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Lecture notes in networks and systems

Noise-Resilient Low-Frequency Signal Analysis Using Quantum Fourier Transform: A Case Study with Gravitational Waves

Rohit Kumar, Ebin Antony, V. Sanal, N. S. Sreekanth, P. Sethumadhavan, V. L. Lajish, M. C. Jobi

Published Nov 12, 2025• 1 citation
Publisher
DOI
10.1007/978-981-95-1746-6_38

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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.
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 new 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) [arXiv:2109.01535]. 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.
A quantum time-dependent spectrum analysis, or simply, quantum spectral analysis (QSA) is presented in this work, and it’s based on Schrödinger’s equation. In the classical world, it is named frequency in time (FIT), which is used here as a complement of the traditional frequency-dependent spectral analysis based on Fourier theory. Besides, FIT is a metric which assesses the impact of the flanks of a signal on its frequency spectrum, not taken into account by Fourier theory and lets alone in real time. Even more, and unlike all derived tools from Fourier Theory (i.e., continuous, discrete, fast, short-time, fractional and quantum Fourier Transform, as well as, Gabor) FIT has the following advantages, among others: 1) compact support with excellent energy output treatment, 2) low computational cost, O(N) for signals and O(N2) for images, 3) it does not have phase uncertainties (i.e., indeterminate phase for a magnitude = 0) as in the case of Discrete and Fast Fourier Transform (DFT, FFT, respectively). Finally, we can apply QSA to a quantum signal, that is, to a qubit stream in order to analyze it spectrally.