摘要
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)⁰¹andU_(CR)¹² , acting on the0\text -1and1\text -2energy transitions of transmons, respectively, directly allow for entanglement on the1\text -2levels. 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)⁰¹andU_(CX)¹² ) and controlled- H( U_(CH)⁰¹andU_(CH)¹² ) gates, which are instances of the proposedU_(CR)gates, with reported gate fidelities of86.14% (99.73%), 84.6% (97.88%), 92.35% (99.39%) , and91.99% (98.99%) , respectively with (and without) noise. We also reveal a two-qutrit Bell state with a fidelity of99.06 ± 0.01% , with a complete Bell state preparation in a∼514ns pulse sequence, which is less than the gate time of the known scheme by cross-Kerr-based entangling gates.