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 Ca-43(+) trapped-ion qubit in the small-error regime and find epsilon(m) < 10(-4) for storage times t less than or similar to 50 ms. This exceeds gate or measurement times by three orders of magnitude. Using randomized benchmarking, at t = 1 ms we measure epsilon(m) = 1.2(7) x 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.