Measurement efficient automated multi-level qudit pulse optimization on quantum devices

Harnessing the existing higher levels in the cQED qudit can significantly increase the resourcefulness of NISQ era quantum devices. However, increased deviations and complexity in the modeling of higher levels, make it challenging to tune up high-fidelity gates on a qudit. We investigate using a model-free pulse optimization of a U(3) gate. We demonstrate that parameterizing the pulse with Hanning windowed basis functions allows for more efficient optimization, as they reduce the number of parameters required, and ensure strict bandwidth limits. We also simplify the cost function and use only state populations instead of full state tomography, reducing the number of measurements required at each evaluation. Our optimization protocol starts with no prior knowledge about the ideal pulse parameters and obtains a gate error of 2e-3 which is primarily coherence limited. Unlike traditional model-based optimization, this model-free approach enables optimization of multi-qutrit gates and is directly applicable to other qubit architectures including protected qubits.