An efficient quantum algorithm for spectral estimation

Steffens A, Rebentrost P, Marvian I, Eisert J, Lloyd S (2017)

Publication Type: Journal article

Publication year: 2017

Journal

New Journal of Physics Institute of Physics: Open Access Journals / Institute of Physics (IoP) and Deutsche Physikalische Gesellschaft

Book Volume: 19

Article Number: 033005

Journal Issue: 3

DOI: 10.1088/1367-2630/aa5e48

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.

Involved external institutions

Freie Universität Berlin DE Germany (DE) Massachusetts Institute of Technology (MIT) US United States (USA) (US)

How to cite

APA:

Steffens, A., Rebentrost, P., Marvian, I., Eisert, J., & Lloyd, S. (2017). An efficient quantum algorithm for spectral estimation. New Journal of Physics, 19(3). https://doi.org/10.1088/1367-2630/aa5e48

MLA:

Steffens, Adrian, et al. "An efficient quantum algorithm for spectral estimation." New Journal of Physics 19.3 (2017).

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