{"paper":{"title":"Quantum algorithm for Valiant-Vazirani reduction","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Michael R. Geller, Patrick Kelly, Victoria S. Ordonez","submitted_at":"2026-06-16T19:22:16Z","abstract_excerpt":"There is growing interest in extensions of the standard model of gate-based quantum computation to include auxiliary degrees of freedom evolving according to a nonlinear Schr\\\"odinger equation. By reducing the Boolean satisfiability problem SAT to quantum state discrimination, Abrams and Lloyd argued that the right type of nonlinearity can be used to solve {\\sf NP} and \\#{\\sf P} problems in polynomial time, at least in an idealized noise-free limit. For practical implementation, however, we are restricted to simulated and emergent nonlinearities, such as that appearing in mean field models for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.18428","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/2606.18428/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"}