{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:E5GEBOYR5K6QSOBBTP45CCJ6AE","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":"0d2238043a5191215a5f7882dc861d022ab20d001893116af08038efb5c9d73a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-07-10T20:32:13Z","title_canon_sha256":"7261c57bbf5d7b5929e5b630f8f73127b42a58d5266a055cf4e7d33caf9803b2"},"schema_version":"1.0","source":{"id":"1207.2485","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.2485","created_at":"2026-05-18T03:35:25Z"},{"alias_kind":"arxiv_version","alias_value":"1207.2485v3","created_at":"2026-05-18T03:35:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.2485","created_at":"2026-05-18T03:35:25Z"},{"alias_kind":"pith_short_12","alias_value":"E5GEBOYR5K6Q","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"E5GEBOYR5K6QSOBB","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"E5GEBOYR","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:60404958bf219b9b5d592e234e3a42a2c7295ff9836cfa6467e584128314fb1e","target":"graph","created_at":"2026-05-18T03:35:25Z","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":"The Poisson equation occurs in many areas of science and engineering. Here we focus on its numerical solution for an equation in d dimensions. In particular we present a quantum algorithm and a scalable quantum circuit design which approximates the solution of the Poisson equation on a grid with error \\varepsilon. We assume we are given a supersposition of function evaluations of the right hand side of the Poisson equation. The algorithm produces a quantum state encoding the solution. The number of quantum operations and the number of qubits used by the circuit is almost linear in d and polylo","authors_text":"Anargyros Papageorgiou, Iasonas Petras, Joseph Traub, Sabre Kais, Yudong Cao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-07-10T20:32:13Z","title":"Quantum algorithm and circuit design solving the Poisson equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.2485","kind":"arxiv","version":3},"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":"sha256:5931cd58a4c691084435f3bf8cd04b954984331a33be8338f3279d57fb9209af","target":"record","created_at":"2026-05-18T03:35:25Z","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":"0d2238043a5191215a5f7882dc861d022ab20d001893116af08038efb5c9d73a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-07-10T20:32:13Z","title_canon_sha256":"7261c57bbf5d7b5929e5b630f8f73127b42a58d5266a055cf4e7d33caf9803b2"},"schema_version":"1.0","source":{"id":"1207.2485","kind":"arxiv","version":3}},"canonical_sha256":"274c40bb11eabd0938219bf9d1093e011ea53fb1d0b9567496d2cbc5d84d0231","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"274c40bb11eabd0938219bf9d1093e011ea53fb1d0b9567496d2cbc5d84d0231","first_computed_at":"2026-05-18T03:35:25.670980Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:25.670980Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"plIvildnTFs5CrXh3MJRHGyJWlVsFPD3whsbikYKOqNPPdecpR+geyhXhfI9qSDcSH6FnOAU/kNqrPkv8ANoDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:25.671773Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.2485","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5931cd58a4c691084435f3bf8cd04b954984331a33be8338f3279d57fb9209af","sha256:60404958bf219b9b5d592e234e3a42a2c7295ff9836cfa6467e584128314fb1e"],"state_sha256":"2d53eef92ddfed5113b2b8bf59da313d9fe29345dbea25201d13adb2aefc379b"}