Fast gates for bit-flip protected superconducting qubits

Superconducting qubits offer an unprecedentedly high degree of flexibility in terms of circuit encoding and parameter choices. However, in designing the qubit parameters one typically faces the conflicting goals of long coherence times and simple control capabilities. Both are determined by the wavefunction overlap of the qubit basis states and the corresponding matrix elements. Here, we address this problem by introducing a qubit architecture with real-time tunable bit-flip protection. In the first, the `heavy' regime, the energy relaxation time can be on the order of hours for fluxons located in two near-degenerate ground states, as recently demonstrated in Ref. [Hassani et al., Nat.~Commun.~14 (2023)]. The second, `light' regime, on the other hand facilitates high-fidelity control on nanosecond timescales without the need for microwave signals. We propose two different tuning mechanisms of the qubit potential and show that base-band flux-pulses of around 10 ns are sufficient to realize a universal set of high-fidelity single- and two-qubit gates. We expect that the concept of real-time wavefunction control can also be applied to other hardware-protected qubit designs.