{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:7BZOOMIKZLMCOR4JSTCOQYHT23","short_pith_number":"pith:7BZOOMIK","schema_version":"1.0","canonical_sha256":"f872e7310acad827478994c4e860f3d6d16c279567bb3689a625d31e9117de4a","source":{"kind":"arxiv","id":"1804.00055","version":2},"attestation_state":"computed","paper":{"title":"An efficient high dimensional quantum Schur transform","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"quant-ph","authors_text":"Hari Krovi","submitted_at":"2018-03-30T21:04:30Z","abstract_excerpt":"The Schur transform is a unitary operator that block diagonalizes the action of the symmetric and unitary groups on an $n$ fold tensor product $V^{\\otimes n}$ of a vector space $V$ of dimension $d$. Bacon, Chuang and Harrow \\cite{BCH07} gave a quantum algorithm for this transform that is polynomial in $n$, $d$ and $\\log\\epsilon^{-1}$, where $\\epsilon$ is the precision. In a footnote in Harrow's thesis \\cite{H05}, a brief description of how to make the algorithm of \\cite{BCH07} polynomial in $\\log d$ is given using the unitary group representation theory (however, this has not been explained in"},"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":"1804.00055","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2018-03-30T21:04:30Z","cross_cats_sorted":["cs.DM","math.CO"],"title_canon_sha256":"e46ff830635cdc089def6690f6b97d9ed1014d57ae455b16bce63bd713177ae9","abstract_canon_sha256":"d45da464bfe4413962ec9dca136ada1df2b864700b9ea326a2d3983382733f03"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:03.046528Z","signature_b64":"09whSn4eTwp7YFKb3nRy33GbGanNTXDlDtmIkM3wYeNui6DdyyQkVbDn5XVvV1HswA/GieAL0s62m7EJUWqCDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f872e7310acad827478994c4e860f3d6d16c279567bb3689a625d31e9117de4a","last_reissued_at":"2026-05-17T23:54:03.046004Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:03.046004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An efficient high dimensional quantum Schur transform","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"quant-ph","authors_text":"Hari Krovi","submitted_at":"2018-03-30T21:04:30Z","abstract_excerpt":"The Schur transform is a unitary operator that block diagonalizes the action of the symmetric and unitary groups on an $n$ fold tensor product $V^{\\otimes n}$ of a vector space $V$ of dimension $d$. Bacon, Chuang and Harrow \\cite{BCH07} gave a quantum algorithm for this transform that is polynomial in $n$, $d$ and $\\log\\epsilon^{-1}$, where $\\epsilon$ is the precision. In a footnote in Harrow's thesis \\cite{H05}, a brief description of how to make the algorithm of \\cite{BCH07} polynomial in $\\log d$ is given using the unitary group representation theory (however, this has not been explained in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.00055","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":"1804.00055","created_at":"2026-05-17T23:54:03.046084+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.00055v2","created_at":"2026-05-17T23:54:03.046084+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.00055","created_at":"2026-05-17T23:54:03.046084+00:00"},{"alias_kind":"pith_short_12","alias_value":"7BZOOMIKZLMC","created_at":"2026-05-18T12:32:11.075285+00:00"},{"alias_kind":"pith_short_16","alias_value":"7BZOOMIKZLMCOR4J","created_at":"2026-05-18T12:32:11.075285+00:00"},{"alias_kind":"pith_short_8","alias_value":"7BZOOMIK","created_at":"2026-05-18T12:32:11.075285+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7BZOOMIKZLMCOR4JSTCOQYHT23","json":"https://pith.science/pith/7BZOOMIKZLMCOR4JSTCOQYHT23.json","graph_json":"https://pith.science/api/pith-number/7BZOOMIKZLMCOR4JSTCOQYHT23/graph.json","events_json":"https://pith.science/api/pith-number/7BZOOMIKZLMCOR4JSTCOQYHT23/events.json","paper":"https://pith.science/paper/7BZOOMIK"},"agent_actions":{"view_html":"https://pith.science/pith/7BZOOMIKZLMCOR4JSTCOQYHT23","download_json":"https://pith.science/pith/7BZOOMIKZLMCOR4JSTCOQYHT23.json","view_paper":"https://pith.science/paper/7BZOOMIK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.00055&json=true","fetch_graph":"https://pith.science/api/pith-number/7BZOOMIKZLMCOR4JSTCOQYHT23/graph.json","fetch_events":"https://pith.science/api/pith-number/7BZOOMIKZLMCOR4JSTCOQYHT23/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7BZOOMIKZLMCOR4JSTCOQYHT23/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7BZOOMIKZLMCOR4JSTCOQYHT23/action/storage_attestation","attest_author":"https://pith.science/pith/7BZOOMIKZLMCOR4JSTCOQYHT23/action/author_attestation","sign_citation":"https://pith.science/pith/7BZOOMIKZLMCOR4JSTCOQYHT23/action/citation_signature","submit_replication":"https://pith.science/pith/7BZOOMIKZLMCOR4JSTCOQYHT23/action/replication_record"}},"created_at":"2026-05-17T23:54:03.046084+00:00","updated_at":"2026-05-17T23:54:03.046084+00:00"}