Experimental Challenges of Implementing Quantum Phase Estimation Algorithms on IBM Quantum Computer

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.