Multilevel control and readout of Transmon

Superconducting circuit are one of the leading platforms for quantum information processing. Previous work has demonstrated high fidelity control and readout on Transmon with long coherence. Typical Transmon has EJ/EC ~ 50-60 to reduce charge dispersion of the two lowest levels while keeping relatively large anharmonicity so that it becomes a nice realization of qubit. In this work, we explored a regime where the Transmon has larger EJ/EC, and more of its energy levels can be used to store and process a qudit quantum states. We demonstrated state preparation with d=7 states and characterized coherence of each level. We found the larger EJ/EC can help suppress charge dispersion on higher level as predicted by traditional Transmon model, and the decay rates are close to bosonic enhancement. Using frequency-multiplexed multi-tone readout, we are able to distinguish all 7 levels in one single shot. We compared different readout strategies and found the 7-state readout fidelity up to 85% with assistance from deep neural network. We performed randomized benchmarks on two-level subspace and qudit state tomography to characterize our control precision and analyze some possible error sources of our system.