AC flux sweet spots in parametrically-modulated superconducting qubits

The ubiquitous presence of $1/f$ flux noise was a significant barrier to long-coherence in superconducting qubits until the development of qubits that could operate in static, flux noise insensitive configurations commonly referred to as `sweet-spots'. Several proposals for entangling gates in superconducting qubits tune the flux bias away from these spots, thus reintroducing the dephasing problem to varying degrees. Here we revisit one such proposal, where interactions are parametrically activated by rapidly modulating the flux bias of the qubits around these sweet-spots, and study the effect of modulation on the sensitivity to flux noise. We explicitly calculate how dephasing rates depend on different components of the flux-noise spectrum, and show that, while these parametric gates are insensitive to $1/f$ flux noise, dephasing rates are increased under modulation, and dominated by white noise. Remarkably, we find that simple filtering of the flux control signal allows for entangling gates to operate in a novel sweet-spot for dephasing under flux modulation. This sweet spot, which we dub the AC sweet spot, is insensitive to $1/f$ flux noise, and much less sensitive to white noise in the control electronics, allowing for interactions of quality that is limited only by higher order effects and other sources of noise.