{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:XFNLZCBEPNIFOH2C7INK4R5A46","short_pith_number":"pith:XFNLZCBE","schema_version":"1.0","canonical_sha256":"b95abc88247b50571f42fa1aae47a0e7afcbe561b2f85ac75bf3ae9bf833c6ce","source":{"kind":"arxiv","id":"1604.01384","version":2},"attestation_state":"computed","paper":{"title":"A Complete Characterization of Unitary Quantum Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Bill Fefferman, Cedric Yen-Yu Lin","submitted_at":"2016-04-05T19:48:48Z","abstract_excerpt":"Motivated by understanding the power of quantum computation with restricted number of qubits, we give two complete characterizations of unitary quantum space bounded computation. First we show that approximating an element of the inverse of a well-conditioned efficiently encoded $2^{k(n)}\\times 2^{k(n)}$ matrix is complete for the class of problems solvable by quantum circuits acting on $\\mathcal{O}(k(n))$ qubits with all measurements at the end of the computation. Similarly, estimating the minimum eigenvalue of an efficiently encoded Hermitian $2^{k(n)}\\times 2^{k(n)}$ matrix is also complete"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1604.01384","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-04-05T19:48:48Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"022220f0fce983a90540dbf5ab625da26faa789705c94f658968e72b0c2fb9ec","abstract_canon_sha256":"e820442e0d10f8489c14c8532203a9bb37ce991221f675f008f59b939ae66f1f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:37.949724Z","signature_b64":"BDgE4bWOuBQLH/+FbKe2BLQjJQPWbO/gsfnu7bBRjH9iRLxARvlhgmUWmALFnzyxc1pnLOLAukyfWJ2W+2WCCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b95abc88247b50571f42fa1aae47a0e7afcbe561b2f85ac75bf3ae9bf833c6ce","last_reissued_at":"2026-05-18T00:57:37.949068Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:37.949068Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Complete Characterization of Unitary Quantum Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Bill Fefferman, Cedric Yen-Yu Lin","submitted_at":"2016-04-05T19:48:48Z","abstract_excerpt":"Motivated by understanding the power of quantum computation with restricted number of qubits, we give two complete characterizations of unitary quantum space bounded computation. First we show that approximating an element of the inverse of a well-conditioned efficiently encoded $2^{k(n)}\\times 2^{k(n)}$ matrix is complete for the class of problems solvable by quantum circuits acting on $\\mathcal{O}(k(n))$ qubits with all measurements at the end of the computation. Similarly, estimating the minimum eigenvalue of an efficiently encoded Hermitian $2^{k(n)}\\times 2^{k(n)}$ matrix is also complete"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.01384","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1604.01384","created_at":"2026-05-18T00:57:37.949169+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.01384v2","created_at":"2026-05-18T00:57:37.949169+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.01384","created_at":"2026-05-18T00:57:37.949169+00:00"},{"alias_kind":"pith_short_12","alias_value":"XFNLZCBEPNIF","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_16","alias_value":"XFNLZCBEPNIFOH2C","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_8","alias_value":"XFNLZCBE","created_at":"2026-05-18T12:30:51.357362+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.18754","citing_title":"Quantum embedding of graphs for subgraph counting","ref_index":16,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XFNLZCBEPNIFOH2C7INK4R5A46","json":"https://pith.science/pith/XFNLZCBEPNIFOH2C7INK4R5A46.json","graph_json":"https://pith.science/api/pith-number/XFNLZCBEPNIFOH2C7INK4R5A46/graph.json","events_json":"https://pith.science/api/pith-number/XFNLZCBEPNIFOH2C7INK4R5A46/events.json","paper":"https://pith.science/paper/XFNLZCBE"},"agent_actions":{"view_html":"https://pith.science/pith/XFNLZCBEPNIFOH2C7INK4R5A46","download_json":"https://pith.science/pith/XFNLZCBEPNIFOH2C7INK4R5A46.json","view_paper":"https://pith.science/paper/XFNLZCBE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.01384&json=true","fetch_graph":"https://pith.science/api/pith-number/XFNLZCBEPNIFOH2C7INK4R5A46/graph.json","fetch_events":"https://pith.science/api/pith-number/XFNLZCBEPNIFOH2C7INK4R5A46/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XFNLZCBEPNIFOH2C7INK4R5A46/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XFNLZCBEPNIFOH2C7INK4R5A46/action/storage_attestation","attest_author":"https://pith.science/pith/XFNLZCBEPNIFOH2C7INK4R5A46/action/author_attestation","sign_citation":"https://pith.science/pith/XFNLZCBEPNIFOH2C7INK4R5A46/action/citation_signature","submit_replication":"https://pith.science/pith/XFNLZCBEPNIFOH2C7INK4R5A46/action/replication_record"}},"created_at":"2026-05-18T00:57:37.949169+00:00","updated_at":"2026-05-18T00:57:37.949169+00:00"}