Realization of a high-fidelity generalized CNOT in a three-level system

In this work, we investigate the physical realization of a three-level generalized CNOT gate on superconducting transmons using microwave pulses by exploiting the principle of cross-resonance scheme. Despite a handful of works on two-qutrit gates using the cross-resonance, cross-cross-resonance, and cross-Kerr schemes, surprisingly, there is still a substantial gap in the literature with regard to gates involving entanglement on all three levels, to the best of our knowledge. We believe this work is important as the realization of entanglement on all three levels using a single pulse substantially decreases errors due to noise and decoherence.

We implement the said gate using the Schrieffer–Wolff transformation of Jaynes-Cummings Hamiltonian for a three-level system followed by the cross-resonance treatment of the drive Hamiltonian, incorporating the transformed frequencies. To study the implemented gate, we explore various benchmarking schemes, like Randomized benchmarking and Cyclic benchmarking. In addition, our work significantly outperforms previous two-qutrit entangling gates in fidelity for key states like GHZ and W-state. The experiments were performed on a custom-made two qutrit pulse simulator using QISKIT and on IBM Brisbane.