Iterative quantum phase estimation with optimized sample complexity

In this work we consider 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 φ, By using increasingly accurate shifts we reduce the number of measurements to the point where only a single measurement is needed for each additional bit. This results in an algorithm that can estimate φ to $m$ + 2 bits of accuracy with probability at least 1- ∊ using $N$ ∊ + $m$ measurements, where $N$ ∊ is a quantity that depends only on ∊ 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 $N$ ∊ .