{"paper":{"title":"Improved quantum data analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Costin B\\u{a}descu, Ryan O'Donnell","submitted_at":"2020-11-22T01:22:37Z","abstract_excerpt":"We provide more sample-efficient versions of some basic routines in quantum data analysis, along with simpler proofs. Particularly, we give a quantum \"Threshold Search\" algorithm that requires only $O((\\log^2 m)/\\epsilon^2)$ samples of a $d$-dimensional state $\\rho$. That is, given observables $0 \\le A_1, A_2, ..., A_m \\le 1$ such that $\\mathrm{tr}(\\rho A_i) \\ge 1/2$ for at least one $i$, the algorithm finds $j$ with $\\mathrm{tr}(\\rho A_j) \\ge 1/2-\\epsilon$. As a consequence, we obtain a Shadow Tomography algorithm requiring only $\\tilde{O}((\\log^2 m)(\\log d)/\\epsilon^4)$ samples, which simult"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.10908","kind":"arxiv","version":4},"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/2011.10908/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"}