{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:63FLBTLBBQ62V6WVRPUUL6CKKP","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":"3dd0dfc01be5ade69804ffe220a8078a5249e3c9bddabe7356abe2b15ebdac2d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-01-28T20:18:28Z","title_canon_sha256":"984de86a57fcffcc82859efc10f242cb90407fcc960152829c4154de23482ee4"},"schema_version":"1.0","source":{"id":"0901.4515","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.4515","created_at":"2026-05-18T04:39:59Z"},{"alias_kind":"arxiv_version","alias_value":"0901.4515v2","created_at":"2026-05-18T04:39:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.4515","created_at":"2026-05-18T04:39:59Z"},{"alias_kind":"pith_short_12","alias_value":"63FLBTLBBQ62","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"63FLBTLBBQ62V6WV","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"63FLBTLB","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:a5ef814645d4fe3e11d10f91b8da6fa33bb90d627dfe4cb99af28998bb5ec696","target":"graph","created_at":"2026-05-18T04:39:59Z","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 natural trajectory tracking problem is studied for generic quantum states represented by density operators. A control design based on the Hilbert-Schmidt distance as a Lyapunov function is considered. The control dynamics is redefined on an extended space where the LaSalle invariance principle can be correctly applied even for non-stationary target states. LaSalle's invariance principle is used to derive a general characterization of the invariant set, which is shown to always contain the critical points of the Lyapunov function. Critical point analysis of the latter is used to show that, ","authors_text":"Sonia Schirmer, Xiaoting Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-01-28T20:18:28Z","title":"Analysis of Lyapunov Method for Control of Quantum States"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.4515","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:c32cff5f88dd0e0d42b0e2c74a37ab261aa01f973d3db5070a302f197dee25b6","target":"record","created_at":"2026-05-18T04:39:59Z","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":"3dd0dfc01be5ade69804ffe220a8078a5249e3c9bddabe7356abe2b15ebdac2d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-01-28T20:18:28Z","title_canon_sha256":"984de86a57fcffcc82859efc10f242cb90407fcc960152829c4154de23482ee4"},"schema_version":"1.0","source":{"id":"0901.4515","kind":"arxiv","version":2}},"canonical_sha256":"f6cab0cd610c3daafad58be945f84a53c92c132aa6b09e6fd755ae499b572cd5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6cab0cd610c3daafad58be945f84a53c92c132aa6b09e6fd755ae499b572cd5","first_computed_at":"2026-05-18T04:39:59.656138Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:59.656138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"04gIfayrYugAM/1zfvlq7RPpyWskiy2RjnbW3Pq+gz6vAfiQg/ze39JEeNjrEaeYoOHFZpfsMvSWBXeM5S3ZCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:59.656750Z","signed_message":"canonical_sha256_bytes"},"source_id":"0901.4515","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c32cff5f88dd0e0d42b0e2c74a37ab261aa01f973d3db5070a302f197dee25b6","sha256:a5ef814645d4fe3e11d10f91b8da6fa33bb90d627dfe4cb99af28998bb5ec696"],"state_sha256":"0f0e5fec7b1695067979359d5c35c9693530d2c638a69293ee1b29d2df2bf3bd"}