In the clifford-T decomposition's SK method, we use S* and T* to denote Adjoint(S) and Adjoint(T), respectively. How we specify the basis set for Clifford-T should match with how we specify basis sets in the rest of the ecosystem.
basis_set (tuple[str]) – Basis set to be used for the decomposition and building an approximate set internally. It accepts the following gate terms: ('X', 'Y', 'Z', 'H', 'T', 'T*', 'S', 'S*'), where * refers to the gate adjoint. Default value is ('H', 'S', 'T').
In the above, it should say ('X', 'Y', 'Z', 'H', 'T', 'Adjoint(T)', 'S', 'Adjoint(S)') instead.