{"paper":{"title":"Quantum Advantage via Solving Multivariate Polynomials","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CR"],"primary_cat":"quant-ph","authors_text":"Aayush Jain, Amit Sahai, Itai Dinur, Paul Lou, Pierre Briaud, Riddhi Ghosal","submitted_at":"2025-09-08T23:19:20Z","abstract_excerpt":"In this work, we propose a new way to (non-interactively, verifiably) demonstrate quantum advantage by solving the average-case $\\mathsf{NP}$ search problem of finding a solution to a system of (underdetermined) constant degree multivariate equations over the finite field $\\mathbb{F}_2$ drawn from a specified distribution. In particular, for any $d \\geq 2$, we design a distribution of degree up to $d$ polynomials $\\{p_i(x_1,\\ldots,x_n)\\}_{i\\in [m]}$ for $m<n$ over $\\mathbb{F}_2$ for which we show that there is a expected polynomial-time quantum algorithm that provably simultaneously solves $\\{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.07276","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/2509.07276/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"}