  The quantum phase estimation (QPE) is one of the fundamental algorithms based
on the quantum Fourier transform. It has applications in order-finding,
factoring, and finding the eigenvalues of unitary operators. The major
challenge in running QPE and other quantum algorithms is the noise in quantum
computers. In the present work, we study the impact of incoherent noise on QPE,
modeled as trace-preserving and completely positive quantum channels. Different
noise models such as depolarizing, phase flip, bit flip, and bit-phase flip are
taken to understand the performance of the QPE in the presence of noise. The
simulation results indicate that the standard deviation of the eigenvalue of
the unitary operator has strong exponential dependence upon the error
probability of individual qubits. However, the standard deviation increases
only linearly with the number of qubits for fixed error probability when that
error probability is small.
