Strict Hierarchy for Quantum Channel Certification to Unitary

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\(d/varepsilon²\) 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.