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Uniformity Testing When You Have the Source Code

Authors Clément L. Canonne , Robin Kothari , Ryan O'Donnell

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ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Theory of computation → Quantum computation theory
Keywords
  • distribution testing
  • uniformity testing
  • quantum algorithms

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Abstract

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.

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Clément L. Canonne, Robin Kothari, and Ryan O'Donnell. Uniformity Testing When You Have the Source Code. In 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 350, pp. 7:1-7:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.TQC.2025.7

Author Details

Clément L. Canonne
  • The University of Sydney, Australia
Robin Kothari
  • Google Quantum AI, Santa Barbara, CA, USA
Ryan O'Donnell
  • Carnegie Mellon University, Pittsburgh, PA, USA

Funding

  • Canonne, Clément L.: Supported by an ARC DECRA (DE230101329).
  • O'Donnell, Ryan: Supported by ARO grant W911NF2110001 and by a gift from Google Quantum AI.

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