Error analysis of the cNOT gate constructed by MAP+Z gates in two-qubit circuit QED system

We constructed a controlled-NOT (cNOT) gate in a two-transmon circuit QED system using the MAP (micrwave activated c-phase) and Z gates. We performed tomography and benchmarking in order to measure the fidelity of single- and two- qubit gates. In this presentation, we investigate the source of errors in the constructed cNOT gate in detail. The dominant source is the decoherence during the long gate time, due to limited dephasing time of the qubit. The leakage to non-computational states also contributes to infidelity partly. We suggest a strategy to improve the fidelity