{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:H5O5WBW6DNTMARI56VFCM4JDI2","short_pith_number":"pith:H5O5WBW6","canonical_record":{"source":{"id":"1810.03912","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-10-09T11:12:39Z","cross_cats_sorted":[],"title_canon_sha256":"ceab07fc08bd9ac23e5139e0bd2bf8b03135b9547b0fa9666a334a1d52bb8d11","abstract_canon_sha256":"4f944065bcb724445784ca1fe6b20e3a3fd269809d732a172c567e00117e7c52"},"schema_version":"1.0"},"canonical_sha256":"3f5ddb06de1b66c0451df54a267123468cbe8caf0486154ea6f80e3b374ad67d","source":{"kind":"arxiv","id":"1810.03912","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.03912","created_at":"2026-05-18T00:03:44Z"},{"alias_kind":"arxiv_version","alias_value":"1810.03912v1","created_at":"2026-05-18T00:03:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.03912","created_at":"2026-05-18T00:03:44Z"},{"alias_kind":"pith_short_12","alias_value":"H5O5WBW6DNTM","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"H5O5WBW6DNTMARI5","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"H5O5WBW6","created_at":"2026-05-18T12:32:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:H5O5WBW6DNTMARI56VFCM4JDI2","target":"record","payload":{"canonical_record":{"source":{"id":"1810.03912","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-10-09T11:12:39Z","cross_cats_sorted":[],"title_canon_sha256":"ceab07fc08bd9ac23e5139e0bd2bf8b03135b9547b0fa9666a334a1d52bb8d11","abstract_canon_sha256":"4f944065bcb724445784ca1fe6b20e3a3fd269809d732a172c567e00117e7c52"},"schema_version":"1.0"},"canonical_sha256":"3f5ddb06de1b66c0451df54a267123468cbe8caf0486154ea6f80e3b374ad67d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:44.286129Z","signature_b64":"05KfGNVt+xip8HSttoxIqB7Q0caBJe6vicbtvCivtu9NyrK6OLh1HdFzKvQIYgvYV8KVOthXb+3+c2W1+vsRCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f5ddb06de1b66c0451df54a267123468cbe8caf0486154ea6f80e3b374ad67d","last_reissued_at":"2026-05-18T00:03:44.285672Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:44.285672Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.03912","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":"2026-05-18T00:03:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mB8VtLWyIMAzT9+ly8KScGLWx0JPe7W1h8q3rLLLXOMyXh1iqkLt9OXfPtspl1flNBqdWanc59b/RPNVw44LBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T20:29:16.818309Z"},"content_sha256":"f9a415ed2504b473e956fc64114e258cd5840cbe572f448222624bc7959aa6b8","schema_version":"1.0","event_id":"sha256:f9a415ed2504b473e956fc64114e258cd5840cbe572f448222624bc7959aa6b8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:H5O5WBW6DNTMARI56VFCM4JDI2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum Circuit Depth Lower Bounds For Homological Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Dorit Aharonov, Yonathan Touati","submitted_at":"2018-10-09T11:12:39Z","abstract_excerpt":"We provide an $\\Omega(log(n))$ lower bound for the depth of any quantum circuit generating the unique groundstate of Kitaev's spherical code. No circuit-depth lower bound was known before on this code in the general case where the gates can connect qubits even if they are far away; To the best of our knowledge, this is the first time a quantum circuit-depth lower bound is given for unique ground state of a {\\it gapped} local Hamiltonian. Providing a lower bound in this case seems more challenging, since such systems exhibit exponential decay of correlations and standard lower bound techniques "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.03912","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":"2026-05-18T00:03:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5iN2dCHio3DsQ93oU400H7NQ4RRGOySTvx9OxoDlBQl3OP2ljCFIpWpkvxt07HmF3SZhAxA6G3fZlxoVg/NpBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T20:29:16.818694Z"},"content_sha256":"bf767a92a9ae0fcc0c150485324dde86735f9fb8124b1b670f947de7c502c95d","schema_version":"1.0","event_id":"sha256:bf767a92a9ae0fcc0c150485324dde86735f9fb8124b1b670f947de7c502c95d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H5O5WBW6DNTMARI56VFCM4JDI2/bundle.json","state_url":"https://pith.science/pith/H5O5WBW6DNTMARI56VFCM4JDI2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H5O5WBW6DNTMARI56VFCM4JDI2/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":"2026-06-28T20:29:16Z","links":{"resolver":"https://pith.science/pith/H5O5WBW6DNTMARI56VFCM4JDI2","bundle":"https://pith.science/pith/H5O5WBW6DNTMARI56VFCM4JDI2/bundle.json","state":"https://pith.science/pith/H5O5WBW6DNTMARI56VFCM4JDI2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H5O5WBW6DNTMARI56VFCM4JDI2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:H5O5WBW6DNTMARI56VFCM4JDI2","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":"4f944065bcb724445784ca1fe6b20e3a3fd269809d732a172c567e00117e7c52","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-10-09T11:12:39Z","title_canon_sha256":"ceab07fc08bd9ac23e5139e0bd2bf8b03135b9547b0fa9666a334a1d52bb8d11"},"schema_version":"1.0","source":{"id":"1810.03912","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.03912","created_at":"2026-05-18T00:03:44Z"},{"alias_kind":"arxiv_version","alias_value":"1810.03912v1","created_at":"2026-05-18T00:03:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.03912","created_at":"2026-05-18T00:03:44Z"},{"alias_kind":"pith_short_12","alias_value":"H5O5WBW6DNTM","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"H5O5WBW6DNTMARI5","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"H5O5WBW6","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:bf767a92a9ae0fcc0c150485324dde86735f9fb8124b1b670f947de7c502c95d","target":"graph","created_at":"2026-05-18T00:03:44Z","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":"We provide an $\\Omega(log(n))$ lower bound for the depth of any quantum circuit generating the unique groundstate of Kitaev's spherical code. No circuit-depth lower bound was known before on this code in the general case where the gates can connect qubits even if they are far away; To the best of our knowledge, this is the first time a quantum circuit-depth lower bound is given for unique ground state of a {\\it gapped} local Hamiltonian. Providing a lower bound in this case seems more challenging, since such systems exhibit exponential decay of correlations and standard lower bound techniques ","authors_text":"Dorit Aharonov, Yonathan Touati","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-10-09T11:12:39Z","title":"Quantum Circuit Depth Lower Bounds For Homological Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.03912","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:f9a415ed2504b473e956fc64114e258cd5840cbe572f448222624bc7959aa6b8","target":"record","created_at":"2026-05-18T00:03:44Z","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":"4f944065bcb724445784ca1fe6b20e3a3fd269809d732a172c567e00117e7c52","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-10-09T11:12:39Z","title_canon_sha256":"ceab07fc08bd9ac23e5139e0bd2bf8b03135b9547b0fa9666a334a1d52bb8d11"},"schema_version":"1.0","source":{"id":"1810.03912","kind":"arxiv","version":1}},"canonical_sha256":"3f5ddb06de1b66c0451df54a267123468cbe8caf0486154ea6f80e3b374ad67d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f5ddb06de1b66c0451df54a267123468cbe8caf0486154ea6f80e3b374ad67d","first_computed_at":"2026-05-18T00:03:44.285672Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:44.285672Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"05KfGNVt+xip8HSttoxIqB7Q0caBJe6vicbtvCivtu9NyrK6OLh1HdFzKvQIYgvYV8KVOthXb+3+c2W1+vsRCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:44.286129Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.03912","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f9a415ed2504b473e956fc64114e258cd5840cbe572f448222624bc7959aa6b8","sha256:bf767a92a9ae0fcc0c150485324dde86735f9fb8124b1b670f947de7c502c95d"],"state_sha256":"3328fba3b15d587b76eb0d2810bdc9e0749deb87a304567b78d00c84b0085562"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PH0Aoq+0b/YNXkS92xiBDDvsRU3dnfFq5OMfm4qxeiU9yo9p86A41BgqPX1oLuDVVtN7XGzxK2EPTob0SzwaCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T20:29:16.820920Z","bundle_sha256":"22671debf9bef7b4d6d60014799f383e3ec8570ea9da191931905ec999e8604f"}}