{"paper":{"title":"Mean estimation when you have the source code; or, quantum Monte Carlo methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DS","math.PR","math.ST","stat.TH"],"primary_cat":"quant-ph","authors_text":"Robin Kothari, Ryan O'Donnell","submitted_at":"2022-08-16T05:34:26Z","abstract_excerpt":"Suppose $\\boldsymbol{y}$ is a real random variable, and one is given access to ``the code'' that generates it (for example, a randomized or quantum circuit whose output is $\\boldsymbol{y}$). We give a quantum procedure that runs the code $O(n)$ times and returns an estimate $\\widehat{\\boldsymbol{\\mu}}$ for $\\mu = \\mathrm{E}[\\boldsymbol{y}]$ that with high probability satisfies $|\\widehat{\\boldsymbol{\\mu}} - \\mu| \\leq \\sigma/n$, where $\\sigma = \\mathrm{stddev}[\\boldsymbol{y}]$. This dependence on $n$ is optimal for quantum algorithms. One may compare with classical algorithms, which can only ac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.07544","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/2208.07544/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"}