Impact of incoherent noise on Grover and quantum phase estimation algorithms

The Grover search and phase estimation are two fundamental quantum algorithms. The major challenge in running these two and other quantum algorithms is the noise in quantum computers. This noise is due to the interactions of qubits with the environment and faulty gate operations. Here, we present the impact of incoherent noise on two algorithms. The noise impact is 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 these algorithms in the presence of noise. The simulation results indicate that the probability of success of the Grover algorithm and the standard deviation of the eigenvalue of the unitary operator have strong exponential dependence upon the error probability of individual qubits. Furthermore, the original formulation is compared with the recently proposed generalization in terms of singular value transformation.