMRTHLcvTs3WSyeLkd/C+y8bJWt5l+P/OrU+RvY/9HKQcKuthfzSsJICo0qskU2q2XmhuDlHkXiP/aPGzS7AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T12:42:23.171310Z","bundle_sha256":"2982f6ea3291d6cb6d0969c1769228ef91dc1ad60764ea7a1e36e83668ac2ff0"}}