Performance of Grover's search algorithm with diagonalizable collective noises

TL;DR

This paper investigates how diagonalizable collective noises affect Grover's search algorithm, revealing that certain noises can be mitigated or even improve performance, with implications for NISQ computing.

Contribution

It provides a detailed analysis of the impact of diagonalizable noises on GSA and identifies noise types that can enhance or preserve its quantum advantage.

Findings

Success probability oscillates around 1/2 with noise

Bit flip and bit-phase flip noise can improve GSA performance

GSA with bit-phase flip noise outperforms classical algorithms

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.