Realization of maximally-entangling two-qutrit gates using the Cross-Resonance scheme (2504.15265v3)

Abstract: In this letter, we introduce the generalized cross-resonance scheme (GCR) which is a comprehensive theoretical framework that generalize the qubit-centric cross-resonance (CR) interaction beyond the 0-1 subspace for realizing maximally entangling two-qutrit gates on fixed-frequency transmons and is a microwave-only technique compatible with existing hardware. We use the GCR scheme to design parametric two-qutrit gates, namely, $U_{CR}^{01}$ and $U_{CR}^{12}$, that act on the $0{-}1$ and $1{-}2$ energy transitions of transmons. Our gates improve upon the existing works in two aspects. First, our gates directly allow for entanglement on the $1{-}2$ levels rather than merely relying on $0{-}1$ entanglement, as in previous works. Second, our gates are parametric in nature, enabling us to construct multiple entangling gates of interest, whereas the purview of prior works that use cross-resonance for qutrits was limited to individual gates. Using numerical simulation in Qiskit Dynamics, 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 $99.73\pm 0.01\%, 97.88\pm 0.01\%, 99.39\pm 0.01\%$, and $98.99\pm 0.01\%$, respectively. Finally, we prepare a two-qutrit Bell state $|\psi\rangle = \frac{1}{\sqrt{3}}(|00\rangle + |11\rangle + |22\rangle)$ with a fidelity of $99.06 \pm 0.01\%$. We note that, in our setup, the complete time taken for Bell state preparation is $\sim 514$ ns and is less than the gate time of cross-Kerr-based entangling gates.