High-fidelity operation of a radioactive trapped-ion qubit, $^{133}$Ba$^+$

$^{133}$Ba$^+$ has been identified as an attractive ion for quantum information processing due to the unique combination of its spin-1/2 nucleus, visible wavelength electronic transitions, and long D-state lifetimes ($\tau\sim $1~min). Using a microgram source of radioactive material, we trap and laser-cool the synthetic \textit{A} = 133 radioisotope of barium II ($\tau_{1/2} \approx 10.5$~yr) in a radio-frequency ion trap. To demonstrate high fidelity qubit operations, a number of unknown state energies were needed. We measure the isotope shift and hyperfine structure of the 6$^2$P$_{1/2}\leftrightarrow 5^2$D$_{3/2}$ electronic transition needed for laser cooling, state preparation, and state detection of the clock-state hyperfine and optical qubits. For high-fidelity operations with electron shelving, we report measurements of the 6$^2$P$_{3/2}$ and $5^2$D$_{5/2}$ hyperfine splittings, as well as the~6$^2$P$_{3/2}~\leftrightarrow~6^2$S$_{1/2}$ and ~6$^2$P$_{3/2}~\leftrightarrow~5^2$D$_{5/2}$ transition frequencies. Using these transitions, we demonstrate high-fidelity \ba \ hyperfine qubit manipulation with electron shelving detection to benchmark qubit state preparation and measurement (SPAM). Using single-shot, threshold discrimination, we measure an average SPAM fidelity of $\mathcal{F} = 0.99971(3)$, a factor of $\approx$ 2 improvement over the best reported performance of any qubit.Finally, we report the 6$^2$P$_{1/2}\leftrightarrow 5^2$D$_{3/2}$ electronic transition isotope shift for the rare \textit{A} = 130 and 132 barium nuclides, completing the spectroscopic characterization necessary for laser cooling all long-lived barium II isotopes