  The conventional circuit paradigm, utilizing a limited number of gates to
construct arbitrary quantum circuits, is hindered by significant noise
overhead. For instance, the standard gate paradigm employs two CNOT gates for
the partial CPhase rotation in the quantum Fourier transform, even when the
rotation angle is very small. In contrast, some quantum computer platforms can
directly implement such operations using their native interaction, resulting in
considerably shorter and less noisy implementations for small rotation angles.
Unfortunately, coherent errors stemming from qubit crosstalk and calibration
imperfections render these implementations impractical. In Clifford gates such
as the CNOT, these errors can be addressed through Pauli twirling (also known
as randomized compiling). However, this technique is not applicable to the
non-Clifford native implementations described above. The present work
introduces, analyzes, and experimentally demonstrates a technique called
`Pseudo Twirling' to address coherent errors in general gates and circuits.
Additionally, we experimentally showcase that integrating pseudo twirling with
a quantum error mitigation method called `Adaptive KIK' enables the
simultaneous mitigation of both noise and coherent errors in non-Clifford
gates. Due to its unique features pseudo twirling could become a valuable asset
in enhancing the capabilities of both present and future NISQ devices.
