The query complexity of estimating a function of an unknown unitary under average bias is Θ(Rep_ε(f)), where Rep_ε(f) measures the L2 tail of the function beyond degree 2m polynomials.
A general quantum duality for representations of groups with applications to quantum money, lightning, and fire
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Another generalization of Hadamard test: Optimal sample complexities for learning functions on the unitary group
The query complexity of estimating a function of an unknown unitary under average bias is Θ(Rep_ε(f)), where Rep_ε(f) measures the L2 tail of the function beyond degree 2m polynomials.