Calibrating quantum gates up to 52 qubits in a superconducting processor

Benchmarking large-scale quantum gates, typically involving multiple native two-qubit and singlequbit gates, is crucial in quantum computing. Global fidelity, encompassing information about intergate correlations, offers a comprehensive metric for evaluating and optimizing gate performance, unlike the fidelities of individual local native gates. In this work, utilizing the character-average benchmarking protocol implementable in a shallow circuit, we successfully benchmark gate fidelities up to 52 qubits. Notably, we achieved a fidelity of 63.09$\pm $0.23% for a 44-qubit parallel CZ gate. Utilizing the global fidelity of the parallel CZ gate, we explore the correlations among local CZ gates by introducing an inter-gate correlation metric, enabling one to simultaneously quantify crosstalk error when benchmarking gate fidelity. Finally, we apply our methods in gate optimization. By leveraging global fidelity for optimization, we enhance the fidelity of a 6-qubit parallel CZ gate from 87.65% to 92.04% and decrease the gate correlation from 3.53% to 3.22%, compared to local gate fidelitybased optimization. The experimental results align well with our established composite noise model, incorporating depolarizing and ZZ-coupling noises, and provide valuable insight into further study and mitigation of correlated noise.