The Parametric iSWAP Gate
Modulating a qubit's flux at the frequency difference between two qubits drives a resonant exchange of excitation without a static resonance.
Parametric Modulation
Two detuned qubits do not exchange excitations because energy is not conserved by a simple swap. If, however, one qubit's frequency is modulated sinusoidally at the difference between the two qubit frequencies, sidebands appear in its spectrum. One sideband lands on the neighbor's frequency, restoring the resonance condition and enabling a coherent exchange of a single excitation. This is the parametric, or activated, iSWAP.
The advantage is that both qubits can sit near their sweet spots, where dephasing is minimized, for the entire gate. Only a small oscillating flux is applied, and the interaction is turned on precisely by the modulation frequency and off by stopping it.
Gate Duration and Angle
- Driving for a full exchange period gives iSWAP, a complete swap of excitations with a phase.
- Driving for half the period gives the square-root-of-iSWAP, a maximally entangling gate.
- The effective exchange rate scales with the modulation amplitude, so the gate time is tunable.
Calibration Considerations
Frequency modulation shifts the time-averaged qubit frequency, an effect that must be tracked and corrected with single-qubit phase adjustments. Higher harmonics of the modulation can drive unwanted transitions, so the modulation amplitude is bounded. As with all flux-based gates, the flux line's transfer function distorts the intended waveform and is compensated by pre-distortion.
Where It Fits
Parametric gates are attractive in architectures where keeping qubits at their sweet spots is a priority, and in systems using tunable couplers, where the coupler rather than a computational qubit is modulated. The result is a family of fast, low-dephasing entangling gates that complement the controlled-phase approach.