  Grover's search algorithm (GSA) is known to experience a loss of its
quadratic speedup when exposed to quantum noise. In this study, we partially
agree with this result and present our findings. First, we examine different
typical diagonalizable noises acting on the oracles in GSA and find that the
success probability decreases and oscillates around $1/2$ as the number of
iterations increases. Secondly, our results show that the performance of GSA
can be improved by certain types of noise, such as bit flip and bit-phase flip
noise. Finally, we determine the noise threshold for bit-phase flip noise to
achieve a desired success probability and demonstrate that GSA with bit-phase
flip noise still outperforms its classical counterpart. These results suggest
new avenues for research in noisy intermediate-scale quantum (NISQ) computing,
such as evaluating the feasibility of quantum algorithms with noise and
exploring their applications in machine learning.
