Microwave-driven i swap-like gate for fixed-frequency superconducting transmon qutrits

High-fidelity two-qubit gates are crucial for the scalability of superconducting quantum processors. While quantum information processing is typically based on qubits, qutrits (or qudits) provide a larger state space for quantum information storage and processing. In this study, we analyze a high-fidelity two-qutrit gate using microwave pulses on fixed-frequency superconducting transmon qutrits and show that a high-fidelity imaginary swap-like ($i$swap-like) gate can be achieved. Perturbation theory is employed to derive an effective interaction Hamiltonian, allowing us to estimate the gate time for the two-qutrit system. Moreover, by employing a microwave-activation scheme, we can realize a high-fidelity $i$swap-like gate on different excited states of the two qutrits. Our numerical results indicate that the proposed scheme can be readily extended to multiqutrit scenarios. Additionally, we investigate the impact of microwave pulse ramp time and qutrit relaxation on gate fidelity. The results demonstrate that, with a longer ramp time and the currently accessible qutrit relaxation time, the gate error remains sufficiently small. This proposed gate scheme enables the implementation of qutrit-qutrit entangling gates, providing a promising approach to realizing superconducting quantum computation.