Unbiased quantum phase estimation

Quantum phase estimation algorithm (PEA) is one of the most important algorithms in early studies of quantum computation. 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. We also show that a maximum likelihood estimation (MLE) post-processing step applied on UPEA has a smaller mean absolute error than MLE applied on PEA. In the end, we apply UPEA to quantum counting, and use an additional correction step to make the quantum counting algorithm unbiased.