# Practical sampling schemes for quantum phase estimation

## TL;DR

This paper presents practical sampling schemes for quantum phase estimation that significantly reduce measurement requirements by using adaptive phase shifts, enabling efficient and accurate phase estimation.

## Contribution

The work introduces new sampling algorithms with theoretical bounds that minimize measurements needed for quantum phase estimation, improving upon previous methods.

## Key findings

- Reduced measurements to a single per bit with accurate phase shifts
- Provided theoretical bounds and numerical evaluations for measurement counts
- Achieved phase estimation with high probability using fewer resources

## Abstract

In this work we consider practical implementations of Kitaev's algorithm for quantum phase estimation. We analyze the use of phase shifts that simplify the estimation of successive bits in the estimation of unknown phase $\varphi$. By using increasingly accurate shifts we reduce the number of measurements to the point where only a single measurements in needed for each additional bit. This results in an algorithm that can estimate $\varphi$ to an accuracy of $2^{-(m+2)}$ with probability at least $1-\epsilon$ using $N_{\epsilon} + m$ measurements, where $N_{\epsilon}$ is a constant that depends only on $\epsilon$ and the particular sampling algorithm. We present different sampling algorithms and study the exact number of measurements needed through careful numerical evaluation, and provide theoretical bounds and numerical values for $N_{\epsilon}$.