Strict Hierarchy for Quantum Channel Certification to Unitary
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910177635074048 |
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| author | Chen, Kean Wang, Qisheng Zhang, Zhicheng |
| author_facet | Chen, Kean Wang, Qisheng Zhang, Zhicheng |
| contents | We consider the problem of quantum channel certification to unitary, where one is given access to an unknown $d$-dimensional channel $\mathcal{E}$, and wants to test whether $\mathcal{E}$ is equal to a target unitary channel or is $\varepsilon$-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:
(i) $Θ(d/\varepsilon^2)$ queries suffice for incoherent access model, matching the lower bound due to Fawzi, Flammarion, Garivier, and Oufkir (COLT 2023).
(ii) $Θ(d/\varepsilon)$ queries suffice for coherent access model, matching the lower bound due to Regev and Schiff (ICALP 2008).
(iii) $Θ(\sqrt{d}/\varepsilon)$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_26900 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Strict Hierarchy for Quantum Channel Certification to Unitary Chen, Kean Wang, Qisheng Zhang, Zhicheng Quantum Physics Computational Complexity Data Structures and Algorithms We consider the problem of quantum channel certification to unitary, where one is given access to an unknown $d$-dimensional channel $\mathcal{E}$, and wants to test whether $\mathcal{E}$ is equal to a target unitary channel or is $\varepsilon$-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: (i) $Θ(d/\varepsilon^2)$ queries suffice for incoherent access model, matching the lower bound due to Fawzi, Flammarion, Garivier, and Oufkir (COLT 2023). (ii) $Θ(d/\varepsilon)$ queries suffice for coherent access model, matching the lower bound due to Regev and Schiff (ICALP 2008). (iii) $Θ(\sqrt{d}/\varepsilon)$ 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. |
| title | Strict Hierarchy for Quantum Channel Certification to Unitary |
| topic | Quantum Physics Computational Complexity Data Structures and Algorithms |
| url | https://arxiv.org/abs/2604.26900 |