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

## TL;DR

This paper measures extremely low qubit memory errors in trapped-ion systems, demonstrating errors below 10^{-4} for 50 ms storage and around 10^{-6} at 1 ms, surpassing previous benchmarks and highlighting stability challenges.

## Contribution

It provides direct measurements of qubit memory errors at the part-per-million level, revealing error rates much lower than gate times and identifying clock instability as a limiting factor.

## Key findings

- Memory error $oldsymbol{ extless} 10^{-4}$ for 50 ms storage
- Randomized benchmarking shows $oldsymbol{ extapprox} 10^{-6}$ error at 1 ms
- Errors are limited by atomic clock instability

## 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 $\epsilon_m=1.2(7)\times10^{-6}$, 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.