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arXiv:2109.01535

A quantum algorithm for gravitational wave matched filtering

Sijia Gao, F. J. Hayes, Sarah Croke, Christopher Messenger, John Veitch

Published Sep 3, 2021• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.2109.01535

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Matched filtering is a powerful signal searching technique used in several employments from radar and communications applications to gravitational-wave detection. Here we devise a method for matched filtering with the use of quantum bits. Our method's asymptotic time complexity does not depend on template length and, including encoding, is O(L(log⁡2L)2)\mathcal{O}(L(\log_2L)^2)O(L(log2​L)2) for a data with length LLL and a template with length NNN, which is classically O(NL)\mathcal{O}(NL)O(NL). Hence our method has superior time complexity over the classical computation for long templates. We demonstrate our method with real quantum hardware on 4 qubits and also with simulations.