{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:IYMXRYLBAHESLPHTNKD5RBAN44","short_pith_number":"pith:IYMXRYLB","canonical_record":{"source":{"id":"1710.10983","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-10-30T14:41:57Z","cross_cats_sorted":[],"title_canon_sha256":"58bec94ac971203c72919fc3d81ff7c65fc80abd08dfc07ca5d36f7aad2f1f2f","abstract_canon_sha256":"8ea988e2c4c7dea94db3e593dde76e2bf01dececc8dca7f5a6fcc6d9a90dab38"},"schema_version":"1.0"},"canonical_sha256":"461978e16101c925bcf36a87d8840de736f9dee6c9f044d231ef496d0b9bcd43","source":{"kind":"arxiv","id":"1710.10983","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.10983","created_at":"2026-05-18T00:08:44Z"},{"alias_kind":"arxiv_version","alias_value":"1710.10983v3","created_at":"2026-05-18T00:08:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.10983","created_at":"2026-05-18T00:08:44Z"},{"alias_kind":"pith_short_12","alias_value":"IYMXRYLBAHES","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IYMXRYLBAHESLPHT","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IYMXRYLB","created_at":"2026-05-18T12:31:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:IYMXRYLBAHESLPHTNKD5RBAN44","target":"record","payload":{"canonical_record":{"source":{"id":"1710.10983","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-10-30T14:41:57Z","cross_cats_sorted":[],"title_canon_sha256":"58bec94ac971203c72919fc3d81ff7c65fc80abd08dfc07ca5d36f7aad2f1f2f","abstract_canon_sha256":"8ea988e2c4c7dea94db3e593dde76e2bf01dececc8dca7f5a6fcc6d9a90dab38"},"schema_version":"1.0"},"canonical_sha256":"461978e16101c925bcf36a87d8840de736f9dee6c9f044d231ef496d0b9bcd43","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:44.107436Z","signature_b64":"iJZ8RmHLDkbaUxN/culdD8pn1xmc6hFVFc1ZOJJkMyhGd9Tv00LQnZ9so1GkGC4HPH4fv/ye7wHQyrlBf70gBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"461978e16101c925bcf36a87d8840de736f9dee6c9f044d231ef496d0b9bcd43","last_reissued_at":"2026-05-18T00:08:44.106759Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:44.106759Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.10983","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":"2026-05-18T00:08:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hczVUCkhq1+ERhmkBPGG2yQZBmk128ncqZ795cHj/Qj0Z4IKtSYabiJzsQMofQB7ikTGAPoVg80GoUpXVMLADg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T14:08:32.807054Z"},"content_sha256":"3ca16ff1080a3d91b3909a334571b662773c6a5b98e4e98256296d078c0e3e30","schema_version":"1.0","event_id":"sha256:3ca16ff1080a3d91b3909a334571b662773c6a5b98e4e98256296d078c0e3e30"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:IYMXRYLBAHESLPHTNKD5RBAN44","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bipartite unitary gates and billiard dynamics in the Weyl chamber","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Antonio Mandarino, Karol \\.Zyczkowski, Tomasz Linowski","submitted_at":"2017-10-30T14:41:57Z","abstract_excerpt":"Long time behavior of a unitary quantum gate $U$, acting sequentially on two subsystems of dimension $N$ each, is investigated. We derive an expression describing an arbitrary iteration of a two-qubit gate making use of a link to the dynamics of a free particle in a $3D$ billiard. Due to ergodicity of such a dynamics an average along a trajectory $V^t$ stemming from a generic two-qubit gate $V$ in the canonical form tends for a large $t$ to the average over an ensemble of random unitary gates distributed according to the flat measure in the Weyl chamber - the minimal $3D$ set containing points"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10983","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":""},"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":"2026-05-18T00:08:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"15i+1eO1TwHLYhLY5BDaGx2/LjH8uWgV2TEz1Koxw2vhW3mz34+hc8ewBROtz3amBuFhjezBGRvlKeE/cobNBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T14:08:32.807715Z"},"content_sha256":"871967c06ad095707e2df3fea07699be9f0da9e628ae3a704fac01aeda065e1f","schema_version":"1.0","event_id":"sha256:871967c06ad095707e2df3fea07699be9f0da9e628ae3a704fac01aeda065e1f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IYMXRYLBAHESLPHTNKD5RBAN44/bundle.json","state_url":"https://pith.science/pith/IYMXRYLBAHESLPHTNKD5RBAN44/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IYMXRYLBAHESLPHTNKD5RBAN44/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":"2026-05-30T14:08:32Z","links":{"resolver":"https://pith.science/pith/IYMXRYLBAHESLPHTNKD5RBAN44","bundle":"https://pith.science/pith/IYMXRYLBAHESLPHTNKD5RBAN44/bundle.json","state":"https://pith.science/pith/IYMXRYLBAHESLPHTNKD5RBAN44/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IYMXRYLBAHESLPHTNKD5RBAN44/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:IYMXRYLBAHESLPHTNKD5RBAN44","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":"8ea988e2c4c7dea94db3e593dde76e2bf01dececc8dca7f5a6fcc6d9a90dab38","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-10-30T14:41:57Z","title_canon_sha256":"58bec94ac971203c72919fc3d81ff7c65fc80abd08dfc07ca5d36f7aad2f1f2f"},"schema_version":"1.0","source":{"id":"1710.10983","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.10983","created_at":"2026-05-18T00:08:44Z"},{"alias_kind":"arxiv_version","alias_value":"1710.10983v3","created_at":"2026-05-18T00:08:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.10983","created_at":"2026-05-18T00:08:44Z"},{"alias_kind":"pith_short_12","alias_value":"IYMXRYLBAHES","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IYMXRYLBAHESLPHT","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IYMXRYLB","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:871967c06ad095707e2df3fea07699be9f0da9e628ae3a704fac01aeda065e1f","target":"graph","created_at":"2026-05-18T00:08:44Z","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":"Long time behavior of a unitary quantum gate $U$, acting sequentially on two subsystems of dimension $N$ each, is investigated. We derive an expression describing an arbitrary iteration of a two-qubit gate making use of a link to the dynamics of a free particle in a $3D$ billiard. Due to ergodicity of such a dynamics an average along a trajectory $V^t$ stemming from a generic two-qubit gate $V$ in the canonical form tends for a large $t$ to the average over an ensemble of random unitary gates distributed according to the flat measure in the Weyl chamber - the minimal $3D$ set containing points","authors_text":"Antonio Mandarino, Karol \\.Zyczkowski, Tomasz Linowski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-10-30T14:41:57Z","title":"Bipartite unitary gates and billiard dynamics in the Weyl chamber"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10983","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":"sha256:3ca16ff1080a3d91b3909a334571b662773c6a5b98e4e98256296d078c0e3e30","target":"record","created_at":"2026-05-18T00:08:44Z","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":"8ea988e2c4c7dea94db3e593dde76e2bf01dececc8dca7f5a6fcc6d9a90dab38","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-10-30T14:41:57Z","title_canon_sha256":"58bec94ac971203c72919fc3d81ff7c65fc80abd08dfc07ca5d36f7aad2f1f2f"},"schema_version":"1.0","source":{"id":"1710.10983","kind":"arxiv","version":3}},"canonical_sha256":"461978e16101c925bcf36a87d8840de736f9dee6c9f044d231ef496d0b9bcd43","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"461978e16101c925bcf36a87d8840de736f9dee6c9f044d231ef496d0b9bcd43","first_computed_at":"2026-05-18T00:08:44.106759Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:44.106759Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iJZ8RmHLDkbaUxN/culdD8pn1xmc6hFVFc1ZOJJkMyhGd9Tv00LQnZ9so1GkGC4HPH4fv/ye7wHQyrlBf70gBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:44.107436Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.10983","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ca16ff1080a3d91b3909a334571b662773c6a5b98e4e98256296d078c0e3e30","sha256:871967c06ad095707e2df3fea07699be9f0da9e628ae3a704fac01aeda065e1f"],"state_sha256":"fc1d907ac0f0df877527583adc285e5efb1ec8940617391425db6c525280f28a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4AB2m/bNcDHaw2dx8kO822Qg95pVLUF2LfZZORMorjNZVUoZM0YCj0oPRiCfUJJyrgX6qBqzu3K7mKfiE+N/AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T14:08:32.810850Z","bundle_sha256":"3d88088940336cd024a7f088605aad65f8bbdcfcd7fe2520b1bd3682d4e39939"}}