The ubiquitous presence of $1/f$ flux noise was a significant barrier to long coherence times 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 various 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, although the qubits are parked at flux-insensitive points, the modulation results in increased dephasing rate due to the multiplicative $1/f$ noise and white noise components. Remarkably, we find a sweet spot under flux modulation, which we dub the “ac sweet spot,” that is insensitive to $1/f$ flux noise. We show that simple filtering of the flux control signal additionally protects parametric entangling gates from white noise in the control electronics at this ac sweet spot, allowing interactions of quality that is limited only by higher-order effects and other sources of noise.

• Received 25 June 2019
• Revised 26 September 2019

DOI:https://doi.org/10.1103/PhysRevApplied.12.054015