2026-07-21T20:03:28Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:24056 2025-12-12T14:56:10Z ddc:004 open_access

Uniformity Testing When You Have the Source Code Canonne, Clément L. Kothari, Robin O'Donnell, Ryan distribution testing uniformity testing quantum algorithms We study quantum algorithms for verifying properties of the output probability distribution of a classical or quantum circuit, given access to the source code that generates the distribution. We consider the basic task of uniformity testing, which is to decide if the output distribution is uniform on [d] or ε-far from uniform in total variation distance. More generally, we consider identity testing, which is the task of deciding if the output distribution equals a known hypothesis distribution, or is ε-far from it. For both problems, the previous best known upper bound was O(min{d^{1/3}/ε²,d^{1/2}/ε}). Here we improve the upper bound to O(min{d^{1/3}/ε^{4/3}, d^{1/2}/ε}), which we conjecture is optimal. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Clément L. Canonne and Robin Kothari and Ryan O'Donnell 2025 Is Part Of LIPIcs, Volume 350, 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.TQC.2025.7 urn:nbn:de:0030-drops-240561 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2025.7 eng https://creativecommons.org/licenses/by/4.0/legalcode