Universally robust control sequences for high-dimensional superconducting qubits*

Recently superconducting transmon qubits are consistently being implemented as the building blocks of large-scale quantum processors due to their longer coherence times, potential for precise optimal control using microwave electronics, and microelectronics scalability. Working with higher-order Fock states, transmon qubits could be implemented as a d-dimensional Hilbert-space quantum system, or qudit, where quantum information is encoded in the higher Jaynes-Cummings levels of the transmon system which reduces circuit complexity for non-classical gate operations and algorithms. It is necessary for these high-dimensional qudits to hold long coherence times in both relaxation and dephasing pathways so that the transmon logic gates can be implemented with high fidelity. In an effort to suppress decoherence in these qudits, here we demonstrate robust dynamical decoupling (DD) using precise pulse sequences to mediate systematic errors and dephasing that occur in the evolution of these higher-order qudits. We demonstrate the effectiveness of several DD pulse sequences applied on the higher-order transitions of a transmon qudit coupled to a readout microwave resonator during Ramsey measurements. These pulse sequences mediate the dephasing effect in this superposition state which resulted in improved dephasing times (T₂) at the microsecond scale.