{"paper":{"title":"Quantum Circuits for the Black-Scholes equations via Schr\\\"{o}dingerisation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"quant-ph","authors_text":"Lei Zhang, Shi Jin, Xu Yin, Zihao Tang","submitted_at":"2025-05-07T10:21:12Z","abstract_excerpt":"In this paper, we construct quantum circuits for the Black-Scholes equations, a cornerstone of financial modeling, based on a quantum algorithm that overcome the cure of high dimensionality. Our approach leverages the Schr\\\"odingerisation technique, which converts linear partial and ordinary differential equations with non-unitary dynamics into a system evolved by unitary dynamics. This is achieved through a warped phase transformation that lifts the problem into a higher-dimensional space, enabling the simulation of the Black-Scholes equation on a quantum computer. We will conduct a thorough "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.04304","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/2505.04304/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"}