{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:QJEYRFOIFDFQQ54H3Z34BH2PQC","short_pith_number":"pith:QJEYRFOI","schema_version":"1.0","canonical_sha256":"82498895c828cb087787de77c09f4f809becd728f2de5ddcb186519d50bf4974","source":{"kind":"arxiv","id":"2607.13191","version":1},"attestation_state":"computed","paper":{"title":"Two-Tower Quantum Matrix Chain Multiplication: Trading Qubits for Depth","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Alessandro Berti, Alessandro Poggiali, Anna Bernasconi, Giacomo Antonioli, Gianna M. Del Corso","submitted_at":"2026-07-14T18:42:40Z","abstract_excerpt":"Matrix chain multiplication -- computing $\\mathcal{W} = M^{(0)}\\cdots M^{(K-1)}$ where $M^{(k)} \\in \\mathbb{R}^{P_k \\times P_{k+1}}$ -- arises in scientific computing, machine learning, and graph analysis. Despite the importance of this problem, for chains of distinct matrices, the classical number of operations grows linearly with the chain length $K$ and polynomially in the matrix dimensions. We present \\emph{Two-Tower Matrix Multiplication}, a quantum subroutine that encodes the product $\\mathcal{W}$ of the $K$ matrices into a quantum state in circuit depth $\\mathcal{O}(\\max_{k} \\mathrm{pol"},"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":"2607.13191","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-07-14T18:42:40Z","cross_cats_sorted":[],"title_canon_sha256":"42e8e7738322cfa7ace8aaf90439631ed6d7d78f7bedecfab23d199b5c085d6b","abstract_canon_sha256":"4155a07f599bd2daeede0a68879cfc62d27a8fc60f1ec635a0e6c6963d2ee190"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-16T00:22:02.126400Z","signature_b64":"1s1ahHZh88f+AtFWEeMNcMH7sCU1ejKuGyljpY0wLOuST89FRAqU/qSR31dj8E+nymDiXidqN92JGwDKoFLrAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"82498895c828cb087787de77c09f4f809becd728f2de5ddcb186519d50bf4974","last_reissued_at":"2026-07-16T00:22:02.125544Z","signature_status":"signed_v1","first_computed_at":"2026-07-16T00:22:02.125544Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Two-Tower Quantum Matrix Chain Multiplication: Trading Qubits for Depth","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Alessandro Berti, Alessandro Poggiali, Anna Bernasconi, Giacomo Antonioli, Gianna M. Del Corso","submitted_at":"2026-07-14T18:42:40Z","abstract_excerpt":"Matrix chain multiplication -- computing $\\mathcal{W} = M^{(0)}\\cdots M^{(K-1)}$ where $M^{(k)} \\in \\mathbb{R}^{P_k \\times P_{k+1}}$ -- arises in scientific computing, machine learning, and graph analysis. Despite the importance of this problem, for chains of distinct matrices, the classical number of operations grows linearly with the chain length $K$ and polynomially in the matrix dimensions. We present \\emph{Two-Tower Matrix Multiplication}, a quantum subroutine that encodes the product $\\mathcal{W}$ of the $K$ matrices into a quantum state in circuit depth $\\mathcal{O}(\\max_{k} \\mathrm{pol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.13191","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.13191/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2607.13191","created_at":"2026-07-16T00:22:02.125996+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.13191v1","created_at":"2026-07-16T00:22:02.125996+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.13191","created_at":"2026-07-16T00:22:02.125996+00:00"},{"alias_kind":"pith_short_12","alias_value":"QJEYRFOIFDFQ","created_at":"2026-07-16T00:22:02.125996+00:00"},{"alias_kind":"pith_short_16","alias_value":"QJEYRFOIFDFQQ54H","created_at":"2026-07-16T00:22:02.125996+00:00"},{"alias_kind":"pith_short_8","alias_value":"QJEYRFOI","created_at":"2026-07-16T00:22:02.125996+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/QJEYRFOIFDFQQ54H3Z34BH2PQC","json":"https://pith.science/pith/QJEYRFOIFDFQQ54H3Z34BH2PQC.json","graph_json":"https://pith.science/api/pith-number/QJEYRFOIFDFQQ54H3Z34BH2PQC/graph.json","events_json":"https://pith.science/api/pith-number/QJEYRFOIFDFQQ54H3Z34BH2PQC/events.json","paper":"https://pith.science/paper/QJEYRFOI"},"agent_actions":{"view_html":"https://pith.science/pith/QJEYRFOIFDFQQ54H3Z34BH2PQC","download_json":"https://pith.science/pith/QJEYRFOIFDFQQ54H3Z34BH2PQC.json","view_paper":"https://pith.science/paper/QJEYRFOI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.13191&json=true","fetch_graph":"https://pith.science/api/pith-number/QJEYRFOIFDFQQ54H3Z34BH2PQC/graph.json","fetch_events":"https://pith.science/api/pith-number/QJEYRFOIFDFQQ54H3Z34BH2PQC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QJEYRFOIFDFQQ54H3Z34BH2PQC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QJEYRFOIFDFQQ54H3Z34BH2PQC/action/storage_attestation","attest_author":"https://pith.science/pith/QJEYRFOIFDFQQ54H3Z34BH2PQC/action/author_attestation","sign_citation":"https://pith.science/pith/QJEYRFOIFDFQQ54H3Z34BH2PQC/action/citation_signature","submit_replication":"https://pith.science/pith/QJEYRFOIFDFQQ54H3Z34BH2PQC/action/replication_record"}},"created_at":"2026-07-16T00:22:02.125996+00:00","updated_at":"2026-07-16T00:22:02.125996+00:00"}