{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:6WSUXA374GXPRCCCNXTPMKBXCV","short_pith_number":"pith:6WSUXA37","canonical_record":{"source":{"id":"1807.04563","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-07-12T12:15:57Z","cross_cats_sorted":[],"title_canon_sha256":"5d45d724cec82ab8d9a3ac033da1cbe82c949af4138fc0673411993274e3acf5","abstract_canon_sha256":"c2d504c4d88bfe2c696efbfedf6a3050f871079f95389478b28a58dfdb17e902"},"schema_version":"1.0"},"canonical_sha256":"f5a54b837fe1aef888426de6f6283715499bc02d741bfb0d728893a05ccffd53","source":{"kind":"arxiv","id":"1807.04563","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.04563","created_at":"2026-05-17T23:57:40Z"},{"alias_kind":"arxiv_version","alias_value":"1807.04563v1","created_at":"2026-05-17T23:57:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.04563","created_at":"2026-05-17T23:57:40Z"},{"alias_kind":"pith_short_12","alias_value":"6WSUXA374GXP","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6WSUXA374GXPRCCC","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6WSUXA37","created_at":"2026-05-18T12:32:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:6WSUXA374GXPRCCCNXTPMKBXCV","target":"record","payload":{"canonical_record":{"source":{"id":"1807.04563","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-07-12T12:15:57Z","cross_cats_sorted":[],"title_canon_sha256":"5d45d724cec82ab8d9a3ac033da1cbe82c949af4138fc0673411993274e3acf5","abstract_canon_sha256":"c2d504c4d88bfe2c696efbfedf6a3050f871079f95389478b28a58dfdb17e902"},"schema_version":"1.0"},"canonical_sha256":"f5a54b837fe1aef888426de6f6283715499bc02d741bfb0d728893a05ccffd53","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:40.840475Z","signature_b64":"6JDmSshpGbA1pKnU/7SkEztohyMgVRZjQMArD5+nE4cX5lflelMhrbtU9/Ud+ckwP1tgxxzWEEH8y/vzN21xDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f5a54b837fe1aef888426de6f6283715499bc02d741bfb0d728893a05ccffd53","last_reissued_at":"2026-05-17T23:57:40.839992Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:40.839992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.04563","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":"2026-05-17T23:57:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DB8XpbIDr0Lyc3ugp3LyuUy5T1wG8FnDnR9QDiseeNBArAiCB2XU319YXABvwzUqYm9851pql1ASVP2jVhoRBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T21:02:58.457738Z"},"content_sha256":"ff6ab44c3d5b8544e42b2916b61673a3d36a1d9a98442adc9e15a4fa43f17201","schema_version":"1.0","event_id":"sha256:ff6ab44c3d5b8544e42b2916b61673a3d36a1d9a98442adc9e15a4fa43f17201"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:6WSUXA374GXPRCCCNXTPMKBXCV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum Circulant Preconditioner for Linear System of Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Changpeng Shao, Hua Xiang","submitted_at":"2018-07-12T12:15:57Z","abstract_excerpt":"We consider the quantum linear solver for $Ax=b$ with the circulant preconditioner $C$. The main technique is the singular value estimation (SVE) introduced in [I. Kerenidis and A. Prakash, Quantum recommendation system, in ITCS 2017]. However, some modifications of SVE should be made to solve the preconditioned linear system $C^{-1} Ax = C^{-1} b$. Moreover, different from the preconditioned linear system considered in [B. D. Clader, B. C. Jacobs, C. R. Sprouse, Preconditioned quantum linear system algorithm, Phys. Rev. Lett., 2013], the circulant preconditioner is easy to construct and can b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.04563","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":"2026-05-17T23:57:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5mrbls8ykLLP9ku3NSaAFl/ljJxgulJ5MvBzUOFqmAdBAIIRs2pRSPOMGyrGetC3B4vkUDJA1yopmgnf8BhIBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T21:02:58.458338Z"},"content_sha256":"91c047dfcc5463b7cf3a7efc0159cfba9daecfe375d3116ce271ee73f436d725","schema_version":"1.0","event_id":"sha256:91c047dfcc5463b7cf3a7efc0159cfba9daecfe375d3116ce271ee73f436d725"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6WSUXA374GXPRCCCNXTPMKBXCV/bundle.json","state_url":"https://pith.science/pith/6WSUXA374GXPRCCCNXTPMKBXCV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6WSUXA374GXPRCCCNXTPMKBXCV/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":"2026-05-25T21:02:58Z","links":{"resolver":"https://pith.science/pith/6WSUXA374GXPRCCCNXTPMKBXCV","bundle":"https://pith.science/pith/6WSUXA374GXPRCCCNXTPMKBXCV/bundle.json","state":"https://pith.science/pith/6WSUXA374GXPRCCCNXTPMKBXCV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6WSUXA374GXPRCCCNXTPMKBXCV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6WSUXA374GXPRCCCNXTPMKBXCV","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":"c2d504c4d88bfe2c696efbfedf6a3050f871079f95389478b28a58dfdb17e902","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-07-12T12:15:57Z","title_canon_sha256":"5d45d724cec82ab8d9a3ac033da1cbe82c949af4138fc0673411993274e3acf5"},"schema_version":"1.0","source":{"id":"1807.04563","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.04563","created_at":"2026-05-17T23:57:40Z"},{"alias_kind":"arxiv_version","alias_value":"1807.04563v1","created_at":"2026-05-17T23:57:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.04563","created_at":"2026-05-17T23:57:40Z"},{"alias_kind":"pith_short_12","alias_value":"6WSUXA374GXP","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6WSUXA374GXPRCCC","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6WSUXA37","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:91c047dfcc5463b7cf3a7efc0159cfba9daecfe375d3116ce271ee73f436d725","target":"graph","created_at":"2026-05-17T23:57:40Z","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 consider the quantum linear solver for $Ax=b$ with the circulant preconditioner $C$. The main technique is the singular value estimation (SVE) introduced in [I. Kerenidis and A. Prakash, Quantum recommendation system, in ITCS 2017]. However, some modifications of SVE should be made to solve the preconditioned linear system $C^{-1} Ax = C^{-1} b$. Moreover, different from the preconditioned linear system considered in [B. D. Clader, B. C. Jacobs, C. R. Sprouse, Preconditioned quantum linear system algorithm, Phys. Rev. Lett., 2013], the circulant preconditioner is easy to construct and can b","authors_text":"Changpeng Shao, Hua Xiang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-07-12T12:15:57Z","title":"Quantum Circulant Preconditioner for Linear System of Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.04563","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:ff6ab44c3d5b8544e42b2916b61673a3d36a1d9a98442adc9e15a4fa43f17201","target":"record","created_at":"2026-05-17T23:57:40Z","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":"c2d504c4d88bfe2c696efbfedf6a3050f871079f95389478b28a58dfdb17e902","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-07-12T12:15:57Z","title_canon_sha256":"5d45d724cec82ab8d9a3ac033da1cbe82c949af4138fc0673411993274e3acf5"},"schema_version":"1.0","source":{"id":"1807.04563","kind":"arxiv","version":1}},"canonical_sha256":"f5a54b837fe1aef888426de6f6283715499bc02d741bfb0d728893a05ccffd53","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5a54b837fe1aef888426de6f6283715499bc02d741bfb0d728893a05ccffd53","first_computed_at":"2026-05-17T23:57:40.839992Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:40.839992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6JDmSshpGbA1pKnU/7SkEztohyMgVRZjQMArD5+nE4cX5lflelMhrbtU9/Ud+ckwP1tgxxzWEEH8y/vzN21xDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:40.840475Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.04563","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff6ab44c3d5b8544e42b2916b61673a3d36a1d9a98442adc9e15a4fa43f17201","sha256:91c047dfcc5463b7cf3a7efc0159cfba9daecfe375d3116ce271ee73f436d725"],"state_sha256":"1c376f5d61302efde5f9b0c5a12f13ee9e5649e0368124fd5613af1844f965fd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EvrYqoCOEv7wk6qpikbfC7UhuJV2JNINAVFuCmhkvT/nctatDRSu+ow0VitIeq69I3g/TpJWsw9nmR4Wi/PRAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T21:02:58.461350Z","bundle_sha256":"9ce5c49f2bfb87aa88df9b3c1b5ba0742cf9fed367033f22553da12fa1ef343d"}}