Generalized cross-resonance scheme for maximally-entangling two-qutrit gates

To utilize higher-dimensional quantum systems, in this Letter, we derive a generalized cross-resonance (GCR) scheme for realizing maximally entangling two-qutrit gates on fixed-frequency transmons beyond the 0-1 subspace. Our two-qutrit gates, namely, $U_{CR}^{01}$ and $U_{CR}^{12}$, acting on the $0\text{-}1$ and $1\text{-}2$ energy transitions of transmons, respectively, directly allow for entanglement on the $1\text{-}2$ levels. Unlike the known works, our gate is parametric in nature, enabling us to construct multiple entangling gates of interest. By performing simulations in Qiskit, we demonstrate two-qutrit generalized controlled-$X$ ($U_{CX}^{01}$ and $U_{CX}^{12}$) and controlled-$H$ ($U_{CH}^{01}$ and $U_{CH}^{12}$) gates, which are instances of the proposed $U_{CR}$ gates, with reported gate fidelities of $86.14\mathrm{\%}(99.73\mathrm{\%}),84.6\mathrm{\%}(97.88\mathrm{\%}),92.35\mathrm{\%}(99.39\mathrm{\%})$, and $91.99\mathrm{\%}(98.99\mathrm{\%})$, respectively with (and without) noise. We also reveal a two-qutrit Bell state with a fidelity of $99.06\pm 0.01\mathrm{\%}$, with a complete Bell state preparation in a $\sim 514$ ns pulse sequence, which is less than the gate time of the known scheme by cross-Kerr-based entangling gates.