Long-algorithm based quantum search for gravitational wave

Abstract

Gravitational wave astronomy is rapidly advancing with the development of new observatories, leading to an increasing volume and complexity of data. This trend places growing pressure on classical data analysis methods and motivates the exploration of quantum approaches. In this work, we introduce a quantum matched filtering framework for gravitational-wave detection based on the Long algorithm, marking its first application to the gravitational-wave data analysis. Numerical simulations show that the proposed approach preserves the quadratic speedup of quantum search while exhibiting significantly improved robustness, thereby overcoming key limitations of the Grover-algorithm based methods.

Figures (5)

• Figure 1: The success probability of Grover's algorithm
• Figure 2: Comparison of the number of evaluations of the oracle function $f$ required to retrieve a matching template of Grover-based QMF and Long-based QMF in 1,000 simulations at threshold $\rho_{\text{thr}} = 800, 850, 860, 870$ for MBHB case. (a) (b) (e) (f) and (c) (d) (g) (h) subplot shows the distribution of function evaluations across trials of Grover-based QMF and Long-based QMF, respectively. 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 3: Comparison of the number of evaluations of the oracle function $f$ required to retrieve a matching template of Grover-based QMF and Long-based QMF in 1,000 simulations precision parameter $p=10,11,12$ for $\rho_{\text{thr}} = 800$ MBHB case. (a-c) and (d-f) subplot shows the distribution of function evaluations across trials of Grover-based QMF and Long-based QMF, respectively. 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 the number of evaluations of the oracle function $f$ required to retrieve a matching template of Grover-based QMF and Long-based QMF in 1,000 simulations precision parameter $p=10,11,12$ for $\rho_{\text{thr}} = 870$ MBHB case. (a-c) and (d-f) subplot shows the distribution of function evaluations across trials of Grover-based QMF and Long-based QMF, respectively. 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 5: Comparison of the number of evaluations of the oracle function $f$ required to retrieve a matching template of Grover-based QMF and Long-based QMF in 1,000 simulations at threshold $\rho_{\text{thr}} = 18, 16$ for GW150914 case. (a) (b) and (c) (d) subplot shows the distribution of function evaluations across trials of Grover-based QMF and Long-based QMF, respectively. 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.