Unbiased quantum phase estimation

TL;DR

This paper introduces an unbiased quantum phase estimation algorithm (UPEA) that improves the accuracy of quantum counting and other algorithms by removing bias and enhancing robustness through post-processing and correction steps.

Contribution

The paper proposes a novel unbiased phase estimation algorithm (UPEA) and demonstrates its application and improvements in quantum counting.

Findings

UPEA achieves unbiased phase estimation.

Post-processing enhances robustness.

Application to quantum counting improves accuracy.

Abstract

Quantum phase estimation algorithm (PEA) is one of the most important algorithms in early studies of quantum computation. It is also a key for many other quantum algorithms, such as the quantum counting algorithm and the Shor's integer factorization algorithm. However, we find that the PEA is not an unbiased estimation, which prevents the estimation error from achieving an arbitrarily small level. In this paper, we propose an unbiased phase estimation algorithm (UPEA) based on the original PEA, and study its application in quantum counting. We also show that a maximum likelihood post-processing step can further improve its robustness. In the end, we apply UPEA to quantum counting, and use an additional correction step to make the quantum counting algorithm unbiased.