{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:TUVUWSQGDSOSUIARHMN4KTMAOV","short_pith_number":"pith:TUVUWSQG","canonical_record":{"source":{"id":"2311.01531","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2023-11-02T18:29:31Z","cross_cats_sorted":[],"title_canon_sha256":"793414e8adf3fd3cd441536b4b6aa24d560c74a02e20a31c610f11031502477f","abstract_canon_sha256":"5d53933683821aa69abab164f0bf901d63b4cd976b0a672d0a0ac90162f3f95e"},"schema_version":"1.0"},"canonical_sha256":"9d2b4b4a061c9d2a20113b1bc54d80754b214268871db4240d985e194748d043","source":{"kind":"arxiv","id":"2311.01531","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.01531","created_at":"2026-07-05T08:36:05Z"},{"alias_kind":"arxiv_version","alias_value":"2311.01531v2","created_at":"2026-07-05T08:36:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.01531","created_at":"2026-07-05T08:36:05Z"},{"alias_kind":"pith_short_12","alias_value":"TUVUWSQGDSOS","created_at":"2026-07-05T08:36:05Z"},{"alias_kind":"pith_short_16","alias_value":"TUVUWSQGDSOSUIAR","created_at":"2026-07-05T08:36:05Z"},{"alias_kind":"pith_short_8","alias_value":"TUVUWSQG","created_at":"2026-07-05T08:36:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:TUVUWSQGDSOSUIARHMN4KTMAOV","target":"record","payload":{"canonical_record":{"source":{"id":"2311.01531","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2023-11-02T18:29:31Z","cross_cats_sorted":[],"title_canon_sha256":"793414e8adf3fd3cd441536b4b6aa24d560c74a02e20a31c610f11031502477f","abstract_canon_sha256":"5d53933683821aa69abab164f0bf901d63b4cd976b0a672d0a0ac90162f3f95e"},"schema_version":"1.0"},"canonical_sha256":"9d2b4b4a061c9d2a20113b1bc54d80754b214268871db4240d985e194748d043","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:36:05.305149Z","signature_b64":"ZRU0+6BqRAjJoSW0WlCZjBIPR+LVRryT2WuiT3w82/hZEh5jXoWck6hvUzBIveyRrJV7YsAUkV8+CGYSAAbEAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d2b4b4a061c9d2a20113b1bc54d80754b214268871db4240d985e194748d043","last_reissued_at":"2026-07-05T08:36:05.304640Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:36:05.304640Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2311.01531","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:36:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LuGRpv8OByHiNJdyKMVbNmLchcqXhCSqj9uKGuj+Q8GJqkJhiMoM9lZID0rZFby0p+jinsY3GEq5ba8p05paBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T18:50:09.469388Z"},"content_sha256":"472b65b48c95b1c01b0cc5e82bc1e8e9f0c38d6b0c2751ae910f161d78f00756","schema_version":"1.0","event_id":"sha256:472b65b48c95b1c01b0cc5e82bc1e8e9f0c38d6b0c2751ae910f161d78f00756"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:TUVUWSQGDSOSUIARHMN4KTMAOV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum Variational Solving of Nonlinear and Multi-Dimensional Partial Differential Equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Abhijat Sarma, Mudassir Moosa, Peter L. McMahon, Thomas W. Watts, Yilian Liu","submitted_at":"2023-11-02T18:29:31Z","abstract_excerpt":"A variational quantum algorithm for numerically solving partial differential equations (PDEs) on a quantum computer was proposed by Lubasch et al. In this paper, we generalize the method introduced by Lubasch et al. to cover a broader class of nonlinear PDEs as well as multidimensional PDEs, and study the performance of the variational quantum algorithm on several example equations. Specifically, we show via numerical simulations that the algorithm can solve instances of the Single-Asset Black-Scholes equation with a nontrivial nonlinear volatility model, the Double-Asset Black-Scholes equatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.01531","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2311.01531/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:36:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VyBM3HH8SfPQRDN2YRKraAhDfhcOXWCEvxpzoChbSKfIcyk6Qmn9XLbFx+oOUgMMmeJq7Bt0ILoQ+kcno5WjDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T18:50:09.469757Z"},"content_sha256":"54aa3a0a23c23e0744694f627cd056beb77c2883baa99dfe8c83b02ccf46f9b6","schema_version":"1.0","event_id":"sha256:54aa3a0a23c23e0744694f627cd056beb77c2883baa99dfe8c83b02ccf46f9b6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TUVUWSQGDSOSUIARHMN4KTMAOV/bundle.json","state_url":"https://pith.science/pith/TUVUWSQGDSOSUIARHMN4KTMAOV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TUVUWSQGDSOSUIARHMN4KTMAOV/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-09T18:50:09Z","links":{"resolver":"https://pith.science/pith/TUVUWSQGDSOSUIARHMN4KTMAOV","bundle":"https://pith.science/pith/TUVUWSQGDSOSUIARHMN4KTMAOV/bundle.json","state":"https://pith.science/pith/TUVUWSQGDSOSUIARHMN4KTMAOV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TUVUWSQGDSOSUIARHMN4KTMAOV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:TUVUWSQGDSOSUIARHMN4KTMAOV","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":"5d53933683821aa69abab164f0bf901d63b4cd976b0a672d0a0ac90162f3f95e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2023-11-02T18:29:31Z","title_canon_sha256":"793414e8adf3fd3cd441536b4b6aa24d560c74a02e20a31c610f11031502477f"},"schema_version":"1.0","source":{"id":"2311.01531","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.01531","created_at":"2026-07-05T08:36:05Z"},{"alias_kind":"arxiv_version","alias_value":"2311.01531v2","created_at":"2026-07-05T08:36:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.01531","created_at":"2026-07-05T08:36:05Z"},{"alias_kind":"pith_short_12","alias_value":"TUVUWSQGDSOS","created_at":"2026-07-05T08:36:05Z"},{"alias_kind":"pith_short_16","alias_value":"TUVUWSQGDSOSUIAR","created_at":"2026-07-05T08:36:05Z"},{"alias_kind":"pith_short_8","alias_value":"TUVUWSQG","created_at":"2026-07-05T08:36:05Z"}],"graph_snapshots":[{"event_id":"sha256:54aa3a0a23c23e0744694f627cd056beb77c2883baa99dfe8c83b02ccf46f9b6","target":"graph","created_at":"2026-07-05T08:36:05Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2311.01531/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A variational quantum algorithm for numerically solving partial differential equations (PDEs) on a quantum computer was proposed by Lubasch et al. In this paper, we generalize the method introduced by Lubasch et al. to cover a broader class of nonlinear PDEs as well as multidimensional PDEs, and study the performance of the variational quantum algorithm on several example equations. Specifically, we show via numerical simulations that the algorithm can solve instances of the Single-Asset Black-Scholes equation with a nontrivial nonlinear volatility model, the Double-Asset Black-Scholes equatio","authors_text":"Abhijat Sarma, Mudassir Moosa, Peter L. McMahon, Thomas W. Watts, Yilian Liu","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2023-11-02T18:29:31Z","title":"Quantum Variational Solving of Nonlinear and Multi-Dimensional Partial Differential Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.01531","kind":"arxiv","version":2},"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":"sha256:472b65b48c95b1c01b0cc5e82bc1e8e9f0c38d6b0c2751ae910f161d78f00756","target":"record","created_at":"2026-07-05T08:36:05Z","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":"5d53933683821aa69abab164f0bf901d63b4cd976b0a672d0a0ac90162f3f95e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2023-11-02T18:29:31Z","title_canon_sha256":"793414e8adf3fd3cd441536b4b6aa24d560c74a02e20a31c610f11031502477f"},"schema_version":"1.0","source":{"id":"2311.01531","kind":"arxiv","version":2}},"canonical_sha256":"9d2b4b4a061c9d2a20113b1bc54d80754b214268871db4240d985e194748d043","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d2b4b4a061c9d2a20113b1bc54d80754b214268871db4240d985e194748d043","first_computed_at":"2026-07-05T08:36:05.304640Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:36:05.304640Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZRU0+6BqRAjJoSW0WlCZjBIPR+LVRryT2WuiT3w82/hZEh5jXoWck6hvUzBIveyRrJV7YsAUkV8+CGYSAAbEAg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:36:05.305149Z","signed_message":"canonical_sha256_bytes"},"source_id":"2311.01531","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:472b65b48c95b1c01b0cc5e82bc1e8e9f0c38d6b0c2751ae910f161d78f00756","sha256:54aa3a0a23c23e0744694f627cd056beb77c2883baa99dfe8c83b02ccf46f9b6"],"state_sha256":"a72d4ea1de85e4f5aa5dc5e80eedcde0cd66884cc5a7ea8b9ee123ebf8e285f2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H0S/5aL8iSozQbpiQXdJq8151E66DFfAVXF5Qk3li3C/hvaINIO6fAeMIuqef7yOIpopVvCar1bPcmv3khR9AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-09T18:50:09.471593Z","bundle_sha256":"d90aa692ac69a1c504def80b967b9d067485335ec9f522ed52b9f1d61218fa92"}}