Symmetric Clifford twirling for cost-optimal quantum error mitigation in early FTQC regime

Twirling noise affecting quantum gates is essential in understanding and controlling errors, but applicable operations to noise are usually restricted by symmetries inherent in quantum gates. In this Letter, we propose symmetric Clifford twirling, a Clifford twirling utilizing only symmetric Clifford operators that commute with certain Pauli subgroups. We fully characterize how each Pauli noise is converted through the twirling and show that certain Pauli noise can be scrambled to a noise exponentially close to the global white noise. We further provide numerical demonstrations for highly structured circuits, such as Trotterized Hamiltonian simulation circuits, that noise effect on typical observables can be described by the global white noise, and also that even a single use of CNOT gate for twirling can significantly accelerate the scrambling. These findings enable us to mitigate errors in non-Clifford operations with minimal sampling overhead in the early stages of fault-tolerant quantum computing.