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With the development of controllable quantum systems, fast and practicalcharacterization for multi-qubit gates is essential for building high-fidelityquantum computing devices. The usual way to fulfill this requirement viarandomized benchmarking asks for the complicated implementation of numerousmulti-qubit twirling gates. How to efficiently and reliably estimate thefidelity of a quantum process remains an open problem. In this work, we proposea character-cycle benchmarking protocol and a character-average benchmarkingprotocol only using local twirling gates to estimate the process fidelity of anindividual multi-qubit operation. Our protocols can characterize a large classof quantum gates including and beyond the Clifford group via the local gaugetransformation, which forms a universal gate set for quantum computing. Wenumerically demonstrate our protocols for a non-Clifford gate --controlled-$(TX)$ and a Clifford gate -- five-qubit quantum error-correctingencoding circuit. The numerical results show that our protocols can efficientlyand reliably characterize the gate process fidelities. Compared with thecross-entropy benchmarking, the simulation results show that thecharacter-average benchmarking achieves three orders of magnitude improvementsin terms of sampling complexity.

Scalable fast benchmarking for individual quantum gates with local twirling