Iterative Optimizations to Quantum Phase Estimation and Related Algorithms

The quantum phase estimation algorithm (QPEA) is of fundamental importance in quantum computation. It can be used to perform digital simulation of quantum Hamiltonians on quantum information processors. We study the different optimizations of the QPEA, including circular statistics and iterative optimization, compared to the default majority rule algorithm by comparing their performance when simulating Heisenberg-type Hamiltonians in quantum simulations and in experiments on IBM quantum computers. We investigate to what extent the clear improvement the technique of iterative optimization of the algorithm shows for the Heisenberg-type dynamics can be reproduced for other quantum algorithms. We present results for both simulations and actual implementation on IBM quantum computers.