An efficient quantum algorithm for spectral estimation
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by
A. Steffens, P. Rebentrost, I. Marvian, J. Eisert, S. Lloyd
2016
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 only exponentially few
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.
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