2026-07-25T02:44:17Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:14003 2024-03-06T10:53:22Z ddc:004 open_access

Pauli Error Estimation via Population Recovery Flammia, Steven T. O'Donnell, Ryan Pauli channels population recovery Goldreich-Levin sparse recovery quantum channel tomography 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 ε in 𝓁_∞ using just O(1/ε²) log(n/ε) 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/ε) 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 ≤ 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-η. In the regime of small η we extend our algorithm to achieve multiplicative precision 1 ± ε (i.e., additive precision εη) using just O(1/(ε²η)) log(n/ε) applications of the channel. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Steven T. Flammia and Ryan O'Donnell 2021 Is Part Of LIPIcs, Volume 197, 16th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.TQC.2021.8 urn:nbn:de:0030-drops-140034 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2021.8 eng https://creativecommons.org/licenses/by/4.0/legalcode