A quantum Fourier transform and its application to a quantum algorithm for phase estimation is discussed. It has been shown that the approximate quantum Fourier transform can be successfully used for the phase estimation instead of the full one. The lower bound for the probability to get a correct result in a single run of the algorithm has been obtained. The validity of the results is demonstrated by simulation of the algorithm in case of the phase shift operator using the QuantumCircuit package written in the Wolfram Mathematica language. All relevant calculations and visualizations are done with the Wolfram Mathematica system.
['Alexander N. Prokopenya']
Approximate Quantum Fourier Transform and Quantum Algorithm for Phase Estimation