A cross-resonance pulse sequence can implement a CNOT gate between a transmon and a parity-protected qubit with simulated average fidelity above 0.998.
Martinis, and John Clarke
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Construction of new type of CNOT gate using cross-resonance pulse in the transmon-PPQ system
A cross-resonance pulse sequence can implement a CNOT gate between a transmon and a parity-protected qubit with simulated average fidelity above 0.998.