  Superconducting qubits are one of the most promising candidates to implement
quantum computers. The superiority of superconducting quantum computers over
any classical device in simulating random but well-determined quantum circuits
has already been shown in two independent experiments and important steps have
been taken in quantum error correction. However, the currently wide-spread
qubit designs do not yet provide high enough performance to enable practical
applications or efficient scaling of logical qubits owing to one or several
following issues: sensitivity to charge or flux noise leading to decoherence,
too weak non-linearity preventing fast operations, undesirably dense excitation
spectrum, or complicated design vulnerable to parasitic capacitance. Here, we
introduce and demonstrate a superconducting-qubit type, the unimon, which
combines the desired properties of high non-linearity, full insensitivity to dc
charge noise, insensitivity to flux noise, and a simple structure consisting
only of a single Josephson junction in a resonator. We measure the qubit
frequency, $\omega_{01}/(2\pi)$, and anharmonicity $\alpha$ over the full
dc-flux range and observe, in agreement with our quantum models, that the qubit
anharmonicity is greatly enhanced at the optimal operation point, yielding, for
example, 99.9% and 99.8% fidelity for 13-ns single-qubit gates on two qubits
with $(\omega_{01},\alpha)=(4.49~\mathrm{GHz}, 434~\mathrm{ MHz})\times 2\pi$
and $(3.55~\mathrm{GHz}, 744~\mathrm{ MHz})\times 2\pi$, respectively. The
energy relaxation time $T_1\lesssim 10~\mu\mathrm{s}$ is stable for hours and
seems to be limited by dielectric losses. Thus, future improvements of the
design, materials, and gate time may promote the unimon to break the 99.99%
fidelity target for efficient quantum error correction and possible quantum
advantage with noisy systems.
