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 ε_{m} for a ^{43}Ca^{+} trapped-ion qubit in the small-error regime and find ε_{m}<10^{-4} for storage times t≲50  ms. This exceeds gate or measurement times by three orders of magnitude. Using randomized benchmarking, at t=1  ms we measure ε_{m}=1.2(7)×10^{-6}, around ten times smaller than that extrapolated from the T_{2}^{*} time, and limited by instability of the atomic clock reference used to benchmark the qubit.