Realizing high-fidelity qudit gates on a transmon via optimal control*

Many physical quantum architectures have access to a wider range of possible states. Previous theoretical studies [1] have shown that using these higher qudit states can significantly reduce the depth and width of a quantum circuit, increasing the computation volume of quantum computers with limited coherence and size. However, in order to fully investigate the viability of using qudit states for computation, control pulses corresponding to qudit gates have to be designed and their quality evaluated on actual hardware. Using optimal control methods, we explicitly construct short-duration pulses of high theoretical fidelity (>0.999) for single qutrits and ququarts to realize practical gate types that can explore the entire state space. We successfully demonstrate their experimental implementation on a superconducting transmon with four well-characterized energy levels and estimate their fidelity via quantum process tomography. Our findings motivate further research in higher-radix quantum computing architectures and tailored compiler design.

[1] Jonathan M Baker, Casey Duckering, and Frederic T Chong. Efficient quantum circuit decompositions via intermediate qudits. In 2020 IEEE 50th International Symposium on Multiple-Valued Logic (ISMVL), pages 303–308. IEEE, 2020.