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Kitaev's 0-$\pi $ qubit encodes quantum information in two protected,near-degenerate states of a superconducting quantum circuit. In a recent work,we have shown that the coherence times of a realistic 0-$\pi $ device cansurpass that of today's best superconducting qubits [Groszkowski et al., NewJournal of Physics 20 043053 (2018)]. Here we address controllability of the0-$\pi $ qubit. Specifically, we investigate the potential for dispersivecontrol and readout, and introduce a new, fast and high-fidelity single-qubitgate that can interpolate smoothly between logical X and Z. We characterize theaction of this gate using a multi-level treatment of the device, and analyzethe impact of circuit element disorder and deviations in control and circuitparameters from their optimal values. Furthermore, we propose a cooling schemeto decrease the photon shot-noise dephasing rate, which we previously found tolimit the coherence times of 0-$\pi $ devices within reach of currentexperiments. Using this approach, we predict coherence time enhancementsbetween one and three orders of magnitude, depending on parameter regime.

Control and Coherence Time Enhancement of the 0-$\pi $ Qubit