Complete population transfer between next-adjacent energy levels of a transmon qudit

The utilization of qudits in quantum systems has led to significant advantages in quantum computation and information processing. Therefore, qudits have gained increased attention in recent research for their precise and efficient operations. In this work, we demonstrate the complete population transfer between the next-adjacent energy levels of a transmon qudit using the Pythagorean coupling method and energy level mapping. We achieve a |0〉 to |2〉 transfer with a process fidelity of 97.76% in the subspace spanned by |0〉 to |2〉. Moreover, the transfer operation is achieved within a remarkably fast timescale, as short as 20 ns. This study may present a promising avenue for enhancing the operation flexibility and efficiency of qudits in future implementations.