First-principles analysis of the cross-resonance gate*

As quantum circuits grow in complexity, it is crucial to have precise but practical methods for characterization, optimization and scaling of the two-qubit gates. Here, we present a theoretical study of cross-resonance (CR) covering gate parameters, gate error, spectator qubits and multi-qubit frequency collisions [1]. Our analysis is based on obtaining an effective gate Hamiltonian using Schrieffer-Wolff perturbation theory [2]. Accounting for Josephson nonlinearity, we derive an improved starting model with renormalized qubit-qubit and drive interaction rates leading to an approximately 15 percent relative correction of the effective gate parameters compared to Kerr theory. The gate operation strongly depends on the ratio of qubit-qubit detuning and anharmonicity. We characterize five distinct regions of operation and propose optimal parameters to achieve high gate speed and low coherent gate error. Our characterization of spectator qubits and collisions lays out the groundwork for scaling up CR gates in a quantum processor.
[1]. Phys. Rev. A 102, 042605
[2]. Phys. Rev. A 101, 052308