SU(4) Gate Design via Unitary Process Tomography: Its Application to Cross-Resonance-Based Superconducting Quantum Devices

In this article, 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 $ZZ$-interactions. Leveraging the Weyl chamber's geometric structure, we successfully realize a continuous two-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 $R_{ZZ}(\theta)$ to confirm the advantages of our implementation.