Determine gate performance near the hard 0-$\pi$ regime

Characterize the performance of the proposed microwave-activated controlled-Z gate for capacitively coupled 0-$\pi$ qubits as the devices approach the hard 0-$\pi$ regime.

Background

The paper analyzes soft 0-$\pi$ qubits using a zero-disorder approximation and a phenomenological decoherence model. Its numerical results therefore establish a best-case benchmark for the proposed controlled-Z gate rather than a complete prediction for devices with stronger protection.

The hard 0-$\pi$ regime has different circuit parameters and motivates alternative protected gate constructions. The authors explicitly identify the behavior of their proposed gate as devices approach that regime as unresolved, while noting that incorporating realistic noise into protected-gate frameworks is an important next step.