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Open Quantum Systems Decoherence

On Clifford hierarchy testing and near-extremizers of noncommutative uniformity norms

arXiv
Authors: Zongbo, Bao, Jop Briët, Davi Castro-Silva, Philippe van Dordrecht, Jonas Helsen

Year

2026

Paper ID

67437

Status

Preprint

Abstract Read

~2 min

Abstract Words

114

Citations

N/A

Abstract

We consider the problem of testing whether an unknown unitary is close to a specified level of the Clifford hierarchy. Bu, Gu, and Jaffe proposed a candidate tester for this task based on a connection with noncommutative analogues of the Gowers uniformity norms. The complexity of this tester - whose analysis depends on a robust characterization of the near-extremizers of these norms - was left open. We establish such a characterization for the fourth noncommutative uniformity norm and, as a consequence, obtain an efficient tester for the third level of the Clifford hierarchy. We further discuss possible routes toward resolving the problem of testing for all higher levels, highlighting the main barriers that remain.

Why This Paper Matters

  • This paper contributes to the Open Quantum Systems & Decoherence research area in the Quantum Articles archive.
  • It adds a 2026 reference point for readers tracking recent quantum research.
  • We consider the problem of testing whether an unknown unitary is close to a specified level of the Clifford hierarchy.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2605.26983 [2] arXiv https://arxiv.org/abs/2605.26983 [3] Publisher https://arxiv.org/abs/2605.26983

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