Group twirling and noise tailoring for multi-qubit controlled phase gates

Understand

Group twirling is crucial in quantum information processing, particularly in randomized benchmarking and random compiling.

• While protocols based on Pauli twirling have been effectively crafted to transform arbitrary noise channels into Pauli channels for Clifford gates -- thereby facilitating efficient benchmarking and mitigating worst-case errors -- practical twirling groups for multi-qubit non-Clifford gates are lacking.
• In this work, we study the issue of finding twirling groups for generic quantum gates within a widely used circuit structure in randomized benchmarking or random compiling.
• For multi-qubit controlled phase gates, which are essential in both the quantum Fourier transform and quantum search algorithms, we identify optimal twirling groups within the realm of classically replaceable unitary operations.