{"paper":{"title":"Quantum algorithm for multivariate polynomial interpolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DS"],"primary_cat":"quant-ph","authors_text":"Andrew M. Childs, Jianxin Chen, Shih-Han Hung","submitted_at":"2017-01-15T04:07:40Z","abstract_excerpt":"How many quantum queries are required to determine the coefficients of a degree-$d$ polynomial in $n$ variables? We present and analyze quantum algorithms for this multivariate polynomial interpolation problem over the fields $\\mathbb{F}_q$, $\\mathbb{R}$, and $\\mathbb{C}$. We show that $k_{\\mathbb{C}}$ and $2k_{\\mathbb{C}}$ queries suffice to achieve probability $1$ for $\\mathbb{C}$ and $\\mathbb{R}$, respectively, where $k_{\\mathbb{C}}=\\smash{\\lceil\\frac{1}{n+1}{n+d\\choose d}\\rceil}$ except for $d=2$ and four other special cases. For $\\mathbb{F}_q$, we show that $\\smash{\\lceil\\frac{d}{n+d}{n+d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.03990","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":""},"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"}