{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:JH3R4CH6SC7XV3WM7CQHHW55TA","short_pith_number":"pith:JH3R4CH6","canonical_record":{"source":{"id":"2309.08155","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2023-09-15T04:41:10Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"f92ee786dbdad7a6aaabf2fa32819d69afe8cb2cd61dcc586a46e350cb828a99","abstract_canon_sha256":"c982558db9d08faa62c7ec054cd1f2e33f4d0a686e5758c7470f693db6fa3dd6"},"schema_version":"1.0"},"canonical_sha256":"49f71e08fe90bf7aeeccf8a073dbbd983f36eafcb87461c507e4f7898d657b02","source":{"kind":"arxiv","id":"2309.08155","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.08155","created_at":"2026-07-05T09:55:06Z"},{"alias_kind":"arxiv_version","alias_value":"2309.08155v3","created_at":"2026-07-05T09:55:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.08155","created_at":"2026-07-05T09:55:06Z"},{"alias_kind":"pith_short_12","alias_value":"JH3R4CH6SC7X","created_at":"2026-07-05T09:55:06Z"},{"alias_kind":"pith_short_16","alias_value":"JH3R4CH6SC7XV3WM","created_at":"2026-07-05T09:55:06Z"},{"alias_kind":"pith_short_8","alias_value":"JH3R4CH6","created_at":"2026-07-05T09:55:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:JH3R4CH6SC7XV3WM7CQHHW55TA","target":"record","payload":{"canonical_record":{"source":{"id":"2309.08155","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2023-09-15T04:41:10Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"f92ee786dbdad7a6aaabf2fa32819d69afe8cb2cd61dcc586a46e350cb828a99","abstract_canon_sha256":"c982558db9d08faa62c7ec054cd1f2e33f4d0a686e5758c7470f693db6fa3dd6"},"schema_version":"1.0"},"canonical_sha256":"49f71e08fe90bf7aeeccf8a073dbbd983f36eafcb87461c507e4f7898d657b02","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:55:06.612048Z","signature_b64":"PxdbwBwsQHiWc4rJ2SiwUgAzCu7OqvZhlPRsbaxj4FmjYZnGNghEASpFL3dVQrXQXgpnIt/2U+/p5BCn4pFqDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"49f71e08fe90bf7aeeccf8a073dbbd983f36eafcb87461c507e4f7898d657b02","last_reissued_at":"2026-07-05T09:55:06.611596Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:55:06.611596Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2309.08155","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:55:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MlanrlBG2p6Nz9qmAUgTibSl2CsHvZ2cvdHLGGqKqN4e4v29tShAfV06oJUg/m6C2/HPl4rnzXWP3DVT+SipCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T12:16:34.825841Z"},"content_sha256":"38df47e55339a031fdf14f8fc5613f02171bf8a41d40f91f13c585cbcd04dc54","schema_version":"1.0","event_id":"sha256:38df47e55339a031fdf14f8fc5613f02171bf8a41d40f91f13c585cbcd04dc54"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:JH3R4CH6SC7XV3WM7CQHHW55TA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Designs from Local Random Quantum Circuits with SU(d) Symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Han Zheng, Junyu Liu, Liang Jiang, Zimu Li, Zi-Wen Liu","submitted_at":"2023-09-15T04:41:10Z","abstract_excerpt":"The generation of $k$-designs (pseudorandom distributions that emulate the Haar measure up to $k$ moments) with local quantum circuit ensembles is a problem of fundamental importance in quantum information and physics. Despite the extensive understanding of this problem for ordinary random circuits, the crucial situations where symmetries or conservation laws are in play are known to pose fundamental challenges and remain little understood. We construct, for the first time, explicit local unitary ensembles that can achieve high-order unitary $k$-designs under transversal continuous symmetry, i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.08155","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2309.08155/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T09:55:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CNfPrVqj26ZJsTzPD8DH2q5PdDxap7JJrTIN8b38k34c4dglNXBdI7SO3xyiufejU64RntQ9ps60X/QZQrH4DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T12:16:34.826407Z"},"content_sha256":"fc268da07ca548a36e4417e78f8a91e64ac1b66f8e4f6c052ff9afc485f03ca1","schema_version":"1.0","event_id":"sha256:fc268da07ca548a36e4417e78f8a91e64ac1b66f8e4f6c052ff9afc485f03ca1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JH3R4CH6SC7XV3WM7CQHHW55TA/bundle.json","state_url":"https://pith.science/pith/JH3R4CH6SC7XV3WM7CQHHW55TA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JH3R4CH6SC7XV3WM7CQHHW55TA/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":"2026-08-07T12:16:34Z","links":{"resolver":"https://pith.science/pith/JH3R4CH6SC7XV3WM7CQHHW55TA","bundle":"https://pith.science/pith/JH3R4CH6SC7XV3WM7CQHHW55TA/bundle.json","state":"https://pith.science/pith/JH3R4CH6SC7XV3WM7CQHHW55TA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JH3R4CH6SC7XV3WM7CQHHW55TA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:JH3R4CH6SC7XV3WM7CQHHW55TA","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":"c982558db9d08faa62c7ec054cd1f2e33f4d0a686e5758c7470f693db6fa3dd6","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2023-09-15T04:41:10Z","title_canon_sha256":"f92ee786dbdad7a6aaabf2fa32819d69afe8cb2cd61dcc586a46e350cb828a99"},"schema_version":"1.0","source":{"id":"2309.08155","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.08155","created_at":"2026-07-05T09:55:06Z"},{"alias_kind":"arxiv_version","alias_value":"2309.08155v3","created_at":"2026-07-05T09:55:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.08155","created_at":"2026-07-05T09:55:06Z"},{"alias_kind":"pith_short_12","alias_value":"JH3R4CH6SC7X","created_at":"2026-07-05T09:55:06Z"},{"alias_kind":"pith_short_16","alias_value":"JH3R4CH6SC7XV3WM","created_at":"2026-07-05T09:55:06Z"},{"alias_kind":"pith_short_8","alias_value":"JH3R4CH6","created_at":"2026-07-05T09:55:06Z"}],"graph_snapshots":[{"event_id":"sha256:fc268da07ca548a36e4417e78f8a91e64ac1b66f8e4f6c052ff9afc485f03ca1","target":"graph","created_at":"2026-07-05T09:55:06Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2309.08155/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The generation of $k$-designs (pseudorandom distributions that emulate the Haar measure up to $k$ moments) with local quantum circuit ensembles is a problem of fundamental importance in quantum information and physics. Despite the extensive understanding of this problem for ordinary random circuits, the crucial situations where symmetries or conservation laws are in play are known to pose fundamental challenges and remain little understood. We construct, for the first time, explicit local unitary ensembles that can achieve high-order unitary $k$-designs under transversal continuous symmetry, i","authors_text":"Han Zheng, Junyu Liu, Liang Jiang, Zimu Li, Zi-Wen Liu","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2023-09-15T04:41:10Z","title":"Designs from Local Random Quantum Circuits with SU(d) Symmetry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.08155","kind":"arxiv","version":3},"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":"sha256:38df47e55339a031fdf14f8fc5613f02171bf8a41d40f91f13c585cbcd04dc54","target":"record","created_at":"2026-07-05T09:55:06Z","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":"c982558db9d08faa62c7ec054cd1f2e33f4d0a686e5758c7470f693db6fa3dd6","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2023-09-15T04:41:10Z","title_canon_sha256":"f92ee786dbdad7a6aaabf2fa32819d69afe8cb2cd61dcc586a46e350cb828a99"},"schema_version":"1.0","source":{"id":"2309.08155","kind":"arxiv","version":3}},"canonical_sha256":"49f71e08fe90bf7aeeccf8a073dbbd983f36eafcb87461c507e4f7898d657b02","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"49f71e08fe90bf7aeeccf8a073dbbd983f36eafcb87461c507e4f7898d657b02","first_computed_at":"2026-07-05T09:55:06.611596Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:55:06.611596Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PxdbwBwsQHiWc4rJ2SiwUgAzCu7OqvZhlPRsbaxj4FmjYZnGNghEASpFL3dVQrXQXgpnIt/2U+/p5BCn4pFqDw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:55:06.612048Z","signed_message":"canonical_sha256_bytes"},"source_id":"2309.08155","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:38df47e55339a031fdf14f8fc5613f02171bf8a41d40f91f13c585cbcd04dc54","sha256:fc268da07ca548a36e4417e78f8a91e64ac1b66f8e4f6c052ff9afc485f03ca1"],"state_sha256":"3580c0816caed3cf456d5599c0a2e83a30a4b9a9d0a747f78143a2134440a7bb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZExtGO40bQxFY9XA61qXOpRb1/i95vWbH3w7/hzzEYt6A+ZEVzr42uvEI6EBSPS00F98+S8LmD3L5gnZfoG0CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T12:16:34.830074Z","bundle_sha256":"1441d53c903c3d6325a5cfed81f42c7626826b6f5f6289714775443546ed864d"}}