Two circuit designs for fast gate control in fluxonium qubits are proposed: one uses externally tuned EJ via magnetic flux, and the other employs switchable capacitance, both aiming to minimize phase-coordinate overlap and decoherence while enabling high-fidelity gates.

A Lindblad-based time evolution framework models decoherence and analyzes energy-relaxation times (T1) and potential relaxation errors during gates, indicating robustness against typical trade-offs.

Simulations scan EC/h around 0.25 GHz, EL/h around 0.5 GHz, and EJ/h from 1 to 12 GHz, showing how switching between heavy and light regimes optimizes storage and manipulation.

Coherence in the heavy regime can extend to hours for fluxons in near-degenerate ground states, while gate operations in the light regime offer fast, high-fidelity performance.

The architecture enables real-time tunable bit-flip protection by adjusting wavefunction overlap and matrix elements, balancing long coherence with manageable control.

IST Austria-led team demonstrates high-fidelity single- and two-qubit gates in superconducting qubits using base-band flux-pulses of about 10 nanoseconds, achieving fast control without microwave signals.

Overall, the work outlines a path to robust, scalable quantum processors by integrating long coherence with fast, controllable gate operations through tunable, protected fluxonium qubits.

A 7.5 ns Hadamard-like single-qubit gate with a 1.5 ns flat-top pulse achieves high precision, with a closed-system gate infidelity around 2×10^-5 under specific EJ conditions.

Qubits operate in two regimes: a heavy regime with exponentially suppressed transitions that protects information but complicates control, and a light regime that enables rapid gate operations and larger matrix elements.

Tunable Josephson energy is realized via flux control of a dc-SQUID, allowing in-situ adjustment of EJ or EC to modulate the potential landscape and wavefunction overlap.