  With the development of controllable quantum systems, fast and practical
characterization for multi-qubit gates is essential for building high-fidelity
quantum computing devices. The usual way to fulfill this requirement via
randomized benchmarking asks for the complicated implementation of numerous
multi-qubit twirling gates. How to efficiently and reliably estimate the
fidelity of a quantum process remains an open problem. In this work, we propose
a character-cycle benchmarking protocol and a character-average benchmarking
protocol only using local twirling gates to estimate the process fidelity of an
individual multi-qubit operation. Our protocols can characterize a large class
of quantum gates including and beyond the Clifford group via the local gauge
transformation, which forms a universal gate set for quantum computing. We
numerically demonstrate our protocols for a non-Clifford gate --
controlled-$(TX)$ and a Clifford gate -- five-qubit quantum error-correcting
encoding circuit. The numerical results show that our protocols can efficiently
and reliably characterize the gate process fidelities. Compared with the
cross-entropy benchmarking, the simulation results show that the
character-average benchmarking achieves three orders of magnitude improvements
in terms of sampling complexity.
