SU(4) gate design via unitary process tomography: its application to cross-resonance based superconducting quantum devices

We present a novel approach for implementing pulse-efficient SU(4) gates on cross resonance (CR)-based superconducting quantum devices. Our method introduces a parameterized unitary derived from the CR-Hamiltonian propagator, which accounts for static-$ZZ$ interactions. Leveraging the Weyl chamber's geometric structure, we successfully realize a continuous 2-qubit basis gate, $R_{ZZ}(\theta)$, as an echo-free pulse schedule on the IBM Quantum device ibm_kawasaki. We evaluate the average fidelity and gate time of various SU(4) gates generated using the $R_{ZZ}(\theta)$ to confirm the advantages of our implementation.