{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:PCTXKLFLSOTRJK63HL7C2LOV4H","short_pith_number":"pith:PCTXKLFL","canonical_record":{"source":{"id":"1903.03999","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2019-03-10T14:36:01Z","cross_cats_sorted":[],"title_canon_sha256":"4ec6de4ab5d462ad108ca2689e49ae5166b8f565ac3495df15c6c1fc265b208e","abstract_canon_sha256":"b737fc454582bb7773f096130d96b04ce90765f268e96e01b2bb1b0a53025a5b"},"schema_version":"1.0"},"canonical_sha256":"78a7752cab93a714abdb3afe2d2dd5e1d2a195b103070e45456e74ced4287d10","source":{"kind":"arxiv","id":"1903.03999","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.03999","created_at":"2026-05-17T23:49:14Z"},{"alias_kind":"arxiv_version","alias_value":"1903.03999v2","created_at":"2026-05-17T23:49:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.03999","created_at":"2026-05-17T23:49:14Z"},{"alias_kind":"pith_short_12","alias_value":"PCTXKLFLSOTR","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"PCTXKLFLSOTRJK63","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"PCTXKLFL","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:PCTXKLFLSOTRJK63HL7C2LOV4H","target":"record","payload":{"canonical_record":{"source":{"id":"1903.03999","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2019-03-10T14:36:01Z","cross_cats_sorted":[],"title_canon_sha256":"4ec6de4ab5d462ad108ca2689e49ae5166b8f565ac3495df15c6c1fc265b208e","abstract_canon_sha256":"b737fc454582bb7773f096130d96b04ce90765f268e96e01b2bb1b0a53025a5b"},"schema_version":"1.0"},"canonical_sha256":"78a7752cab93a714abdb3afe2d2dd5e1d2a195b103070e45456e74ced4287d10","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:14.489447Z","signature_b64":"IcjICihi1ko5+lpjBLVvmylRDx/o0iOgams28gZ/QnMvrAyi90dDkLj0Bbs9SYxH9+lrAB1V4n/wJSKguqdhBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78a7752cab93a714abdb3afe2d2dd5e1d2a195b103070e45456e74ced4287d10","last_reissued_at":"2026-05-17T23:49:14.488717Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:14.488717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.03999","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:49:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bQQX4ZT9m0lvsiyVZH36LKp6FWAoE527tZs2531hSZk/nBF7vaUG5sEyFqRpqRgOrL3w+pK9C+LgkzDcndZ9AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T16:13:22.409652Z"},"content_sha256":"fbdcc2d982af9b1fb2163a27884b8e7a3caf7827fda9694b02f86ff6417962c2","schema_version":"1.0","event_id":"sha256:fbdcc2d982af9b1fb2163a27884b8e7a3caf7827fda9694b02f86ff6417962c2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:PCTXKLFLSOTRJK63HL7C2LOV4H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Improved Algorithm for Quantum Principal Component Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Changpeng Shao","submitted_at":"2019-03-10T14:36:01Z","abstract_excerpt":"Principal component analysis is an important dimension reduction technique in machine learning. In [S. Lloyd, M. Mohseni and P. Rebentrost, Nature Physics 10, 631-633, (2014)], a quantum algorithm to implement principal component analysis on quantum computer was obtained by computing the Hamiltonian simulation of unknown density operators. The complexity is $O((\\log d)t^2/\\epsilon)$, where $d$ is the dimension, $t$ is the evolution time and $\\epsilon$ is the precision. We improve this result into $O((\\log d)t^{1+\\frac{1}{k}}/\\epsilon^{\\frac{1}{k}})$ for arbitrary constant integer $k\\geq 1$. As"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.03999","kind":"arxiv","version":2},"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":"2026-05-17T23:49:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"901pZVOIpS6h/sxW1ZwfH78cN2whZHjXHHx0glPq9JrrtmPwUJOQpgu16mc6VSHnWVNJrXRPswVPcgEQiVfOBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T16:13:22.410388Z"},"content_sha256":"e9577929d1811666c3221f16f8eae22cd0587d13f255fbee119d0b7eea84bf26","schema_version":"1.0","event_id":"sha256:e9577929d1811666c3221f16f8eae22cd0587d13f255fbee119d0b7eea84bf26"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PCTXKLFLSOTRJK63HL7C2LOV4H/bundle.json","state_url":"https://pith.science/pith/PCTXKLFLSOTRJK63HL7C2LOV4H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PCTXKLFLSOTRJK63HL7C2LOV4H/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":"2026-05-25T16:13:22Z","links":{"resolver":"https://pith.science/pith/PCTXKLFLSOTRJK63HL7C2LOV4H","bundle":"https://pith.science/pith/PCTXKLFLSOTRJK63HL7C2LOV4H/bundle.json","state":"https://pith.science/pith/PCTXKLFLSOTRJK63HL7C2LOV4H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PCTXKLFLSOTRJK63HL7C2LOV4H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:PCTXKLFLSOTRJK63HL7C2LOV4H","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":"b737fc454582bb7773f096130d96b04ce90765f268e96e01b2bb1b0a53025a5b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2019-03-10T14:36:01Z","title_canon_sha256":"4ec6de4ab5d462ad108ca2689e49ae5166b8f565ac3495df15c6c1fc265b208e"},"schema_version":"1.0","source":{"id":"1903.03999","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.03999","created_at":"2026-05-17T23:49:14Z"},{"alias_kind":"arxiv_version","alias_value":"1903.03999v2","created_at":"2026-05-17T23:49:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.03999","created_at":"2026-05-17T23:49:14Z"},{"alias_kind":"pith_short_12","alias_value":"PCTXKLFLSOTR","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"PCTXKLFLSOTRJK63","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"PCTXKLFL","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:e9577929d1811666c3221f16f8eae22cd0587d13f255fbee119d0b7eea84bf26","target":"graph","created_at":"2026-05-17T23:49:14Z","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":"Principal component analysis is an important dimension reduction technique in machine learning. In [S. Lloyd, M. Mohseni and P. Rebentrost, Nature Physics 10, 631-633, (2014)], a quantum algorithm to implement principal component analysis on quantum computer was obtained by computing the Hamiltonian simulation of unknown density operators. The complexity is $O((\\log d)t^2/\\epsilon)$, where $d$ is the dimension, $t$ is the evolution time and $\\epsilon$ is the precision. We improve this result into $O((\\log d)t^{1+\\frac{1}{k}}/\\epsilon^{\\frac{1}{k}})$ for arbitrary constant integer $k\\geq 1$. As","authors_text":"Changpeng Shao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2019-03-10T14:36:01Z","title":"An Improved Algorithm for Quantum Principal Component Analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.03999","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:fbdcc2d982af9b1fb2163a27884b8e7a3caf7827fda9694b02f86ff6417962c2","target":"record","created_at":"2026-05-17T23:49:14Z","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":"b737fc454582bb7773f096130d96b04ce90765f268e96e01b2bb1b0a53025a5b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2019-03-10T14:36:01Z","title_canon_sha256":"4ec6de4ab5d462ad108ca2689e49ae5166b8f565ac3495df15c6c1fc265b208e"},"schema_version":"1.0","source":{"id":"1903.03999","kind":"arxiv","version":2}},"canonical_sha256":"78a7752cab93a714abdb3afe2d2dd5e1d2a195b103070e45456e74ced4287d10","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78a7752cab93a714abdb3afe2d2dd5e1d2a195b103070e45456e74ced4287d10","first_computed_at":"2026-05-17T23:49:14.488717Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:14.488717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IcjICihi1ko5+lpjBLVvmylRDx/o0iOgams28gZ/QnMvrAyi90dDkLj0Bbs9SYxH9+lrAB1V4n/wJSKguqdhBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:14.489447Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.03999","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fbdcc2d982af9b1fb2163a27884b8e7a3caf7827fda9694b02f86ff6417962c2","sha256:e9577929d1811666c3221f16f8eae22cd0587d13f255fbee119d0b7eea84bf26"],"state_sha256":"099d0c8dd790c4701c789f69e4fe49159f0e96ca8041bf067176de15530a04a9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EOZFx53wQ9XX7VPG8Z1+mDpTpzCJLyH2N0ASZc5fsKK9bO4MqBqBfdVI7sSQmV1KKu8vkCCtMApLQDvNOtjADQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T16:13:22.414022Z","bundle_sha256":"6e7ec8bd7b52465fd47e9aa9a30bc27a67df42f08c9477323aa7bc908f95fcca"}}