# Experimental demonstration of cheap and accurate phase estimation

## TL;DR

This paper demonstrates a robust, resource-efficient phase estimation method for trapped ion qubits that achieves high precision without requiring perfect operations or ancillae, validated against gate set tomography.

## Contribution

It introduces a practical implementation of robust phase estimation that is both accurate and resource-efficient, suitable for real-world quantum systems.

## Key findings

- Achieved phase uncertainties less than 4e-4 radians.
- Used as few as 176 samples per phase for estimation.
- Demonstrated Heisenberg scaling in phase estimation.

## Abstract

We demonstrate experimental implementation of robust phase estimation (RPE) to learn the phases of X and Y rotations on a trapped $\textrm{Yb}^+$ ion qubit. We estimate these phases with uncertainties less than $4\cdot10^{-4}$ radians using as few as 176 total experimental samples per phase, and our estimates exhibit Heisenberg scaling. Unlike standard phase estimation protocols, RPE neither assumes perfect state preparation and measurement, nor requires access to ancillae. We cross-validate the results of RPE with the more resource-intensive protocol of gate set tomography.