{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:G3OQ2L6Q234K2KGFJKVCABAN3U","short_pith_number":"pith:G3OQ2L6Q","schema_version":"1.0","canonical_sha256":"36dd0d2fd0d6f8ad28c54aaa20040ddd1479625e7a990019489f24c63afad04c","source":{"kind":"arxiv","id":"1503.08579","version":2},"attestation_state":"computed","paper":{"title":"Translating between the roots of the identity in quantum computers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"quant-ph","authors_text":"Alexis De Vos, Jeroen Demeyer, Mathias Soeken, Oliver Keszocze, Wouter Castryck","submitted_at":"2015-03-30T08:01:18Z","abstract_excerpt":"The Clifford+$T$ quantum computing gate library for single qubit gates can create all unitary matrices that are generated by the group $\\langle H, T\\rangle$. The matrix $T$ can be considered the fourth root of Pauli $Z$, since $T^4 = Z$ or also the eighth root of the identity $I$. The Hadamard matrix $H$ can be used to translate between the Pauli matrices, since $(HTH)^4$ gives Pauli $X$. We are generalizing both these roots of the Pauli matrices (or roots of the identity) and translation matrices to investigate the groups they generate: the so-called Pauli root groups. In this work we introdu"},"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":"1503.08579","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-03-30T08:01:18Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"4ddc13f8ca9c3d6ed01e1e87e3062f2bbefa5851fe9158264d366aa2045a0864","abstract_canon_sha256":"e81d43538c19f3d4641ca348710a3b5160ac9dae8d1ee06165490ceda1f71392"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:31.710199Z","signature_b64":"P/AwZ18Pa5KLLaOp1AginSYb/o6KV/MmimH9Og6FubF4opdcTRokCQyEoN6Z5s+DOAse/OJCZPgfsEi6AH6LCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36dd0d2fd0d6f8ad28c54aaa20040ddd1479625e7a990019489f24c63afad04c","last_reissued_at":"2026-05-18T01:29:31.709607Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:31.709607Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Translating between the roots of the identity in quantum computers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"quant-ph","authors_text":"Alexis De Vos, Jeroen Demeyer, Mathias Soeken, Oliver Keszocze, Wouter Castryck","submitted_at":"2015-03-30T08:01:18Z","abstract_excerpt":"The Clifford+$T$ quantum computing gate library for single qubit gates can create all unitary matrices that are generated by the group $\\langle H, T\\rangle$. The matrix $T$ can be considered the fourth root of Pauli $Z$, since $T^4 = Z$ or also the eighth root of the identity $I$. The Hadamard matrix $H$ can be used to translate between the Pauli matrices, since $(HTH)^4$ gives Pauli $X$. We are generalizing both these roots of the Pauli matrices (or roots of the identity) and translation matrices to investigate the groups they generate: the so-called Pauli root groups. In this work we introdu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08579","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":"1503.08579","created_at":"2026-05-18T01:29:31.709688+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.08579v2","created_at":"2026-05-18T01:29:31.709688+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.08579","created_at":"2026-05-18T01:29:31.709688+00:00"},{"alias_kind":"pith_short_12","alias_value":"G3OQ2L6Q234K","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_16","alias_value":"G3OQ2L6Q234K2KGF","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_8","alias_value":"G3OQ2L6Q","created_at":"2026-05-18T12:29:22.688609+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/G3OQ2L6Q234K2KGFJKVCABAN3U","json":"https://pith.science/pith/G3OQ2L6Q234K2KGFJKVCABAN3U.json","graph_json":"https://pith.science/api/pith-number/G3OQ2L6Q234K2KGFJKVCABAN3U/graph.json","events_json":"https://pith.science/api/pith-number/G3OQ2L6Q234K2KGFJKVCABAN3U/events.json","paper":"https://pith.science/paper/G3OQ2L6Q"},"agent_actions":{"view_html":"https://pith.science/pith/G3OQ2L6Q234K2KGFJKVCABAN3U","download_json":"https://pith.science/pith/G3OQ2L6Q234K2KGFJKVCABAN3U.json","view_paper":"https://pith.science/paper/G3OQ2L6Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.08579&json=true","fetch_graph":"https://pith.science/api/pith-number/G3OQ2L6Q234K2KGFJKVCABAN3U/graph.json","fetch_events":"https://pith.science/api/pith-number/G3OQ2L6Q234K2KGFJKVCABAN3U/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G3OQ2L6Q234K2KGFJKVCABAN3U/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G3OQ2L6Q234K2KGFJKVCABAN3U/action/storage_attestation","attest_author":"https://pith.science/pith/G3OQ2L6Q234K2KGFJKVCABAN3U/action/author_attestation","sign_citation":"https://pith.science/pith/G3OQ2L6Q234K2KGFJKVCABAN3U/action/citation_signature","submit_replication":"https://pith.science/pith/G3OQ2L6Q234K2KGFJKVCABAN3U/action/replication_record"}},"created_at":"2026-05-18T01:29:31.709688+00:00","updated_at":"2026-05-18T01:29:31.709688+00:00"}