Probing Qubit Memory Errors at the Part-per-Million Level

Robust qubit memory is essential for quantum computing, both for near-term devices operating without error correction, and for the long-term goal of a fault-tolerant processor. We directly measure the memory error $epsilon_m$ for a $^{43}$Ca$^+$ trapped-ion qubit in the small-error regime and find $epsilon_m<10^{-4}$ for storage times $tlesssim50,mbox{ms}$. This exceeds gate or measurement times by three orders of magnitude. Using randomized benchmarking, at $t=1,mbox{ms}$ we measure $epsilon_m=1.2(7)times10^{-6}$, around ten times smaller than that extrapolated from the $T_{2}^{ast}$ time, and limited by instability of the atomic clock reference used to benchmark the qubit.