ABSTRACT
The Kitaev's Phase Estimation Algorithm (also referred to as quantum eigenvalue estimation algorithm) is a quantum algorithm to estimate the phase (or eigenvalue) of an eigenvector of a unitary operator. We explain the algorithm and indicate an example of the determination of the eigenvalue of the T gate. Then we introduce the quantum counting algorithm that is based on the quantum phase estimation algorithm and on the Grover's search algorithm. Quantum counting algorithm is a quantum algorithm for counting the number of solutions for a given search problem.
