Quantum Search for Gravitational Wave of Massive Black Hole Binaries

TL;DR

The paper addresses the high computational cost of detecting massive black hole binaries (MBHBs) with large template banks in gravitational-wave data analysis. It proposes a quantum matched filtering framework that combines Grover’s search and quantum counting to achieve a theoretical $O(sqrt(N))$ scaling for template-space search, potentially reducing costs from $O(N)$ to $O(sqrt(N))$. Simulations reveal that while average performance can be more efficient than exhaustive classical search, the quantum approach exhibits instability and strong sensitivity to detection thresholds, indicating robustness challenges. The work demonstrates a promising quantum-direction for accelerating gravitational-wave data analysis and outlines the need for more robust algorithms and realistic hardware considerations to realize practical gains.

Abstract

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, quantum approach can reduce the computational complexity from $O(N)$ to $O(\sqrt{N})$ 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.

Figures (6)

• Figure 1: The probability distributions of outcomes from measuring the counting register transformed to estimates on the number of matching templates $r_\ast$ for each of the different cases of $\rho_{\text{thr}}$. The distributions are compared to the true number of matching templates $r$ (dotted).
• Figure 2: The probability distributions of outcomes from measuring the counting register transformed to estimates on the optimal number of Grover’s applications $k_\ast$ for each of the different cases of $\rho_{\text{thr}}$. The probabilities are compared to the true $k$ (dotted) for each case.
• Figure 3: Number of evaluations of the oracle function $f$ required to retrieve a matching template in 1,000 simulations at different threshold levels $\rho_{\text{thr}} = 800, 850, 860, 870$. (a–d) Each subplot shows the distribution of function evaluations across trials. Blue histograms represent using a fixed $k_*$ estimated from a single Signal Detection step; red histograms correspond to re-estimating $k_*$ for each failed retrieval. Dashed lines indicate mean values. The black dotted line shows the classical case where all $2^{17}$ templates are evaluated.
• Figure 4: Comparison of algorithm efficiency for detection thresholds $\rho_{\text{thr}} = 16$ and $\rho_{\text{thr}} = 18$ using 1000 simulations given the GW150914 example. The $\rho_{\text{thr}} = 18$ case reproduces the results reported in Ref. gao2022quantum, while the $\rho_{\text{thr}} = 16$ case shows the results when lowering the threshold. This comparison highlights the sensitivity of the quantum matched filtering algorithm’s performance to the choice of threshold.
• Figure 5: Number of oracle function $f$ evaluations required to retrieve a matching template in 1,000 simulations, for precision values $p = 10, 11, 12$, with the threshold set to $\rho_\text{thr}=800$.