Eliminating Leakage Errors in Hyperfine Qubits

Population leakage outside the qubit subspace presents a particularly harmful source of error that cannot be handled by standard error correction methods. Using a trapped Yb$^+$ ion, we demonstrate an optical pumping scheme to suppress leakage errors in atomic hyperfine qubits. The selection rules and narrow linewidth of a quadrupole transition are used to selectively pump population out of leakage states and back into the qubit subspace. Each pumping cycle reduces the leakage population by a factor of $\sim 3$, allowing for an exponential suppression in the number of cycles. We use interleaved randomized benchmarking on the qubit subspace to show that this pumping procedure has negligible side-effects on un-leaked qubits, bounding the induced qubit memory error by $\leq 2.0(8) \times 10^{-5}$ per cycle, and qubit population decay to $\leq 1.4(3) \times 10^{-7}$ per cycle. These results clear a major obstacle for implementations of quantum error correction and error mitigation protocols.