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The algorithm learns an exact tomographic description of t<\/mml:mi><\/mml:math>-doped stabilizer states in terms of Pauli observables. This is possible because such states are countable and form a discrete set. To tackle the problem, we introduce a novel algebraic framework for t<\/mml:mi><\/mml:math>-doped stabilizer states, which extends beyond T<\/mml:mi><\/mml:math>-gates and includes doping with any kind of local non-Clifford gate. The algorithm requires resources of complexity poly<\/mml:mi>&#x2061;<\/mml:mo>(<\/mml:mo>n<\/mml:mi>,<\/mml:mo>2<\/mml:mn>t<\/mml:mi><\/mml:msup>)<\/mml:mo><\/mml:math> and exhibits an exponentially small probability of failure.<\/jats:p>","DOI":"10.22331\/q-2024-05-27-1361","type":"journal-article","created":{"date-parts":[[2024,5,27]],"date-time":"2024-05-27T10:45:27Z","timestamp":1716806727000},"page":"1361","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":38,"title":["Learning t-doped stabilizer states"],"prefix":"10.22331","volume":"8","author":[{"given":"Lorenzo","family":"Leone","sequence":"first","affiliation":[{"name":"Physics Department, University of Massachusetts Boston, 02125, USA"},{"name":"Dahlem Center for Complex Quantum Systems, Freie Universit\u00e4t Berlin, 14195 Berlin, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Salvatore F. 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