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

TL;DR

This paper investigates optimal twirling groups for multi-qubit controlled phase gates, crucial for quantum algorithms, revealing larger groups than Pauli twirling for Clifford gates and highlighting noise tailoring challenges.

Contribution

It identifies optimal twirling groups for multi-qubit controlled phase gates, expanding the understanding of noise tailoring beyond Clifford gates in randomized benchmarking.

Findings

Optimal twirling groups are larger than Pauli groups for these gates.

Twirling groups are within classically replaceable unitaries.

Highlights overhead in noise tailoring for non-Clifford gates.

Abstract

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. In contrast to the simplicity of the Pauli twirling group for Clifford gates, the optimal groups for such gates are much larger, highlighting the overhead of tailoring noise channels in the presence of global non-Clifford gates.