Performance of Grover's search algorithm with diagonalizable collective noises

Abstract: 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.