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

Abstract

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 $t\lesssim50\,\mbox{ms}$. This exceeds gate or measurement times by three orders of magnitude. Using randomized benchmarking, at $t=1\,\mbox{ms}$ we measure ${\epsilon }_m=1.2(7)\times 10^{-6}$, 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.

8 pages, 5 figures