{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/pauli-error-estimation-via-population","title":"Pauli error estimation via Population Recovery","arxiv_id":"2105.02885","date":"2021-05-06","proceeding":null,"authors":["Steven T. Flammia","Ryan O'Donnell"],"abstract":"Motivated by estimation of quantum noise models, we study the problem of learning a Pauli channel, or more generally the Pauli error rates of an arbitrary channel. By employing a novel reduction to the \"Population Recovery\" problem, we give an extremely simple algorithm that learns the Pauli error rates of an $n$-qubit channel to precision $\\epsilon$ in $\\ell_\\infty$ using just $O(1/\\epsilon^2) \\log(n/\\epsilon)$ applications of the channel. This is optimal up to the logarithmic factors. Our algorithm uses only unentangled state preparation and measurements, and the post-measurement classical runtime is just an $O(1/\\epsilon)$ factor larger than the measurement data size. It is also impervious to a limited model of measurement noise where heralded measurement failures occur independently with probability $\\le 1/4$. We then consider the case where the noise channel is close to the identity, meaning that the no-error outcome occurs with probability $1-\\eta$. In the regime of small $\\eta$ we extend our algorithm to achieve multiplicative precision $1 \\pm \\epsilon$ (i.e., additive precision $\\epsilon \\eta$) using just $O\\bigl(\\frac{1}{\\epsilon^2 \\eta}\\bigr) \\log(n/\\epsilon)$ applications of the channel.","url_abs":"https://arxiv.org/abs/2105.02885v2","url_pdf":"https://arxiv.org/pdf/2105.02885v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"pauli-error-estimation-via-population","repo_url":"https://github.com/sflammia/paulipoprec","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}