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Strict Hierarchy for Quantum Channel Certification to Unitary

Authors Kean Chen , Qisheng Wang , Zhicheng Zhang

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LIPIcs.ICALP.2026.59.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Quantum computation theory
  • Theory of computation → Algorithm design techniques
Keywords
  • Quantum algorithms
  • quantum channels
  • quantum certification
  • query complexity
  • entanglement fidelity

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Abstract

We consider the problem of quantum channel certification to unitary, where one is given access to an unknown d-dimensional channel ℰ, and wants to test whether ℰ is equal to a target unitary channel or is ε-far from it in the diamond norm. We present optimal quantum algorithms for this problem, settling the query complexities in three access models with increasing power. Specifically, we show that:
1) Θ(d/ε²) queries suffice for incoherent access model, matching the lower bound due to Fawzi, Flammarion, Garivier, and Oufkir (COLT 2023). 
2) Θ(d/ε) queries suffice for coherent access model, matching the lower bound due to Regev and Schiff (ICALP 2008). 
3) Θ(√d/ε) queries suffice for source-code access model, matching the lower bound due to Jeon and Oh (npj Quantum Inf. 2026).
This demonstrates a strict hierarchy of complexities for quantum channel certification to unitary across various access models.

Cite As Get BibTex

Kean Chen, Qisheng Wang, and Zhicheng Zhang. Strict Hierarchy for Quantum Channel Certification to Unitary. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 59:1-59:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ICALP.2026.59

Author Details

Kean Chen
  • Department of Computer and Information Science, University of Pennsylvania, Philadelphia, PA, USA
Qisheng Wang
  • School of Computer Science, Shanghai Jiao Tong University, Shanghai, China
Zhicheng Zhang
  • School of Information and Communication Technology, Griffith University, Brisbane, QLD, Australia

Funding

  • Wang, Qisheng: Supported by startup funding from Shanghai Jiao Tong University.
  • Zhang, Zhicheng: Supported in part by the Australian Research Council under Grant DP250102952.

Acknowledgements

Part of the work of Zhicheng Zhang was done when the author was with the Centre for Quantum Software and Information, University of Technology Sydney, Australia.

References

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