  Many researchers have been heavily investigated on quantum phase estimation
(QPE) algorithms to find the unknown phase, since QPE is the core building
block of the most quantum algorithms such as the Shor's factoring algorithm,
quantum sampling algorithms, and finding the eigenvalues of unitary matrices.
Kitaev's algorithm and QPE algorithms using inverse Quantum Fourier transform
were proposed and widely used by researchers as a key component for their
quantum algorithms. In this paper, we explore the experimental challenges of
QPE algorithms on Noisy Intermediate-Scale Quantum (NISQ) computers by
implementing various QPE algorithms on the state-of-the-art IBM quantum
computer. Our experimental results demonstrate that the accuracy of finding the
phase using these algorithms are severely constrained by NISQ's physical
characteristics such as coherence time and error rates. To mitigate such
physical limitations, we propose modified solutions of these algorithms by
reducing the number of control gates and phase shift operations. Our
experimental results showed that our solutions can significantly increase the
accuracy of the finding phase in near-term quantum computers.
