Optimal failure-probability dependence for Clifford learning

Determine whether the sample complexity for learning an unknown n-qubit Clifford unitary from forward queries can retain the optimal linear dependence on n while improving the dependence on the failure probability $\delta$, particularly when $\delta$ is exponentially small in n.

Background

The paper derives a forward-query upper bound of $2n+\lceil\log_2(1/\delta)\rceil+4$ for learning an n-qubit Clifford unitary by learning its Choi state, and proves that the n-dependence is optimal. However, for exponentially small failure probabilities this bound can exceed a previously known exact-learning bound of roughly $4n$, leaving the optimal $\delta$-dependence unresolved for Clifford learning.