An efficient quantum algorithm for spectral estimation
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Steffens-2017-An efficient quantum algorithm f.pdf
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882.97 KB
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Author(s)
Eisert, Jens
Steffens, Adrian
Rebentrost, Frank
Marvian Mashhad, Iman
Lloyd, Seth
Date Issued
March 2017
Journal
New Journal of Physics
Publisher
IOP Publishing
Citation
Steffens, Adrian et al. “An Efficient Quantum Algorithm for Spectral Estimation.” New Journal of Physics 19.3 (2017): 033005. © 2017 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft
Version
Final published version
Abstract
We develop an efficient quantum implementation of an important signal processing algorithm for line spectral estimation: the matrix pencil method, which determines the frequencies and damping factors of signals consisting of finite sums of exponentially damped sinusoids. Our algorithm provides a quantum speedup in a natural regime where the sampling rate is much higher than the number of sinusoid components. Along the way, we develop techniques that are expected to be useful for other quantum algorithms as well—consecutive phase estimations to efficiently make products of asymmetric low rank matrices classically accessible and an alternative method to efficiently exponentiate non-Hermitian matrices. Our algorithm features an efficient quantum–classical division of labor: the time-critical steps are implemented in quantum superposition, while an interjacent step, requiring much fewer parameters, can operate classically. We show that frequencies and damping factors can be obtained in time logarithmic in the number of sampling points, exponentially faster than known classical algorithms.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
Massachusetts Institute of Technology. Research Laboratory of Electronics
Terms of Use
Creative Commons Attribution 4.0 International License
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DOI of Published Version
https://doi.org/10.1088/1367-2630/aa5e48
