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

43 pages,13 figures

References in corpus (16)

• Randomized Benchmarking of Quantum Gates
• Robust randomized benchmarking of quantum processes
• Realization of the quantum Toffoli gate with trapped ions
• Symmetrised Characterisation of Noisy Quantum Processes
• High-fidelity three-qubit iToffoli gate for fixed-frequency superconducting qubits
• Programmable Heisenberg interactions between Floquet qubits
• The learnability of Pauli noise
• Reducing the Depth of Linear Reversible Quantum Circuits
• Pauli error estimation via Population Recovery
• Character randomized benchmarking for non-multiplicity-free groups with applications to subspace, leakage, and matchgate randomized benchmarking
• Estimating gate-set properties from random sequences
• Benchmarking universal quantum gates via channel spectrum
• Randomized Benchmarking Beyond Groups
• Scalable fast benchmarking for individual quantum gates with local twirling
• Classically Replaceable Operations
• Robust Estimation of Nonlinear Properties of Quantum Processes

Cited by in corpus (5)

• Phase Estimation with Compressed Controlled Time Evolution
• Benchmarking non-Clifford gates using only Pauli twirling group
• Assessing the dynamical assumptions in Tsirelson inequality tests of non-classicality in harmonic oscillators
• Fermionic Averaged Circuit Eigenvalue Sampling
• Approximate Quantum Error Correction with 1D Log-Depth Circuits