Group twirling and noise tailoring for multiqubit controlled phase gates

Abstract

Group twirling is crucial in quantum information processing, particularly in randomized benchmarking and randomized 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—the lack of practical twirling groups for multiqubit non-Clifford gates remains a challenge. To address this gap, we study the issue of finding twirling groups for generic quantum gates, focusing on a widely used circuit structure in randomized benchmarking or randomized compiling. Specifically, for multiqubit controlled phase gates, which are essential in quantum algorithms and directly implementable in practice, we determine optimal twirling groups within the realm of classically replaceable unitary operations. Contrasting with the local Pauli twirling group for Clifford gates, the optimal groups for such gates contain nonlocal operations, highlighting the overhead of tailoring noise in global non-Clifford contexts. We design new benchmarking procedures for multiqubit controlled phase gates based on the optimal twirling groups. Our simulation results show that our scheme can improve the precision and accuracy of benchmarking in small-scale systems. Published by the American Physical Society 2024