Simulation and ananlysis of quantum phase estimation algorithm in the presence of incoherent quantum noise channels

The quantum phase estimation (QPE) is one of the fundamental algorithms based on the quantum Fourier transform (QFT). 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. This noise is due to the interactions of qubits with the environment and due to the faulty gate operations. 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. Furthermore, the standard deviation increases with the number of qubits for fixed error probability.Comment: 6 pages, 4 figure