Theory of Parametric fSim Gate in superconducting qubits

Most quantum computation architectures typically depend on a specific type of two-qubit gate to form a universal gate set. However, the introduction of flexible native entanglement gates can significantly reduce circuit complexity, which is crucial for the performance of NISQ (Noisy Intermediate-Scale Quantum) devices. In this study, we propose a novel scheme to implement a continuous fermionic simulation gate (fSim gate) for superconducting qubits. Our approach involves the simultaneous application of two parametric drives with distinct frequencies, each targeting different transitions. This enables the realization of iSWAP-type and CPhase-type operations within a single gate cycle, with tunable angles controlled by drive amplitudes and frequencies. We provide analytical formulas for effective coupling strengths that span from the dispersive regime to the strong drive regime. Our findings open new avenues for more versatile gate schemes in quantum computing.