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arXiv:2408.13177

Gravitational-wave matched filtering with variational quantum algorithms

Jason Pye, Edric Matwiejew, Aidan Smith, M. Kovalam, Jingbo B. Wang, L. Wen

Published Aug 23, 2024• 0 citations
arXivHTMLPDF

Abstract

In this paper, we explore the application of variational quantum algorithms designed for classical optimization to the problem of matched filtering in the detection of gravitational waves. Matched filtering for detecting gravitational wave signals requires searching through a large number of template waveforms, to find one which is highly correlated with segments of detector data. This computationally intensive task needs to be done quickly for low latency searches in order to aid with follow-up multi-messenger observations. The variational quantum algorithms we study for this task consist of quantum walk-based generalizations of the Quantum Approximate Optimization Algorithm (QAOA). We present results of classical numerical simulations of these quantum algorithms using open science data from LIGO. These results show that the tested variational quantum algorithms are outperformed by an unstructured restricted-depth Grover search algorithm, suggesting that the latter is optimal for this computational task.

DOI
10.48550/arxiv.2408.13177

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Quantum computational devices currently under development have the potential to accelerate data analysis techniques beyond the ability of any classical algorithm. We propose the application of a quantum algorithm for the detection of unknown signals in noisy data. We apply Grover's algorithm to matched filtering, a signal processing technique that compares data to a number of candidate signal templates. In comparison to the classical method, this provides a speedup proportional to the square root of the number of templates, which would make possible otherwise intractable searches. We demonstrate both a proof-of-principle quantum circuit implementation and a simulation of the algorithm's application to the detection of the gravitational wave signal GW150914. We discuss the time complexity and space requirements of our algorithm as well as its implications for the currently computationally limited searches for continuous gravitational waves.
Quantum computational devices, currently under development, have the potential to accelerate data analysis techniques beyond the ability of any classical algorithm. We propose the application of a quantum algorithm for the detection of unknown signals in noisy data. We apply Grover's algorithm to matched-filtering, a signal processing technique that compares data to a number of candidate signal templates. In comparison to the classical method, this provides a speed-up proportional to the square-root of the number of templates, which would make possible otherwise intractable searches. We demonstrate both a proof-of-principle quantum circuit implementation, and a simulation of the algorithm's application to the detection of the first gravitational wave signal GW150914. We discuss the time complexity and space requirements of our algorithm as well as its implications for the currently computationally-limited searches for continuous gravitational waves.
Abstract Gravitational waves carry information about far away phenomena which astronomers can use to form a better picture of the universe. Over the past few years, numerous gravitational waves have been detected using a method called matched filtering; however, this approach has two main drawbacks. First, it requires knowledge of the sought-after waveform beforehand. Second, it is infeasible for gravitational wave searches which are precise or cover a long time span. While attempts have been made to use classical machine learning to overcome these difficulties, the usage of quantum machine learning in this context is relatively unexplored. Quantum variational rewinding is a hybrid quantum-classical machine learning algorithm for time series anomaly detection. This work makes the first steps in investigating its potential for gravitational wave detection. Training and testing the algorithm was done without depending on synthetic data. In a noiseless simulated environment, quantum variational rewinding was able to pick out all confirmed gravitational wave signals from the background noise of a detector with perfect accuracy when filtering was applied before hand and was able to do so to a high degree of success without filtering. Anomaly detection with this algorithm was performed with two signals on quantum hardware as a proof of concept. Using Fisher information, both the capacity and the trainability of quantum variational rewinding are described so that future approaches can be compared in these regards. With new gravitational wave detectors under development, even more data will be generated for analysis in the future, compounding the existing bottlenecks in the search pipeline. As such, approaches which help tackle issues with the current approach to gravitational wave analysis are in demand, and the empirical results from this work assert that quantum computing should not be overlooked in this process.
The speedup of heavy numerical tasks by quantum computing is now actively investigated in various fields including data analysis in physics and astronomy. In this paper, we propose a quantum algorithm for matched filtering in gravitational wave (GW) data analysis based on the previous work by Gao et al. [Phys. Rev. Research 4, 023006 (2022)]. Our approach uses the quantum algorithm for Monte Carlo integration for the signal-to-noise ratio (SNR) calculation instead of the fast Fourier transform used in Gao et al. and searches signal templates with high SNR by quantum amplitude amplification. In this way, we achieve an exponential reduction of the qubit number compared with Gao et al.'s algorithm, keeping a quadratic speedup over classical GW matched filtering with respect to the template number.
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.
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)O(N)O(N) to O(N)O(\sqrt{N})O(N​) theoretically, where NNN 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.