Quantum search for gravitational wave of massive black hole binaries

Matched filtering is a common method for detecting gravitational waves. However, the computational costs of searching large template banks limit the efficiency of classical algorithms when searching for massive black hole binary (MBHB) systems. This work explores the application of a quantum matched filtering algorithm based on Grover's algorithm to MBHB signals. Under certain simplifying assumptions, the quantum approach can reduce the computational complexity from $O(N)$ to O(√N) theoretically, where N is the size of the template bank. Simulated results illustrate the potential reduction in computational costs, while also showing that the performance can degrade in some cases due to instability of the algorithm. These findings reveal both the potential and the limitations of quantum search for MBHB signals, pointing to the importance of developing more robust and stable search strategies alongside realistic modeling in future work.