An efficient quantum algorithm for spectral estimation
Author(s)
Eisert, Jens; Steffens, Adrian; Rebentrost, Frank; Marvian Mashhad, Iman; Lloyd, Seth
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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.
Date issued
2017-03Department
Massachusetts Institute of Technology. Department of Mechanical Engineering; Massachusetts Institute of Technology. Research Laboratory of ElectronicsJournal
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
ISSN
1367-2630