Robustness of a universal gate set implementation in transmon systems via Chopped Random Basis optimal control

We numerically study the implementation of a universal two-qubit gate set, composed of CNOT, Hadamard, phase and $\pi \mathrm{/}8$ gates, for transmon-based systems. The control signals to implement such gates are obtained using the Chopped Random Basis optimal control technique, with a target gate infidelity of ${10}^{-2}$. During the optimization processes we account for the leakage toward non-computational states, an important non-ideality affecting transmon qubits. We also test and benchmark the optimal control solutions against the introduction of Gaussian white noise and spectral distortion, two key non-idealities that affect the control signals in transmon systems.